Noncommutative geometry-inspired rotating black hole in three ...
Indian Academy of Sciences (India)
We ﬁnd a new rotating black hole in three-dimensional anti-de Sitter space using an anisotropic perfect ﬂuid inspired by the noncommutative black hole. We deduce the thermodynamical quantities of this black hole and compare them with those of a rotating BTZ solution and give corrections to the area law to get the exact ...
Non-commutative geometry inspired charged black holes
International Nuclear Information System (INIS)
Ansoldi, Stefano; Nicolini, Piero; Smailagic, Anais; Spallucci, Euro
2007-01-01
We find a new, non-commutative geometry inspired, solution of the coupled Einstein-Maxwell field equations describing a variety of charged, self-gravitating objects, including extremal and non-extremal black holes. The metric smoothly interpolates between de Sitter geometry, at short distance, and Reissner-Nordstrom geometry far away from the origin. Contrary to the ordinary Reissner-Nordstrom spacetime there is no curvature singularity in the origin neither 'naked' nor shielded by horizons. We investigate both Hawking process and pair creation in this new scenario
Noncommutative geometry inspired black holes in Rastall gravity
Energy Technology Data Exchange (ETDEWEB)
Ma, Meng-Sen [Shanxi Datong University, Institute of Theoretical Physics, Datong (China); Shanxi Datong University, Department of Physics, Datong (China); Zhao, Ren [Shanxi Datong University, Institute of Theoretical Physics, Datong (China)
2017-09-15
Under two different metric ansatzes, the noncommutative geometry inspired black holes (NCBH) in the framework of Rastall gravity are derived and analyzed. We consider the fluid-type matter with the Gaussian-distribution smeared mass density. Taking a Schwarzschild-like metric ansatz, it is shown that the noncommutative geometry inspired Schwarzschild black hole (NCSBH) in Rastall gravity, unlike its counterpart in general relativity (GR), is not a regular black hole. It has at most one event horizon. After showing a finite maximal temperature, the black hole will leave behind a point-like massive remnant at zero temperature. Considering a more general metric ansatz and a special equation of state of the matter, we also find a regular NCBH in Rastall gravity, which has a similar geometric structure and temperature to that of NCSBH in GR. (orig.)
Accretion onto a noncommutative geometry inspired black hole
Energy Technology Data Exchange (ETDEWEB)
Kumar, Rahul [Jamia Millia Islamia, Centre for Theoretical Physics, New Delhi (India); Ghosh, Sushant G. [Jamia Millia Islamia, Centre for Theoretical Physics, New Delhi (India); Jamia Millia Islamia, Multidisciplinary Centre for Advanced Research and Studies (MCARS), New Delhi (India); University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, Durban (South Africa)
2017-09-15
The spherically symmetric accretion onto a noncommutative (NC) inspired Schwarzschild black hole is treated for a polytropic fluid. The critical accretion rate M, sonic speed a{sub s} and other flow parameters are generalized for the NC inspired static black hole and compared with the results obtained for the standard Schwarzschild black holes. Also explicit expressions for gas compression ratios and temperature profiles below the accretion radius and at the event horizon are derived. This analysis is a generalization of Michel's solution to the NC geometry. Owing to the NC corrected black hole, the accretion flow parameters also have been modified. It turns out that M ∼ M{sup 2} is still achievable but r{sub s} seems to be substantially decreased due to the NC effects. They in turn do affect the accretion process. (orig.)
Bio-inspired optical rotation sensor
O'Carroll, David C.; Shoemaker, Patrick A.; Brinkworth, Russell S. A.
2007-01-01
Traditional approaches to calculating self-motion from visual information in artificial devices have generally relied on object identification and/or correlation of image sections between successive frames. Such calculations are computationally expensive and real-time digital implementation requires powerful processors. In contrast flies arrive at essentially the same outcome, the estimation of self-motion, in a much smaller package using vastly less power. Despite the potential advantages and a few notable successes, few neuromorphic analog VLSI devices based on biological vision have been employed in practical applications to date. This paper describes a hardware implementation in aVLSI of our recently developed adaptive model for motion detection. The chip integrates motion over a linear array of local motion processors to give a single voltage output. Although the device lacks on-chip photodetectors, it includes bias circuits to use currents from external photodiodes, and we have integrated it with a ring-array of 40 photodiodes to form a visual rotation sensor. The ring configuration reduces pattern noise and combined with the pixel-wise adaptive characteristic of the underlying circuitry, permits a robust output that is proportional to image rotational velocity over a large range of speeds, and is largely independent of either mean luminance or the spatial structure of the image viewed. In principle, such devices could be used as an element of a velocity-based servo to replace or augment inertial guidance systems in applications such as mUAVs.
