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This paper discusses the relevance of using physical situations to introduce the concept of angles at elementary school. We compare the effectiveness of two geometry teaching sequences. In the first one (physical sequence), the pupils learned the angle concept by experimenting on the playground (i.e. mesospace) and then modelling the situation. In the second one (paper-and-pencil sequence), the pupils worked solely in the space of a sheet of paper (i.e. microspace). In both sequences, pupils compared areas of space delineated by an angle between two directions. Pupils in two Grade 3 classes were exposed to one of the two teaching sequences. The unfolding of these sequences was videotaped and analyzed, and the pupils were tested individually, before and after teaching, to measure each sequence's effectiveness. Results showed that both sequences are effective to grasp the angle concept: Most pupils overcame the common erroneous conception of comparing angles' sides' lengths instead of angle openness. The comparison of areas of space delineated by an angle between two infinite directions, which is the two sequences' common core, seems to be the key factor underlying angle conceptualization. This paper ends with a discussion of these results' teaching implications and the merits of each sequence. [ABSTRACT FROM AUTHOR]

The article explores the topic of projectile motion through an experiment conducted by Alice and Bob. They used a high-speed camera to capture the movement of a projectile and discovered that its trajectory formed a parabola. The article provides equations and tests to determine the aspect ratio of the trajectories and offers hands-on projects of increasing difficulty related to projectile motion. It emphasizes the importance of accurate measurements and uncertainties in conducting such experiments. The article also discusses the use of scaling and geometric approaches, data fitting, and suggests using simulations and video recordings for analysis. Overall, it provides practical methods for understanding and studying projectile motion. [Extracted from the article]

We extensively survey applications of Clifford Geometric algebra in recent years (mainly 2019–2022). This includes engineering; electric engineering; optical fibers; geographic information systems; geometry; molecular geometry; protein structure; neural networks; artificial intelligence; encryption; physics; signal, image, and video processing; and software. [ABSTRACT FROM AUTHOR]

This paper evaluates possible reasons and motivations for 19th century geometer Julius Plücker's change in direction from his purely mathematical work to experimental physics. The author argues that this change did not happen suddenly in 1846 as is frequently suggested but rather, was a gradual change. This move took more than a decade and was triggered by Plücker's idea to apply his mathematical formalism to physical objects and phenomena, such as crystals and the trajectories of light in crystalline materials, a move which eventually led him to the newly discovered phenomena of diamagnetism. [ABSTRACT FROM AUTHOR]

This survey introduces 101 new publications on applications of Clifford's geometric algebras (GAs) newly published during 2022 (until mid‐January 2023). The selection of papers is based on a comprehensive search with Dimensions.ai, followed by detailed screening and clustering. Readers will learn about the use of GA for mathematics, computation, surface representations, geometry, image, and signal processing, computing and software, quantum computing, data processing, neural networks, medical science, physics, electric engineering, control and robotics. [ABSTRACT FROM AUTHOR]

In his seminar "The Eye and the Gaze," Jacques Lacan is forced to regard the problem of the unconscious through the grid of the Cartesian cogito. In the certainty of "I think, therefore I am," which expresses the complete transparency of the self to its own apprehension, leaves no space for the ineffability of the unconscious. Lacan sees this proto-enlightenment certainty running through all perceptual mechanisms, as in Paul Valèry's poem "La Jeune Parque," which declares, "I saw myself seeing myself." Lacan turns to anamorphosis as a perceptual exception, in which there are two viewing points turned on the same object, neither coinciding with the other, such that classical perspective's fundamental unity of the perceiving subject is alienated from itself—a Spaltung, or split, that enables the unconscious presence of the uncanny and its castrative impression of death. [ABSTRACT FROM AUTHOR]

A thermoacoustic sound generation model, based on the classical balance equations of the continuum mechanics, is here developed for the cylindrical and the spherical thermoacoustic wave generation. In both geometries, the model considers an arbitrary multilayered structure, where each layer can be fluid or solid and it is characterized by the fully coupled thermo-visco-acoustic response. It means that the viscous behavior and the thermal conduction are considered in each layer. The model is based on a unified representation of cylindrical or spherical thermoacoustic waves, which is valid for both fluid and solid phases. Thanks to the continuity of temperature, particle velocity, normal stress, and heat flux between adjacent layers, the model can be implemented by means of a versatile matrix approach, allowing flexible analysis and design of cylindrical or spherical thermophones. Any thermoacoustic variable can be determined at any position, any frequency, and for any input power. The results are compared with the models already existing in the literature, and the underlying physics is thoroughly discussed. The analysis is focused on a better understanding of the thermoacoustic generation with application to the state of the art of the thermophone technology. [ABSTRACT FROM AUTHOR]

These notes give an introduction to the equivalence problem of sub-Riemannian manifolds. We first introduce preliminaries in terms of connections, frame bundles and sub-Riemannian geometry. Then we arrive to the main aim of these notes, which is to give the description of the canonical grading and connection existing on sub-Riemann manifolds with constant symbol. These structures are exactly what is needed in order to determine if two manifolds are isometric. We give three concrete examples, which are Engel (2,3,4)-manifolds, contact manifolds and Cartan (2,3,5)-manifolds. These notes are an edited version of a lecture series given at the 42nd Winter school: Geometry and Physics, Srní, Czech Republic, mostly based on [8] and other earlier work. However, the work on Engel (2,3,4)-manifolds is original research, and illustrate the important special case were our model has the minimal set of isometries. [ABSTRACT FROM AUTHOR]

This note is based on a short talk presented at the "42nd Winter School Geometry and Physics" held in Srni, Czech Republic, January 15th-22nd 2022. We review the notion of Lie superalgebra cohomology and extend it to different form complexes, typical of the superalgebraic setting. In particular, we introduce pseudoforms as infinite-dimensional modules related to sub-superalgebras. We then show how to extend the Koszul-Hochschild-Serre spectral sequence for pseudoforms as a computational method to determine the cohomology groups induced by sub-superalgebras. In particular, we show as an example the case of osp(1 | 4) and choose osp(1 | 2)×sp(2) as sub-algebra. We finally comment on some physical applications of such new cohomology classes related to super-branes. The note is a compact version of [10]. [ABSTRACT FROM AUTHOR]