Noncommutative geometry inspired Einstein–Gauss–Bonnet black holes
Ghosh, Sushant G.
2018-04-01
Low energy limits of a string theory suggests that the gravity action should include quadratic and higher-order curvature terms, in the form of dimensionally continued Gauss–Bonnet densities. Einstein–Gauss–Bonnet is a natural extension of the general relativity to higher dimensions in which the first and second-order terms correspond, respectively, to general relativity and Einstein–Gauss–Bonnet gravity. We obtain five-dimensional (5D) black hole solutions, inspired by a noncommutative geometry, with a static spherically symmetric, Gaussian mass distribution as a source both in the general relativity and Einstein–Gauss–Bonnet gravity cases, and we also analyzes their thermodynamical properties. Owing the noncommutative corrected black hole, the thermodynamic quantities have also been modified, and phase transition is shown to be achievable. The phase transitions for the thermodynamic stability, in both the theories, are characterized by a discontinuity in the specific heat at r_+=rC , with the stable (unstable) branch for r ) rC . The metric of the noncommutative inspired black holes smoothly goes over to the Boulware–Deser solution at large distance. The paper has been appended with a calculation of black hole mass using holographic renormalization.
Near horizon geometry of rotating black holes in five dimensions
International Nuclear Information System (INIS)
Cvetic, M.; Larsen, F.
1998-01-01
We interpret the general rotating black holes in five dimensions as rotating black strings in six dimensions. In the near-horizon limit the geometry is locally AdS 3 x S 3 , as in the non-rotating case. However, the global structure couples the AdS 3 and the S 3 , giving angular velocity to the S 3 . The asymptotic geometry is exploited to count the microstates and recover the precise value of the Bekenstein-Hawking entropy, with rotation taken properly into account. We discuss the perturbation spectrum of the rotating black hole, and its relation to the underlying conformal field theory. (orig.)
A geometry calibration method for rotation translation trajectory
International Nuclear Information System (INIS)
Zhang Jun; Yan Bin; Li Lei; Lu Lizhong; Zhang Feng
2013-01-01
In cone-beam CT imaging system, it is difficult to directly measure the geometry parameters. In this paper, a geometry calibration method for rotation translation trajectory is proposed. Intrinsic parameters are solved from the relationship built on geometry parameter of the system and projection trajectory of calibration object. Parameters of rotation axis are extrapolated from the unified intrinsic parameter, and geometry parameters of the idle trajectory are acquired too. The calibration geometry can be analytically determined using explicit formulae, it can avoid getting into local optimum in iterative way. Simulation experiments are carried out on misaligned geometry, experiment results indicate that geometry artifacts due to misaligned geometry are effectively depressed by the proposed method, and the image quality is enhanced. (authors)
Exotic rotational correlations in quantum geometry
Energy Technology Data Exchange (ETDEWEB)
Hogan, Craig
2017-05-01
It is argued by extrapolation of general relativity and quantum mechanics that a classical inertial frame corresponds to a statistically defined observable that rotationally fluctuates due to Planck scale indeterminacy. Physical effects of exotic nonlocal rotational correlations on large scale field states are estimated. Their entanglement with the strong interaction vacuum is estimated to produce a universal, statistical centrifugal acceleration that resembles the observed cosmological constant.
DEFF Research Database (Denmark)
Davoudinejad, A.; M. Ribo, M.; Pedersen, D. B.
2018-01-01
on. The geometry and fabrication of these surfaces are still under research. In this study, the feasibility of using direct fabrication of microscale features by Additive Manufacturing (AM) processes was investigated. The investigation was carried out using a specifically designed vat...... photopolymerization AM machine-tool suitable for precision manufacturing at the micro dimensional scale which has previously been developed, built and validated at the Technical University of Denmark. It was shown that it was possible to replicate a simplified surface inspired by the Tokay gecko, the geometry...
Rotating optical geometry sensor for inner pipe-surface reconstruction
Ritter, Moritz; Frey, Christan W.
2010-01-01
The inspection of sewer or fresh water pipes is usually carried out by a remotely controlled inspection vehicle equipped with a high resolution camera and a lightning system. This operator-oriented approach based on offline analysis of the recorded images is highly subjective and prone to errors. Beside the subjective classification of pipe defects through the operator standard closed circuit television (CCTV) technology is not suitable for detecting geometrical deformations resulting from e.g. structural mechanical weakness of the pipe, corrosion of e.g. cast-iron material or sedimentations. At Fraunhofer Institute of Optronics, System Technologies and Image Exploitation (IOSB) in Karlsruhe, Germany, a new Rotating Optical Geometry Sensor (ROGS) for pipe inspection has been developed which is capable of measuring the inner pipe geometry very precisely over the whole pipe length. This paper describes the developed ROGS system and the online adaption strategy for choosing the optimal system parameters. These parameters are the rotation and traveling speed dependent from the pipe diameter. Furthermore, a practicable calibration methodology is presented which guarantees an identification of the several internal sensor parameters. ROGS has been integrated in two different systems: A rod based system for small fresh water pipes and a standard inspection vehicle based system for large sewer Pipes. These systems have been successfully applied to different pipe systems. With this measurement method the geometric information can be used efficiently for an objective repeatable quality evaluation. Results and experiences in the area of fresh water pipe inspection will be presented.
Complex structure of Kerr geometry and rotating 'photon rocket' solutions
International Nuclear Information System (INIS)
Burinskii, Alexander
2003-01-01
In the frame of the Kerr-Schild approach, we obtain a generalization of the Kerr solution to a nonstationary case corresponding to a rotating source moving with arbitrary acceleration. Similar to the Kerr solution, the solutions obtained have geodesic and shearfree principal null congruence. The current parameters of the solutions are determined by a complex retarded-time construction via a given complex worldline of source. The real part of the complex worldline defines the values of the boost and acceleration while the imaginary part controls the rotation. The acceleration of the source is accompanied by lightlike radiation along the principal null congruence. The solutions obtained generalize to the rotating case the known Kinnersley class of the 'photon rocket' solutions
Faraday rotation near charged black holes and other electrovacuum geometries
International Nuclear Information System (INIS)
Gerlach, U.H.
1975-01-01
In space permeated by a steady background electromagnetic field a gravitational wave and an electromagnetic wave not only undergo beat frequency oscillations, but the linear polarizations of these waves undergo Faraday rotations as well. The beating and the Faraday rotations are inextricably related. The classification of these phenomena requires three parameters, the three Euler parameters of SU(2). They specify in a more general sense the ''polarization'' of an electrograviton mode. The evolution of the beat frequency oscillations and the Faraday rotations along a propagating wave front is described as a moving point in SU(2). Consequently, a charged black hole serves not only as a catalyst for converting suitably directed electromagnetic radiation into gravitational radiation, but also as an agent that randomized the linear polarizations of radiation emerging from it. An assessment of these phenomena in relation to the origin of Weber's signals is given
Surface geometry of a rotating black hole in a magnetic field
International Nuclear Information System (INIS)
Kulkarni, R.; Dadhich, N.
1986-01-01
We study the intrinsic geometry of the surface of a rotating black hole in a uniform magnetic field, using a metric discovered by Ernst and Wild. Rotating black holes are analogous to material rotating bodies according to Smarr since black holes also tend to become more oblate on being spun up. Our study shows that the presence of a strong magnetic field ensures that a black hole actually becomes increasingly prolate on being spun up. Studying the intrinsic geometry of the black-hole surface also gives rise to an interesting embedding problem. Smarr shows that a Kerr black hole cannot be globally isometrically embedded in R 3 if its specific angular momentum a exceeds (√3 /2)mapprox.0.866. . .m. We show that in the presence of a magnetic field of strength B, satisfying 2- √3 2 m 2 3 for all values of the angular momentum
Low torque hydrodynamic lip geometry for bi-directional rotation seals
Dietle, Lannie L [Houston, TX; Schroeder, John E [Richmond, TX
2009-07-21
A hydrodynamically lubricating geometry for the generally circular dynamic sealing lip of rotary seals that are employed to partition a lubricant from an environment. The dynamic sealing lip is provided for establishing compressed sealing engagement with a relatively rotatable surface, and for wedging a film of lubricating fluid into the interface between the dynamic sealing lip and the relatively rotatable surface in response to relative rotation that may occur in the clockwise or the counter-clockwise direction. A wave form incorporating an elongated dimple provides the gradual convergence, efficient impingement angle, and gradual interfacial contact pressure rise that are conducive to efficient hydrodynamic wedging. Skewed elevated contact pressure zones produced by compression edge effects provide for controlled lubricant movement within the dynamic sealing interface between the seal and the relatively rotatable surface, producing enhanced lubrication and low running torque.