Experimental demonstration of superdirectivity and superscattering phenomena is among the long-standing challenges in electromagnetic theory. Efficient computational algorithms can contribute to this endeavor by suggesting new designs bypassing commonly accepted limitations. Here, we demonstrate a rectangular wire bundle superscatterer designed using a stochastic optimization algorithm. The structure encompassing wires of different lengths demonstrates superior scattering capabilities, bypassing the single channel dipole limit by an order of magnitude. The subwavelength wire bundle supports several resonant higher-order multipoles, which constructively contribute to the scattering, as we demonstrate experimentally. A new generation of genetically designed superscatterers may be used in a range of wireless applications, including point-to-point communications, smart beacons, and radar targets. [ABSTRACT FROM AUTHOR]

This note is based on a short talk presented at the "42nd Winter School Geometry and Physics" held in Srni, Czech Republic, January 15th-22nd 2022. We review the notion of Lie superalgebra cohomology and extend it to different form complexes, typical of the superalgebraic setting. In particular, we introduce pseudoforms as infinite-dimensional modules related to sub-superalgebras. We then show how to extend the Koszul-Hochschild-Serre spectral sequence for pseudoforms as a computational method to determine the cohomology groups induced by sub-superalgebras. In particular, we show as an example the case of osp(1 | 4) and choose osp(1 | 2)×sp(2) as sub-algebra. We finally comment on some physical applications of such new cohomology classes related to super-branes. The note is a compact version of [10]. [ABSTRACT FROM AUTHOR]

These notes give an introduction to the equivalence problem of sub-Riemannian manifolds. We first introduce preliminaries in terms of connections, frame bundles and sub-Riemannian geometry. Then we arrive to the main aim of these notes, which is to give the description of the canonical grading and connection existing on sub-Riemann manifolds with constant symbol. These structures are exactly what is needed in order to determine if two manifolds are isometric. We give three concrete examples, which are Engel (2,3,4)-manifolds, contact manifolds and Cartan (2,3,5)-manifolds. These notes are an edited version of a lecture series given at the 42nd Winter school: Geometry and Physics, Srní, Czech Republic, mostly based on [8] and other earlier work. However, the work on Engel (2,3,4)-manifolds is original research, and illustrate the important special case were our model has the minimal set of isometries. [ABSTRACT FROM AUTHOR]

A fundamental challenge for machine learning (ML) models for electromagnetics is their ability to predict output quantities of interest (such as fields and scattering parameters) in geometries that the model has not been trained for. Addressing this challenge is a key to fulfilling one of the most appealing promises of ML for computational electromagnetics: the rapid solution of problems of interest just by processing the geometry and the sources involved. The impact of such models that can “generalize” to new geometries is more profound for large-scale computations, such as those encountered in wireless propagation scenarios. We present generalizable models for indoor propagation that can predict received signal strengths within new geometries, beyond those of the training set of the model, for transmitters and receivers of multiple positions, and for new frequencies. We show that a convolutional neural network can “learn” the physics of indoor radiowave propagation from ray-tracing solutions of a small set of training geometries so that it can eventually deal with substantially different geometries. We emphasize the role of exploiting physical insights in the training of the network, by defining input parameters and cost functions that assist the network to efficiently learn basic and complex propagation mechanisms. [ABSTRACT FROM AUTHOR]

A powerful spatially extended planar Cherenkov maser project operating in ${W}$ -band is under development in collaboration between Budker Institute of Nuclear Physics of the Russian Academy of Sciences (BINP RAS) (Novosibirsk) and Institute of Applied Physics of the Russian Academy of Sciences (IAP RAS) (Nizhny Novgorod). The ELMI accelerator (1 MeV/5–7 kA/ $3~\mu \text{s}$) forms a sheet electron beam with the transverse size (width) of up to 18 cm, which serves to drive the oscillator. The electrodynamic system of this Cherenkov maser is based on doubly periodical structure, which combines the properties of a slow wave system that realizes conditions for an effective Cherenkov interaction with a high-current rectilinear sheet electron beam and a high- ${Q}$ resonator that implements the mechanism of two-dimensional distributed feedback and provides selective excitation of the operating mode in the strongly oversized interaction space. In this article, the crucial elements and design parameters of the oscillator are discussed, and the results of simulations are presented to demonstrate the possibility of achieving a stable narrow-band generation regime for a transverse system size reaching about 50 wavelengths and a gigawatt output power level. To provide a single-directed output of radiation, a planar Bragg reflector is elaborated for installation at the cathode side of the interaction space. A mode converter formed by a slowly tapered waveguide section for transformation of the radiated wavebeam into a Gaussian-type wavebeam was designed to be installed at the oscillator output. In the electron-optical experiments, the formation of a large-width sheet electron beam with parameters acceptable to drive designed ${W}$ -band Cherenkov maser is demonstrated. [ABSTRACT FROM AUTHOR]

The 2010 MW 7.2 El Mayor-Cucapah, Mexico, earthquake ruptured multiple faults with different faulting mechanisms. Resolving the earthquake rupture process and its relation to the geometric fault complexities is critical to our understanding of the earthquake source physics, but doing so by conventional finite-fault inversion is challenging because modelling errors due to inappropriate assumptions about the fault geometry distort the solution and make robust interpretation difficult. Here, using a potency density tensor approach to finite-fault inversion, we inverted the observed teleseismic P waveforms of the 2010 El Mayor-Cucapah earthquake to simultaneously estimate the rupture process and the fault geometry. We found that the earthquake consisted of an initial normal faulting rupture, which was followed by a strike-slip bilateral rupture towards the southeast and northwest that originated on the northwest side of the epicentre. The southeastern rupture propagated back through the initial rupture area, but with strike-slip faulting. Although the northwestern rupture propagated across the left step in the Puerta fault-accommodation zone, the rupture was temporarily stalled by the associated change of the fault geometry. These results highlight the irregular rupture process, which involved a back-propagating rupture and fluctuating rupture propagation controlled the complexity of the fault system. [ABSTRACT FROM AUTHOR]