Influence of Geometry and Velocity of Rotating Solids on Hydrodynamics of a Confined Volume
Directory of Open Access Journals (Sweden)
Ignacio Carvajal-Mariscal
2017-01-01
Full Text Available Three cylinder-based geometries were evaluated at five different rotating speeds (ω = 20.94, 62.83, 94.25, 125.66, and 157.08 rad·s−1 to obtain the fluid flow pattern in nonsteady conditions. Two of the models were modified at the lower region, also known as tip section, by means of inverted and right truncated cone geometries, respectively. The experimental technique used a visualization cell and a Particle Imaging Velocimetry installation to obtain the vector field at the central plane of the volume. The Line Integral Convolution Method was used to obtain the fluid motion at the plane. In addition, the scalar kinetic energy and the time series were calculated to perform the normal probability plot. This procedure was used to determine the nonlinear fluid flow pattern. It was also used to identify two different flow regimens in physical and numerical results. As the rotation speed increased, the turbulent regions were placed together and moved. The process makes experimental observation difficult. The biphasic and turbulence constitutive equations were solved with the Computational Fluid Dynamics technique. Numerical results were compared with physical experiments for validation. The model with the inverted truncated cone tip presented better stability in the fluid flow pattern along the rotation speed range.
Influence of geometry on mechanical properties of bio-inspired silica-based hierarchical materials
International Nuclear Information System (INIS)
Dimas, Leon S; Buehler, Markus J
2012-01-01
Diatoms, bone, nacre and deep-sea sponges are mineralized natural structures found abundantly in nature. They exhibit mechanical properties on par with advanced engineering materials, yet their fundamental building blocks are brittle and weak. An intriguing characteristic of these structures is their heterogeneous distribution of mechanical properties. Specifically, diatoms exhibit nanoscale porosity in specific geometrical configurations to create regions with distinct stress strain responses, notably based on a single and simple building block, silica. The study reported here, using models derived from first principles based full atomistic studies with the ReaxFF reactive force field, focuses on the mechanics and deformation mechanisms of silica-based nanocomposites inspired by mineralized structures. We examine single edged notched tensile specimens and analyze stress and strain fields under varied sample size in order to gain fundamental insights into the deformation mechanisms of structures with distinct ordered arrangements of soft and stiff phases. We find that hierarchical arrangements of silica nanostructures markedly change the stress and strain transfer in the samples. The combined action of strain transfer in the deformable phase, and stress transfer in the strong phase, acts synergistically to reduce the intensity of stress concentrations around a crack tip, and renders the resulting composites less sensitive to the presence of flaws, for certain geometrical configurations it even leads to stable crack propagation. A systematic study allows us to identify composite structures with superior fracture mechanical properties relative to their constituents, akin to many natural biomineralized materials that turn the weaknesses of building blocks into a strength of the overall system. (paper)
Sossinsky, A B
2012-01-01
The book is an innovative modern exposition of geometry, or rather, of geometries; it is the first textbook in which Felix Klein's Erlangen Program (the action of transformation groups) is systematically used as the basis for defining various geometries. The course of study presented is dedicated to the proposition that all geometries are created equal--although some, of course, remain more equal than others. The author concentrates on several of the more distinguished and beautiful ones, which include what he terms "toy geometries", the geometries of Platonic bodies, discrete geometries, and classical continuous geometries. The text is based on first-year semester course lectures delivered at the Independent University of Moscow in 2003 and 2006. It is by no means a formal algebraic or analytic treatment of geometric topics, but rather, a highly visual exposition containing upwards of 200 illustrations. The reader is expected to possess a familiarity with elementary Euclidean geometry, albeit those lacking t...
Chen, Chen; Duru, Paul; Joseph, Pierre; Geoffroy, Sandrine; Prat, Marc
2017-11-08
Evaporation is a key phenomenon in the natural environment and in many technological systems involving capillary structures. Understanding the evaporation front dynamics enables the evaporation rate from microfluidic devices and porous media to be finely controlled. Of particular interest is the ability to control the position of the front through suitable design of the capillary structure. Here, we show how to design model capillary structures in microfluidic devices so as to control the drying kinetics. This is achieved by acting on the spatial organization of the constrictions that influence the invasion of the structure by the gas phase. Two types of control are demonstrated. The first is intended to control the sequence of primary invasions through the pore space, while the second aims to control the secondary liquid structures: films, bridges, etc., that can form in the region of pore space invaded by the gas phase. It is shown how the latter can be obtained from phyllotaxy-inspired geometry. Our study thus opens up a route toward the control of the evaporation kinetics by means of tailored capillary structures.
Indian Academy of Sciences (India)
. In the previous article we looked at the origins of synthetic and analytic geometry. More practical minded people, the builders and navigators, were studying two other aspects of geometry- trigonometry and integral calculus. These are actually ...
Prasolov, V V
2015-01-01
This book provides a systematic introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. Also included is a chapter on infinite-dimensional generalizations of Euclidean and affine geometries. A uniform approach to different geometries, based on Klein's Erlangen Program is suggested, and similarities of various phenomena in all geometries are traced. An important notion of duality of geometric objects is highlighted throughout the book. The authors also include a detailed presentation of the theory of conics and quadrics, including the theory of conics for non-Euclidean geometries. The book contains many beautiful geometric facts and has plenty of problems, most of them with solutions, which nicely supplement the main text. With more than 150 figures illustrating the arguments, the book can be recommended as a textbook for undergraduate and graduate-level courses in geometry.
Pedoe, Dan
1988-01-01
""A lucid and masterly survey."" - Mathematics Gazette Professor Pedoe is widely known as a fine teacher and a fine geometer. His abilities in both areas are clearly evident in this self-contained, well-written, and lucid introduction to the scope and methods of elementary geometry. It covers the geometry usually included in undergraduate courses in mathematics, except for the theory of convex sets. Based on a course given by the author for several years at the University of Minnesota, the main purpose of the book is to increase geometrical, and therefore mathematical, understanding and to he
Contact geometry at the undersurface of the acromion with and without a rotator cuff tear.
Lee, S B; Itoi, E; O'Driscoll, S W; An, K N
2001-04-01
The purpose of this study was to investigate the difference in contact geometry at the undersurface of acromion in shoulders with and without a rotator cuff (RC) tear. Case-control study. Forty fresh cadaveric shoulders (average age at death, 61 years) without gross osteoarthritic changes were divided into the intact RC group (n = 20) and the RC tear group (n = 20). Clinical impingement was simulated by compressing the humeral head and the intact portion of the RC against the coracoacromial arch with an axial compressive force of 25 kg while the humerus was held abducted 20 degrees in the scapular plane. The contact pattern between the acromion and the RC was measured with Fuji Prescale super low-pressure-sensitive film (Fuji Photo Film Co, Ltd, Tokyo, Japan). The imprint image was analyzed using Global Lab image software (Automatix, Marlboro, MA). The percentage of the maximum anteroposterior dimension of the imprint on Fuji film to the anteroposterior diameter of the acromial undersurface was 29% +/- 9% in intact RC shoulders, and 39% +/- 13% in shoulders with an RC tear (P >.05). The percentage of the maximum mediolateral dimension of the imprint to the mediolateral diameter of the corresponding part of the acromial undersurface was 27% +/- 12% in intact RC shoulders, and 48% +/- 11% in shoulders with an RC tear. This difference was statistically significant (P RC in the anteroposterior dimension, which might be related to the appearance in supraspinatus outlet view, was not significantly different between shoulders with and without an RC tear. These findings suggest that factors other than acromial shape play a significant role in the pathogenesis of RC tears. The implication regarding the role of acromioplasty remains to be clarified.
International Nuclear Information System (INIS)
Mohammadi, J.; Behnamian, Y.; Mostafaei, A.; Gerlich, A.P.