Definition: This entry presents an overview on how mechanics in Greece was linked to geometry. In ancient Greece, mechanics was about lifting heavy bodies, and mathematics almost coincided with geometry. Mathematics interconnected with mechanics at least from the 5th century BCE and became dominant in the Hellenistic period. The contributions by thinkers such as Aristotle, Euclid, and Archytas on fundamental problems such as that of the lever are sketched. This entry can be the starting point for a deeper investigation on the connections of the two disciplines through the ages until our present day. [ABSTRACT FROM AUTHOR]

A single-event effect (SEE) simulation toolkit has been developed at CERN for the whole radiation effects community and released as an open-source code. It has been validated by comparing the simulated energy deposition of inelastic interactions, due to monoenergetic neutrons in the 1.2–17 MeV energy range, to the distribution measured experimentally by a silicon diode detector. [ABSTRACT FROM AUTHOR]

The critical analysis of the starting point of the theory of complex numbers is proposed. The unity of formal logic and rational dialectics is methodological basis of the analysis. The analysis leads to the following main results: (1) the definition of a complex number contradicts to the laws of formal logic, because this definition is the union of two contradictory concepts: the concept of a real number and the concept of a non-real (imaginary) number - an image. The concepts of a real number and a non-real (imaginary) number are in logical relation of contradiction: the essential feature of one concept completely negates the essential feature of another concept. These concepts have no common feature (i.e. these concepts have nothing in common with each other), therefore one cannot compare these concepts with each other. Consequently, the concepts of a real number and a non-real (imaginary) number cannot be united and contained in the definition of a complex number. The concept of a complex number is a gross formal-logical error; (2) the real part of a complex number is the result of a measurement. But the non-real (imaginary) part of a complex number is not the result of a measurement. The non-real (imaginary) part is a meaningless symbol, because the mathematical (quantitative) operation of multiplication of a real number by a meaningless symbol is a meaningless operation. This means that the theory of complex number is not a correct method of calculation. Consequently, mathematical (quantitative) operations on meaningless symbols are a gross formal-logical error; (3) a complex number cannot be represented (interpreted) in the Cartesian geometric coordinate system, because the Cartesian coordinate system is a system of two identical scales (rulers). The standard geometric representation (interpretation) of a complex number leads to the logical contradictions if the scales (rulers) are not identical. This means that the scale of non-real (imaginary) numbers cannot exist in the Cartesian geometric coordinate system. Consequently, the theory of complex numbers and the use of the theory of complex numbers in mathematics and physics (electromagnetism and electrical engineering, fluid dynamics, quantum mechanics, relativity) represent a gross methodological error and lead to gross errors in mathematics and physics. [ABSTRACT FROM AUTHOR]

The critical analysis of the foundations of standard trigonometry is proposed. The unity of formal logic and rational dialectics is methodological basis of the analysis. The analysis leads to the following main results: (1) trigonometry does not treat a right triangle as a material system. Therefore, trigonometry does not satisfy the system principle; (2) trigonometric functions do not satisfy the mathematical definition of a function. The terms "sine", "cosine", "tangent", "cotangent" and others are not identical to the concept of function. Symbols "cos", "sin", "tg", "ctg", etc. indicate only that there is a correspondence (connection) between the values of the quantities of the angle and the lengths of the sides in a right-angled triangle. Therefore, the standard definitions of trigonometric functions do not represent mathematical (quantitative) relationships between the quantities of the angle and the lengths of the sides in a right-angled triangle. Trigonometric functions are neither explicit nor implicit functions; (3) the range of definition of trigonometric functions does not satisfy the condition for the existence of a right-angled triangle because the definitions of trigonometric functions contradict to the system principle. These facts prove the assertion that the trigonometric functions, the trigonometric identities, the trigonometric form of the Pythagorean Theorem and the inverse trigonometric functions are blunders; (4) the values of mathematical quantities are always neutral numbers. Therefore, logical contradictions arise if the quantity of the angle and the symbols "cos", "sin", "tg", "ctg" take on negative values. (5) it is proved that the standard theorems of addition (difference) of two arguments for cosine and sine are blunders. This means that the addition (difference) theorems for all trigonometric functions, the reduction formula, the formula for double and half argument are blunders; (6) in the point of view of the Cartesian coordinate system, the abscissa and ordinate scales are identical and have the dimension "meter". Therefore, the quantity of the angle (which has the dimension "degree") does not exist in the Cartesian coordinate system; (7) the graphs of trigonometric functions are built in an inadmissible coordinate system because the scales are not identical: the abscissa scale has the dimension "degree", and the ordinate scale has the dimension "meter". The non-identity of the dimensions leads to absurdity: "meter" is "degree". Therefore, the graphs of trigonometric functions have no geometric meaning; (8) if the material point is the end point of the moving radius in the material system "circle + mobile radius + Cartesian coordinate system", then the graph of the dependence of the ordinate of the material point on the length of the path traveled (i.e., on the circumference of a given radius) has the form of a sinusoid, but the graph is not a trigonometric sinusoid. Consequently, standard trigonometry is a pseudoscientific theory. [ABSTRACT FROM AUTHOR]

Despite the acclaimed success of the magnetic field (H) formulation for modeling the electromagnetic behavior of superconductors with the finite-element method, the use of vector-dependent variables in nonconducting domains leads to unnecessarily long computation times. In order to solve this issue, we have recently shown how to use a magnetic scalar potential together with the H-formulation in the COMSOL Multiphysics environment to efficiently and accurately solve for the magnetic field surrounding superconducting domains. However, from the definition of the magnetic scalar potential, the nonconducting domains must be made simply connected in order to obey Ampere's law. In this article, we use thin cuts to apply a discontinuity in $\phi$ and make the nonconducting domains simply connected. This approach is shown to be easily implementable in the COMSOL Multiphysics finite-element program, already widely used by the applied superconductivity community. We simulate three different models in two dimensions and three dimensions using superconducting filaments and tapes, and show that the results are in very good agreement with the H-A and H-formulations. Finally, we compare the computation times between the formulations, showing that the H- $\phi$ -formulation can be up to seven times faster than the standard H-formulation in certain applications of interest. [ABSTRACT FROM AUTHOR]