2015-01-01
Highlights: • Tool geometry, rotation and travel speeds show great effect on the microstructure stability of FSW joint. • Increasing rotation and travel speeds resulted in increasing the tensile strength and ductility of the joints. • Better intermixing between Al/Mg alloys was obtained by tapered threaded pin. • A mechanical interlocking mechanism proposed for higher ductility and superior tensile properties in FSW joints. - Abstract: Lap joint friction stir welding (FSW) between dissimilar AZ31B and Al 6061 alloys sheets was conducted using various welding parameters including tool geometry, rotation and travel speeds. Tapered threaded pin and tapered pin tools were applied to fabricate FSW joints, using different rotation and travel speeds. Metallurgical investigations including X-ray diffraction pattern (XRD), optical microscopy images (OM), scanning electron microscopy equipped with an energy-dispersive X-ray spectroscopy (SEM–EDS) and electron probe microanalysis (EPMA) were used to characterize joints microstructures made with different welding parameters. Intermetallic phases were detected in the weld zone (WZ). Various microstructures were observed in the stir zone which can be attributed to using different travel and rotation speeds. Mechanical evaluation including lap shear fracture load test and microhardness measurements indicated that by simultaneously increasing the tool rotation and travel speeds, the joint tensile strength and ductility reached a maximum value. Microhardness studies and extracted results from stress–strain curves indicated that mechanical properties were affected by FSW process. Furthermore, phase analyses by XRD indicated the presence of intermetallic compounds in the weld zone. Finally, in the Al/Mg dissimilar weld, fractography studies showed that intermetallic compounds formation in the weld zone had an influence on the failure mode
Chasalevris, Athanasios; Dohnal, Fadi
2015-02-01
The idea for a journal bearing with variable geometry was formerly developed and investigated on its principles of operation giving very optimistic theoretical results for the vibration quenching of simple and more complicated rotor bearing systems during the passage through the first critical speed. The journal bearing with variable geometry is presented in this paper in its final form with the detailed design procedure. The current journal bearing was constructed in order to be applied in a simple real rotor bearing system that already exists as an experimental facility. The current paper presents details on the manufactured prototype bearing as an experimental continuation of previous works that presented the simulation of the operating principle of this journal bearing. The design parameters are discussed thoroughly under the numerical simulation for the fluid film pressure in dependency of the variable fluid film thickness during the operation conditions. The implementation of the variable geometry bearing in an experimental rotor bearing system is outlined. Various measurements highlight the efficiency of the proposed bearing element in vibration quenching during the passage through resonance. The inspiration for the current idea is based on the fact that the alteration of the fluid film characteristics of stiffness and damping during the passage through resonance results in vibration quenching. This alteration of the bearing characteristics is achieved by the introduction of an additional fluid film thickness using the passive displacement of the lower half-bearing part. • The contribution of the current journal bearing in vibration quenching. • Experimental evidence for the VGJB contribution.
Directory of Open Access Journals (Sweden)
Chifu E. N.
2009-07-01
Full Text Available General Relativistic metric tensors for gravitational fields exterior to homogeneous spherical mass distributions rotating with constant angular velocity about a fixed di- ameter are constructed. The coeffcients of affine connection for the gravitational field are used to derive equations of motion for test particles. The laws of conservation of energy and angular momentum are deduced using the generalized Lagrangian. The law of conservation of angular momentum is found to be equal to that in Schwarzschild’s gravitational field. The planetary equation of motion and the equation of motion for a photon in the vicinity of the rotating spherical mass distribution have rotational terms not found in Schwarzschild’s field.
On the near horizon rotating black hole geometries with NUT charges
Energy Technology Data Exchange (ETDEWEB)
Galajinsky, Anton; Orekhov, Kirill [Tomsk Polytechnic University, Laboratory of Mathematical Physics, Tomsk (Russian Federation)
2016-09-15
The near horizon geometries are usually constructed by implementing a specific limit to a given extreme black hole configuration. Their salient feature is that the isometry group includes the conformal subgroup SO(2, 1). In this work, we turn the logic around and use the conformal invariants for constructing Ricci-flat metrics in d = 4 and d = 5 where the vacuum Einstein equations reduce to a coupled set of ordinary differential equations. In four dimensions the analysis can be carried out in full generality and the resulting metric describes the d = 4 near horizon Kerr-NUT black hole. In five dimensions we choose a specific ansatz whose structure is similar to the d = 5 near horizon Myers-Perry black hole. A Ricci-flat metric involving five arbitrary parameters is constructed. A particular member of this family, which is characterized by three parameters, seems to be a natural candidate to describe the d = 5 near horizon Myers- Perry black hole with a NUT charge. (orig.)
On the near horizon rotating black hole geometries with NUT charges
International Nuclear Information System (INIS)
Galajinsky, Anton; Orekhov, Kirill
2016-01-01
The near horizon geometries are usually constructed by implementing a specific limit to a given extreme black hole configuration. Their salient feature is that the isometry group includes the conformal subgroup SO(2, 1). In this work, we turn the logic around and use the conformal invariants for constructing Ricci-flat metrics in d = 4 and d = 5 where the vacuum Einstein equations reduce to a coupled set of ordinary differential equations. In four dimensions the analysis can be carried out in full generality and the resulting metric describes the d = 4 near horizon Kerr-NUT black hole. In five dimensions we choose a specific ansatz whose structure is similar to the d = 5 near horizon Myers-Perry black hole. A Ricci-flat metric involving five arbitrary parameters is constructed. A particular member of this family, which is characterized by three parameters, seems to be a natural candidate to describe the d = 5 near horizon Myers- Perry black hole with a NUT charge. (orig.)
Tischhauser, Karen
2015-01-01
Students need inspiration to write. Assigning is not teaching. In order to inspire students to write fiction worth reading, teachers must take them through the process of writing. Physical objects inspire good writing with depth. In this article, the reader will be taken through the process of inspiring young writers through the use of boxes.…
International Nuclear Information System (INIS)
Salari, Emad; Jahazi, Mohammad; Khodabandeh, Alireza; Ghasemi-Nanesa, Hadi
2014-01-01
Highlights: • Successful lap joint friction stir welding of AA5456 with two different tempers. • New stepped conical threaded pin for FSW of lap joints is introduced. • Investigated interactions between tool geometry and mechanical properties. • Microstructure and fracture surface analysis of dissimilar lap welds. - Abstract: Friction stir welding of AA5456 aluminum alloy in lap joint configuration is with two different tempers, T321 and O, and different thicknesses, 5 mm and 2.5 mm was investigated. The influences of tool geometry and various rotational speeds on macrostructure, microstructure and joint strength are presented. Specifically, four different tool pin profiles (a conical thread pin, a cylindrical–conical thread pin, a stepped conical thread pin and Flared Triflute pin tool) and two rotational speeds, 600 and 800 rpm, were used. The results indicated that, tool geometry influences significantly material flow in the nugget zone and accordingly control the weld mechanical properties. Of particular interest is the stepped conical threaded pin, which is introduced for the first time in the present investigation. Scanning electron microscopy investigation of the fracture location of samples was carried out and the findings correlated with tool geometry features and their influences on material flow and tension test results. The optimum microstructure and mechanical properties were obtained for the joints produced with the stepped conical thread pin profile and rotational speed of 600 rpm. The characteristics of the nugget zone microstructure, hooking height, and fracture location of the weld joints were used as criteria to quantify the influence of processing conditions on joint performance and integrity. The results are interpreted in the framework of physical metallurgy properties and compared with published literature
Wales, Andrew
1998-01-01
Uses the biography and work of M. C. Escher to introduce a unit on art history. Tells about Escher's influence not only on artists, but also on mathematicians and physicists. Outlines a student project in which students employed one of these themes: impossible geometry, rotating symmetry, or geometry. (DSK)
Steele, Carol Frederick
2011-01-01
In terms of teacher quality, Steele believes the best teachers have reached a stage she terms inspired, and that teachers move progressively through the stages of unaware, aware, and capable until the most reflective teachers finally reach the inspired level. Inspired teachers have a wide repertoire of teaching and class management techniques and…
Pardo-Montero, Juan; Fenwick, John D
2010-06-01
The purpose of this work is twofold: To further develop an approach to multiobjective optimization of rotational therapy treatments recently introduced by the authors [J. Pardo-Montero and J. D. Fenwick, "An approach to multiobjective optimization of rotational therapy," Med. Phys. 36, 3292-3303 (2009)], especially regarding its application to realistic geometries, and to study the quality (Pareto optimality) of plans obtained using such an approach by comparing them with Pareto optimal plans obtained through inverse planning. In the previous work of the authors, a methodology is proposed for constructing a large number of plans, with different compromises between the objectives involved, from a small number of geometrically based arcs, each arc prioritizing different objectives. Here, this method has been further developed and studied. Two different techniques for constructing these arcs are investigated, one based on image-reconstruction algorithms and the other based on more common gradient-descent