Squaring the Circle is a famous geometry problem going all the way back to the ancient Greeks. It is the great quest of constructing a square with the same area as a circle using a compass and straightedge in a finite number of steps. Since it was proven that π was a transcendental number in 1882, the task of Squaring the Circle has been considered impossible. Here, we will show it is possible to Square the Circle in space-time. It is not possible to Square the Circle in Euclidean space alone, but it is fully possible in space-time, and after all we live in a world with not only space, but also time. By drawing the circle from one reference frame and drawing the square from another reference frame, we can indeed Square the Circle. By taking into account space-time rather than just space, the impossible becomes possible! However, it is not enough simply to understand math in order to Square the Circle, one must understand some "basic" space-time physics as well. As a bonus, we have added a solution to the impossibility of Doubling the Cube. As a double bonus, we have also Boxed the Sphere! As we will see, one could claim that we have simply bent the rules and moved the problem from one place to another. One of the essential points of this paper, however, is that we can move challenging space problems out from space and into time, and vice versa. [ABSTRACT FROM AUTHOR]

The recently conjectured knots-quivers correspondence (Kucharski et al. in Phys Rev D 96(12):121902, 2017. arXiv:1707.02991, Adv Theor Math Phys 23(7):1849–1902, 2019. arXiv:1707.04017) relates gauge theoretic invariants of a knot K in the 3-sphere to the representation theory of a quiver Q K associated to the knot. In this paper we provide geometric and physical contexts for this conjecture within the framework of Ooguri-Vafa large N duality (Ooguri and Vafa in Nucl Phys B 577:419–438, 2000), that relates knot invariants to counts of holomorphic curves with boundary on L K , the conormal Lagrangian of the knot in the resolved conifold, and corresponding M-theory considerations. From the physics side, we show that the quiver encodes a 3d N = 2 theory T [ Q K ] whose low energy dynamics arises on the worldvolume of an M5 brane wrapping the knot conormal and we match the (K-theoretic) vortex partition function of this theory with the motivic generating series of Q K . From the geometry side, we argue that the spectrum of (generalized) holomorphic curves on L K is generated by a finite set of basic disks. These disks correspond to the nodes of the quiver Q K and the linking of their boundaries to the quiver arrows. We extend this basic dictionary further and propose a detailed map between quiver data and topological and geometric properties of the basic disks that again leads to matching partition functions. We also study generalizations of A-polynomials associated to Q K and (doubly) refined version of LMOV invariants (Ooguri and Vafa 2000; Labastida and Marino in Commun Math Phys 217(2):423–449, 2001. arXiv:hep-th/0004196; Labastida et al. in JHEP 11:007, 2000. arXiv:hep-th/0010102; Aganagic and Vafa in Large N duality, mirror symmetry, and a Q-deformed A-polynomial for knots. arXiv:1204.4709; Fuji et al. in Nucl Phys B 867:506–546, 2013. arXiv:1205.1515). [ABSTRACT FROM AUTHOR]

There is a substantial literature concerning Liouville quantum gravity (LQG) in two dimensions with conformal matter field of central charge c M ∈ (- ∞ , 1 ] . Via the DDK ansatz, LQG can equivalently be described as the random geometry obtained by exponentiating γ times a variant of the planar Gaussian free field, where γ ∈ (0 , 2 ] satisfies c M = 25 - 6 (2 / γ + γ / 2) 2 . Physics considerations suggest that LQG should also make sense in the regime when c M > 1 . However, the behavior in this regime is rather mysterious in part because the corresponding value of γ is complex, so analytic continuations of various formulas give complex answers which are difficult to interpret in a probabilistic setting. We introduce and study a discretization of LQG which makes sense for all values of c M ∈ (- ∞ , 25) . Our discretization consists of a random planar map, defined as the adjacency graph of a tiling of the plane by dyadic squares which all have approximately the same "LQG size" with respect to the Gaussian free field. We prove that several formulas for dimension-related quantities are still valid for c M ∈ (1 , 25) , with the caveat that the dimension is infinite when the formulas give a complex answer. In particular, we prove an extension of the (geometric) KPZ formula for c M ∈ (1 , 25) , which gives a finite quantum dimension if and only if the Euclidean dimension is at most (25 - c M) / 12 . We also show that the graph distance between typical points with respect to our discrete model grows polynomially whereas the cardinality of a graph distance ball of radius r grows faster than any power of r (which suggests that the Hausdorff dimension of LQG in the case when c M ∈ (1 , 25) is infinite). We include a substantial list of open problems. [ABSTRACT FROM AUTHOR]

This is a critical review of the book Variational Approach to Gravity Field Theories - From Newton to Einstein and Beyond (2017), written by the Italian astrophysicist Alberto Vecchiato. In his work, Vecchiato shows that physics, as we know it, can be built up from simple mathematical models that become more complex step by step by gradually introducing new principles. The reader is invited to follow the steps that lead from classical physics to relativity and to understand how this happens and why. Moreover, while presenting the variational approach to gravity field theories in a clear and elegant manner, Vecchiato shows a constant worry in leading the readers in such a way that they understand the relevance of what the author considers to be the most powerful technique and unifying concept of theoretical physics - and how it works. Each chapter is enriched with exercises, of which a step-by-step solution is offered, so that the reader can gain a real insight into the topic presented and follow the reading as fruitfully as possible. The most innovative aspect of the book, however, is not the rigorousness and the clarity of the treatment of the variational approach but rather the point of view that Vecchiato keeps and that the reader is led to endorse too: physics is a human enterprise, prone to error and open to improvement, and not a complete and definite system of truths about our world. [ABSTRACT FROM AUTHOR]

Finsler geometry naturally appears in the description of various physical systems. In this review, I divide the emergence of Finsler geometry in physics into three categories: dual description of dispersion relations, most general geometric clock and geometry being compatible with the relevant Ehlers–Pirani–Schild axioms. As Finsler geometry is a straightforward generalization of Riemannian geometry there are many attempts to use it as generalized geometry of spacetime in physics. However, this generalization is subtle due to the existence of non-trivial null directions. I review how a pseudo-Finsler spacetime geometry can be defined such that it provides a precise notion of causal curves, observers and their measurements as well as a gravitational field equation determining the Finslerian spacetime geometry dynamically. The construction of such Finsler spacetimes lays the foundation for comparing their predictions with observations, in astrophysics as well as in laboratory experiments. [ABSTRACT FROM AUTHOR]

Many animals are able to sense the earth’s magnetic field, including varieties of arthropods and members of all major vertebrate groups. While the existence of this magnetic sense is widely accepted, the mechanism of action remains unknown. Building from recent work on synthetic magnetoreceptors, we propose a new model for natural magnetosensation based on the rotating magnetocaloric effect (RME), which predicts that heat generated by magnetic nanoparticles may allow animals to detect features of the earth’s magnetic field. Using this model, we identify the conditions for the RME to produce physiological signals in response to the earth’s magnetic field and suggest experiments to distinguish between candidate mechanisms of magnetoreception. [ABSTRACT FROM AUTHOR]

Sharks are top predators across ocean food webs and have a major ecological role in marine ecosystems. Investigating the trophic ecology of this group of species is thus essential to understand ecosystem functioning and inform specific management actions aimed at shark conservation. The Galapagos Islands represent one of the last ocean wildernesses, where populations of sharks and other top marine predators come close to a pristine status. Here we provide the first study on the trophic ecology of the tiger shark (Galeocerdo cuvier) within the Galapagos Marine Reserve (GMR), using a combination of stable isotope analysis, satellite tracking, and passive acoustic telemetry to investigate ontogenetic and spatial variations at two regions. The mean estimated δ13C and δ15N at Isabela island (western region) were -13.9 ± 0.5‰ and 13.7 ± 0.7‰; and for Santa Cruz island (central region) were -13.8 ± 0.3‰ and 13.4 ± 0.7‰, respectively. Green sea turtles (Chelonia mydas) were the main prey item for large tiger sharks (>280 cm TL), while smaller sharks mainly fed on squid and pelagic fish. Tiger sharks exhibited a high degree of philopatry around green sea-turtle nesting areas, with the majority of sharks detected around green sea-turtle nesting areas for at least 10 months after their capture date, and some individuals were even present during the entire three-year study period. Although we did not report statistically significant differences between the two regions, isotopic and electronic tagging data suggest that tiger sharks in the Galapagos could be segregated into specific populations separated by geographical scales of <100 km. The high productivity of the archipelago, along with the protection from industrial fishing granted by the GMR, result in abundant and predictable sources of prey. This high food abundance, combined with the presence of suitable habitats throughout the tiger shark life cycle, might result in a reduction of migratory behaviours when compared to movement patterns of tiger sharks in other ocean basins. Additional studies using genetic tools could provide further evidence on the presence of separate management units, as it has been recently revealed for other shark species inhabiting the GMR. [ABSTRACT FROM AUTHOR]

In order to determine the optimal strategy to run a race on a curved track according to the lane number, we introduce a model based on differential equations for the velocity, the propulsive force and the anaerobic energy which takes into account the centrifugal force. This allows us to analyze numerically the different strategies according to the types of track since different designs of tracks lead to straights of different lengths. In particular, we find that the tracks with shorter straights lead to better performances, while the double bend track with the longest straight leads to the worst performances and the biggest difference between lanes. Then for a race with two runners, we introduce a psychological interaction: there is an attraction to follow someone just ahead, but after being overtaken, there is a delay before any benefit from this interaction occurs. We provide numerical simulations in different cases. Overall, the results agree with the IAAF rules for lane draws in competition, where the highest ranked athletes get the center lanes, the next ones the outside lanes, while the lowest ranked athletes get the inside lanes. [ABSTRACT FROM AUTHOR]

Needles with diameter under 1 mm are used in various medical applications to limit the risk of complication and patient discomfort during the procedure. Next to a small diameter, needle steerability is an important property for reaching targets located deep inside the body accurately and precisely. In this paper, we present a 0.5-mm prototype probe which is able to steer in three dimensions (3D) without the need of axial rotation. The prototype consists of three Nitinol wires (each with a diameter of 0.125 mm) with a pre-curved tip. The wires are kept together by a stainless steel tube. Each wire is clamped to a block which translates along a leadscrew, the rotation of the latter being controlled by a wheel connected at the distal end of the leadscrew. The tip bends upon retraction of one or two wires. When pushed through a soft solid structure (e.g., a soft tissue or soft tissue phantom), the probe deflects due to off-axis forces acting on its tip by the surrounding structure. We tested the performance of the prototype into a 10% wt gelatine phantom, in terms of the predictability of the steering direction and the controllability of the final position after steering inside the substrate. The results showed that the probe steered in the direction of the retracted wire and that the final position varied from small deflections from the straight path when the wires were slightly retracted, to sharp curvatures for large wire retraction. The probe could be used in various applications, from cases where only a small correction of the path in one direction is needed to cases where the path to be followed includes obstacles and curves in multiple directions. [ABSTRACT FROM AUTHOR]

The formation of a membrane-enveloped virus starts with the assembly of a curved layer of capsid proteins lining the interior of the plasma membrane (PM) of the host cell. This layer develops into a spherical shell (capsid) enveloped by a lipid-rich membrane. In many cases, the budding process stalls prior to the release of the virus. Recently, Brownian dynamics simulations of a coarse-grained model system reproduced protracted pausing and stalling, which suggests that the origin of pausing/stalling is to be found in the physics of the budding process. Here, we propose that the pausing/stalling observed in the simulations can be understood as a purely kinetic phenomenon associated with the neck geometry. A geometrical potential energy barrier develops during the budding that must be overcome by capsid proteins diffusing along the membrane prior to incorporation into the capsid. The barrier is generated by a conflict between the positive Gauss curvature of the assembling capsid and the negative Gauss curvature of the neck region. A continuum theory description is proposed and is compared with the Brownian simulations of the budding of enveloped viruses. [ABSTRACT FROM AUTHOR]

Purpose: Glaucoma screening can be performed by assessing the vertical-cup-to-disk ratio (VCDR) of the optic nerve head from fundus photography, but VCDR grading is inherently subjective. This study investigated whether computer software could improve the accuracy and repeatability of VCDR assessment. Methods: In this cross-sectional diagnostic accuracy study, 5 ophthalmologists independently assessed the VCDR from a set of 200 optic disk images, with the median grade used as the reference standard for subsequent analyses. Eight non-ophthalmologists graded each image by two different methods: by visual inspection and with assistance from a custom-made publicly available software program. Agreement with the reference standard grade was assessed for each method by calculating the intraclass correlation coefficient (ICC), and the sensitivity and specificity determined relative to a median ophthalmologist grade of ≥0.7. Results: VCDR grades ranged from 0.1 to 0.9 for visual assessment and from 0.1 to 1.0 for software-assisted grading, with a median grade of 0.4 for each. Agreement between each of the 8 graders and the reference standard was higher for visual inspection (median ICC 0.65, interquartile range 0.57 to 0.82) than for software-assisted grading (median ICC 0.59, IQR 0.44 to 0.71); P = 0.02, Wilcoxon signed-rank test). Visual inspection and software assistance had similar sensitivity and specificity for detecting glaucomatous cupping. Conclusion: The computer software used in this study did not improve the reproducibility or validity of VCDR grading from fundus photographs compared with simple visual inspection. More clinical experience was correlated with higher agreement with the ophthalmologist VCDR reference standard. [ABSTRACT FROM AUTHOR]

The stereo correspondence problem exists because false matches between the images from multiple sensors camouflage the true (veridical) matches. True matches are correspondences between image points that have the same generative source; false matches are correspondences between similar image points that have different sources. This problem of selecting true matches among false ones must be overcome by both biological and artificial stereo systems in order for them to be useful depth sensors. The proposed re-examination of this fundamental issue shows that false matches form a symmetrical pattern in the array of all possible matches, with true matches forming the axis of symmetry. The patterning of false matches can therefore be used to locate true matches and derive the depth profile of the surface that gave rise to them. This reverses the traditional strategy, which treats false matches as noise. The new approach is particularly well-suited to extract the 3-D locations and shapes of camouflaged surfaces and to work in scenes characterized by high degrees of clutter. We demonstrate that the symmetry of false-match signals can be exploited to identify surfaces in random-dot stereograms. This strategy permits novel depth computations for target detection, localization, and identification by machine-vision systems, accounts for physiological and psychophysical findings that are otherwise puzzling and makes possible new ways for combining stereo and motion signals. [ABSTRACT FROM AUTHOR]

Mollusk shells are an ideal model system for understanding the morpho-elastic basis of morphological evolution of invertebrates’ exoskeletons. During the formation of the shell, the mantle tissue secretes proteins and minerals that calcify to form a new incremental layer of the exoskeleton. Most of the existing literature on the morphology of mollusks is descriptive. The mathematical understanding of the underlying coupling between pre-existing shell morphology, de novo surface deposition and morpho-elastic volume growth is at a nascent stage, primarily limited to reduced geometric representations. Here, we propose a general, three-dimensional computational framework coupling pre-existing morphology, incremental surface growth by accretion, and morpho-elastic volume growth. We exercise this framework by applying it to explain the stepwise morphogenesis of seashells during growth: new material surfaces are laid down by accretive growth on the mantle whose form is determined by its morpho-elastic growth. Calcification of the newest surfaces extends the shell as well as creates a new scaffold that constrains the next growth step. We study the effects of surface and volumetric growth rates, and of previously deposited shell geometries on the resulting modes of mantle deformation, and therefore of the developing shell’s morphology. Connections are made to a range of complex shells ornamentations. [ABSTRACT FROM AUTHOR]

Biological systems manifest continuous weak autoluminescence, which is present even in the absence of external stimuli. Since this autoluminescence arises from internal metabolic and physiological processes, several works suggested that it could carry information in the time series of the detected photon counts. However, there is little experimental work which would show any difference of this signal from random Poisson noise and some works were prone to artifacts due to lacking or improper reference signals. Here we apply rigorous statistical methods and advanced reference signals to test the hypothesis whether time series of autoluminescence from germinating mung beans display any intrinsic correlations. Utilizing the fractional Brownian bridge that employs short samples of time series in the method kernel, we suggest that the detected autoluminescence signal from mung beans is not totally random, but it seems to involve a process with a negative memory. Our results contribute to the development of the rigorous methodology of signal analysis of photonic biosignals. [ABSTRACT FROM AUTHOR]

Posturographic signals were recorded for 384 subjects of different ages and with old persons with gait disturbances. Four conditions were used: Eyes Open/Closed vs. Head Normal/Bent Back. ‘Center of Pressure’ (CoP) signals were decomposed into ‘Center of Mass’ (CoM) and the remaining difference between Center of Pressure and Center of Mass (CoPM). The Zero-Crossing points in which the Center of Mass and Center of Pressure paths cross each other have been extracted. Velocity of CoM, velocity of CoPM and acceleration of CoPM in Zero-Crossing points were analyzed to be potential markers of balance efficiency. Three factors causing the deterioration of balance quality were analyzed: closing eyes, bending the head back and patient age. The influence of the given factors was measured using the significance p of the t-Student test and Cohen's d effect size and applied to differences for the logarithms of three of the mentioned above variables measured without and with the given deteriorating factor. In the majority of comparisons, the proposed new parameters of balance quality possessed higher statistical power to detect deteriorated balance quality than the standard parameters: standard deviation of the signal and ellipse area covering 90% of the signal envelope. Most valuable are the velocity and acceleration of CoPM for the medio-lateral direction. Logarithms of the analyzed parameters are proposed to be used in analyses because they possess normal or close to normal distribution and they are less sensitive to single high values occurring often in measurements. [ABSTRACT FROM AUTHOR]

This paper is dedicated to the analysis of the improvement of heat transfer and the reduction of the pressure losses induced by the use of an active exchanger of millimeter size in a cooling loop. For pressure conditions imposed at the terminals of such a mini-channel whose upper wall is deformed by a progressive sinusoidal wave and for low Reynolds numbers (Re < 1000), we study the influence of the deformation parameters on the thermo-hydraulic performance of the exchanger (flow, heat transfer). The mechanical power applied to the deformed wall is connected to these parameters as well as to the pressure difference imposed by the external pump. The overall performance increases slightly with the value of the mechanical power up to a critical value for a given wall corrugation. Nevertheless, overall performance is up to 2 orders of magnitude higher than conventional static corrugated channels. [ABSTRACT FROM AUTHOR]

Two-dimensional optical waveguide mode simulations have been employed to investigate the optimized device structures for ridge-waveguide (Al, In, Ga) N-based green (520 nm) laser diodes (LDs). The effects of thicknesses, alloy compositions, and doping densities of each epitaxially grown layers as well as ridge geometries on optical confinement factors (Γ) and waveguide absorption (α) were comprehensively surveyed. InyGa1-yN (y=0.07–0.1) guiding layers (GLs) with thickness more than 50 nm were effective for realizing high Γ and low α. To minimize the absorption by the anode metal, p-cladding layer (p-CL) was required to be more than 500 nm. At the same time, low index insulator such as SiO2 was preferable for the narrow ridge, where the thickness at the sidewall had to be more than 60 nm. We also found that InGaN barriers layers between the quantum wells (QWs) were superior to GaN barriers to increase Γ and reduce α. Moreover, a thicker last barrier between the topmost QW and the electron blocking layer was also effective to reduce α. Regarding the effect of Mg doping concentration on the absorption, the reduction in Mg in the p-CL and the p-GL was significant to reduce α. Generally, it was confirmed the design for typical 405 nm LDs can be applied for 520 nm LD with the inclusion of InGaN GLs and barriers for the QWs. [ABSTRACT FROM AUTHOR]

Spin networks, namely, the 3nj symbols of quantum angular momentum theory and their generalizations to groups other than SU(2) and to quantum groups, permeate many areas of pure and applied science. The issues of their computation and characterization for large values of their entries are a challenge for diverse fields, such as spectroscopy and quantum chemistry, molecular and condensed matter physics, quantum computing, and the geometry of space time. Here we record progress both in their efficient calculation and in the study of the large j asymptotics. For the 9j symbol, a prototypical entangled network, we present and extensively check numerically formulas that illustrate the passage to the semiclassical limit, manifesting both the occurrence of disentangling and the discrete-continuum transition. [ABSTRACT FROM AUTHOR]

Open-porous polymers form an attractive class of piezoelectric materials. Up to now it has been demonstrated that fibrous polyterafluoroethylene films after proper polarizing are responsible for the high piezoelectric response if confined between two electrically blocking polyfluoroethylene propylene layers. The sandwich structures reveal large quasistatic piezoelectric coefficients of up to 1500 pC/N. Here a theoretical model is proposed for a three-layer sandwich which quantitatively explains the experimentally obtainable polarization and its hysteresis behavior for different poling voltages. It will be reported that each sandwich structure exhibits a limit for the remanent polarization induced by polarization backswitching due to insufficient charge compensation. The correlation of the remanent polarization to the device geometry and the dielectric constants will be highlighted and suggestions for optimization will be given. It will be reported that the limitation of the remanent polarization also limits the obtainable piezoelectric coefficient of the sandwich structures. [ABSTRACT FROM AUTHOR]

We study theoretically the spin-polarized electron transport properties for a weak Rashba spin-orbit coupling (SOC) quantum wire connected nonadiabatically to two normal-conductor electrode leads. The influence of both the mode mixing due to wire-lead connection and Rashba SOC split on the spin-polarized electron transport is treated simultaneously by means of scattering matrix within the framework of effective free-electron approximation. The analytical analysis with numerical examples demonstrates that the purely spin-polarized current can occur for the system with an appropriate system geometry and material parameters. Our result may imply a simple approach to the design of a spin filter device without containing any magnetic materials or applying a magnetic field. [ABSTRACT FROM AUTHOR]

Owing to the increasing importance of orderly placed nanostructures, the following study was conducted on oriented and disoriented nanowires. Use of grazing incidence x-ray diffraction (GIXRD) and normal x-ray diffraction (XRD) as possible tools to assess their alignment is discussed. The property of crystalline nanowires to grow in a preferred direction over a substrate is made use of, in which deviation in diffraction intensities is measured on a group of oriented and disoriented nanowires. We find that the difference is sufficiently large to predict the spread in orientations away from a reference direction. The observed intensity variation is explained using a modeled view of diffraction geometry with different nanowire orientations. An alignment index Anw has been calculated using (110) and (300) peak intensities in XRD and GIXRD measurements. The values were found to be related to the extent of vertical alignment as observed using scanning electron microscopy (SEM). The difference in diffraction geometry and penetration depth between the two techniques is found to give complementary information on the upper and lower portions of the nanowires, respectively. Analysis of the diffraction patterns also shows that bending of these nanowires occurs preferentially about the c axis as compared to bending in other directions. In the present study samples with crystalline α-Fe2O3 nanowires grown on pure Fe substrate by controlled thermal oxidation route have been investigated using GIXRD, XRD, SEM and atomic force microscopy. Morphology of the nanowires is discussed briefly. [ABSTRACT FROM AUTHOR]

A self-consistent nonparabolic calculation of the band structure and intersubband absorption in a V-groove-quantum-wire are presented and analyzed with respect to doping concentration, geometry, and temperature. A comparison with a parabolic flatband model shows that both the self-consistency and the nonparabolicity considerably affect subband edges and the intersubband absorption which are studied when both effects are taken into account. The absorption spectra exhibit a prominent peak in the terahertz region (wavelength range λX=55-95 μm) for the polarization in the direction of the weak confinement (X), while for polarization in the direction of the strong confinement (Y), it shows two groups of peaks, one in a slightly lower wavelength range than for the X polarization, and the second for λY=8-13 μm. Technological parameters considered in our analysis can be used to tailor and adjust the absorption spectra for various applications in the terahertz spectral range. [ABSTRACT FROM AUTHOR]

A dipolar-free sum-over-states expression for the diagonal components of the first hyperpolarizability (β) tensor has been proposed by Kuzyk [Phys. Rev. A 72, 053819 (2005)] as an alternative to the traditional expression. We examine both alternatives for the longitudinal β of four typical push-pull π-conjugated systems using the ab initio CIS and CIS(D) schemes to approximate the excited state properties. Since they are each evaluated approximately the two SOS expressions yield different values for β and it is found that (i) they evolve symmetrically as the number of excited states is increased so that their average is nearly constant; (ii) in the static limit, the two values agree better with one another when their average is close to the “exact” correlated result; and (iii) frequency dispersion can affect the agreement between the alternative expressions. On the basis of (i) and (ii) it appears best for typical push-pull π-conjugated systems to estimate the static β, and the error in the value so obtained, by averaging the Kuzyk and traditional results. [ABSTRACT FROM AUTHOR]

The electric potential close to a boundary between two dielectric material layers reflects the geometry of such an interface. The local variations arise from the combination of material parameters and from the nature of the inhomogeneity. Here, the arising electric field is considered for both a sinusoidally varying boundary and for a “rough,” Gaussian test case. We discuss the applicability of a one-dimensional model with the varying layer thickness as a parameter and the generic scaling of the results. As an application we consider the effect of paper roughness on toner transfer in electrophotographic printing. [ABSTRACT FROM AUTHOR]

Binary complexes of C2 with rare-gas atoms (C2–Rg) have attracted theoretical interest as their potential-energy surfaces are predicted to support linear equilibrium geometries, without the local minimum for the T-shaped geometry that would be expected using a standard pair-potential model. In the present work we have explored the properties of C2–Ne using laser-induced fluorescence detection of the D 1Σu+-X 1Σg+ transition. Bands of the complex were observed in association with the monomer 0-0 and 1-1 transitions. Rotationally resolved data yielded rotational constants of B′=0.099(3) cm-1 and B″=0.100(3) cm-1 for the excited and ground states, respectively. Analysis of the rovibrational energy-level structure for C2(D)–Ne indicates that the complex has a linear equilibrium structure with a barrier to internal rotation of approximately 15 cm-1. Data for the ground state validate a recent high-level ab initio calculation of the potential-energy surface for C2(X)–Ne. [ABSTRACT FROM AUTHOR]

In this study, a plasma display panel (PDP) cell is modeled in a two-dimensional cross-sectional region and plasma discharge characteristics are analyzed by numerical simulations based on the finite difference method developed here. An orthogonal curvilinear coordinate system is introduced to apply to the arbitrary PDP cell geometry for systematic computations. Wall voltage transfer curves derived through experiments and computation are compared in detail. They show good agreement. The effect of PDP cell geometry on the voltage margin and on ultraviolet (UV) photon production efficiency are also studied. Results show that the thickness of front dielectric layer has a marked effect on the voltage margin and UV photon production efficiency. Furthermore, the dielectric ribs prevent the crosstalk of discharge in two ways: they decrease a number of excited species leaking to adjacent PDP cells and decrease charge distribution on the dielectric surface near the cell boundaries. [ABSTRACT FROM AUTHOR]

Ab initio calculations at the multiconfiguration self-consistent field level followed by a multireference configuration interaction were carried out along the two possible collinear approaches of the [LiHHe]+ system, while a three-dimensional calculation of the structures of that complex with LiH+ kept at its equilibrium geometry was also completed at the same level of accuracy. The interaction forces of the lowest two electronic states indicate possible reactive behavior, with the first excited potential-energy surface clearly showing a barrierless path to HeH+ product formation. The details of the reactive pathways and their possible bearing on reaction processes, which could occur at the low temperature of a He nanodroplet holding LiH+ as an impurity, are analyzed and discussed. [ABSTRACT FROM AUTHOR]

We have investigated the geometries as well as the longitudinal dipole moment (μ), polarizability (α), and first hyperpolarizability (β) of polymethineimine oligomers using different approaches [Hartree–Fock (HF), second-order Møller–Plesset (MP2), and hybrid density functional theory (DFT) methods (B3LYP and PBE0)] for evaluating the geometries and the nonlinear optical properties. It turns out that (i) HF and the selected DFT methods provide the incorrect sign for β of short and medium size oligomers. (ii) The B3LYP and PBE0 electron correlation correction are too small for μ, too large for α, and for some oligomer lengths, they are in the wrong direction for β. (iii) On the contrary to polyacetylene, the hybrid-DFT geometries are in poor agreement with MP2 geometries; the former showing much smaller bond length alternations. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Restricted-spin coupled-cluster single-double plus perturbative triple excitation [RCCSD(T)] potential energy functions (PEFs) were calculated for the X 2A″ and à 2A′ states of HPCl employing the augmented correlation-consistent polarized-valence-quadruple-ζ (aug-cc-pVQZ) basis set. Further geometry optimization calculations were carried out on both electronic states of HPCl at the RCCSD(T) level with all electron and quasirelativistic effective core potential basis sets of better than the aug-cc-pVQZ quality, and also including some core electrons, in order to obtain more reliable geometrical parameters and relative electronic energy of the two states. Anharmonic vibrational wave functions of the two states of HPCl and DPCl, and Franck-Condon (FC) factors of the à 2A′-X 2A″ transition were computed employing the RCCSD(T)/aug-cc-pVQZ PEFs. Calculated FC factors with allowance for Duschinsky rotation and anharmonicity were used to simulate the single-vibronic-level (SVL) emission spectra of HPCl and DPCl reported by Brandon et al. [J. Chem. Phys. 119, 2037 (2003)] and the chemiluminescence spectrum reported by Bramwell et al. [Chem. Phys. Lett. 331, 483 (2000)]. Comparison between simulated and observed SVL emission spectra gives the experimentally derived equilibrium geometry of the à 2A′ state of HPCl of re(PCl)=2.0035±0.0015 Å, θe=116.08±0.60°, and re(HP)=1.4063±0.0015 Å via the iterative Franck-Condon analysis procedure. Comparison between simulated and observed chemiluminescence spectra confirms that the vibrational population distribution of the à 2A′ state of HPCl is non-Boltzmann, as proposed by Baraille et al. [Chem. Phys. 289, 263 (2003)]. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]