algorithms. The difficulty of dealing with organs abutting the target, briefly reported in previous work of the authors, has been investigated using partial OAR unblocking. Optimality of the solutions has been investigated by comparison with a Pareto front obtained from inverse planning. A relative Euclidean distance has been used to measure the distance of these plans to the Pareto front, and dose volume histogram comparisons have been used to gauge the clinical impact of these distances. A prostate geometry has been used for the study. For geometries where a blocked OAR abuts the target, moderate OAR unblocking can substantially improve target dose distribution and minimize hot spots while not overly compromising dose sparing of the organ. Image-reconstruction type and gradient-descent blocked-arc computations generate similar results. The Pareto front for the prostate geometry, reconstructed using a large number of inverse plans, presents a hockey-stick shape
Stephens, Susanna L; Bittner, Dror M; Mikhailov, Victor A; Mizukami, Wataru; Tew, David P; Walker, Nicholas R; Legon, Anthony C
2014-10-06
The molecular geometries of isolated complexes in which a single molecule of C2H4 or C2H2 is bound to CuCl have been determined through pure rotational spectroscopy and ab-initio calculations. The C2H2···CuCl and C2H4···CuCl complexes are generated through laser vaporization of a copper rod in the presence of a gas sample undergoing supersonic expansion and containing C2H2 (or C2H4), CCl4, and Ar. Results are presented for five isotopologues of C2H2···CuCl and six isotopologues of C2H4···CuCl. Both of these complexes adopt C(2v), T-shaped geometries in which the hydrocarbon binds to the copper atom through its π electrons such that the metal is equidistant from all H atoms. The linear and planar geometries of free C2H2 and C2H4, respectively, are observed to distort significantly on attachment to the CuCl unit, and the various changes are quantified. The ∠(*-C-H) parameter in C2H2 (where * indicates the midpoint of the C≡C bond) is measured to be 192.4(7)° in the r0 geometry of the complex representing a significant change from the linear geometry of the free molecule. This distortion of the linear geometry of C2H2 involves the hydrogen atoms moving away from the copper atom within the complex. Ab-initio calculations at the CCSD(T)(F12*)/AVTZ level predict a dihedral ∠(HCCCu) angle of 96.05° in C2H4···CuCl, and the experimental results are consistent with such a distortion from planarity. The bonds connecting the carbon atoms within each of C2H2 and C2H4, respectively, extend by 0.027 and 0.029 Å relative to the bond lengths in the isolated molecules. Force constants, k(σ), and nuclear quadrupole coupling constants, χ(aa)(Cu), [χ(bb)(Cu) - χ(cc)(Cu)], χ(aa)(Cl), and [χ(bb)(Cl) - χ(cc)(Cl)], are independently determined for all isotopologues of C2H2···CuCl studied and for four isotopologues of C2H4···CuCl.
AUTHOR|(CDS)2266999
2017-01-01
CERN has been involved in the dissemination of scientific results since its early days and has continuously updated the distribution channels. Currently, Inspire hosts catalogues of articles, authors, institutions, conferences, jobs, experiments, journals and more. Successful orientation among this amount of data requires comprehensive linking between the content. Inspire has lacked a system for linking experiments and articles together based on which accelerator they were conducted at. The purpose of this project has been to create such a system. Records for 156 accelerators were created and all 2913 experiments on Inspire were given corresponding MARC tags. Records of 18404 accelerator physics related bibliographic entries were also tagged with corresponding accelerator tags. Finally, as a part of the endeavour to broaden CERN's presence on Wikipedia, existing Wikipedia articles of accelerators were updated with short descriptions and links to Inspire. In total, 86 Wikipedia articles were updated. This repo...
Spinning geometry = Twisted geometry
International Nuclear Information System (INIS)
Freidel, Laurent; Ziprick, Jonathan
2014-01-01
It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries are not continuous across the faces. Here we show that this phase space can also be represented by continuous, piecewise-flat three-geometries called spinning geometries. These are composed of metric-flat three-cells glued together consistently. The geometry of each cell and the manner in which they are glued is compatible with the choice of fluxes and holonomies. We first remark that the fluxes provide each edge with an angular momentum. By studying the piecewise-flat geometries which minimize edge lengths, we show that these angular momenta can be literally interpreted as the spin of the edges: the geometries of all edges are necessarily helices. We also show that the compatibility of the gluing maps with the holonomy data results in the same conclusion. This shows that a spinning geometry represents a way to glue together the three-cells of a twisted geometry to form a continuous geometry which represents a point in the loop gravity phase space. (paper)
Energy Technology Data Exchange (ETDEWEB)
Paidar, Moslem; Sarab, Mahsa Lali; Taheri, Morteza; Khodabandeh, Alireza [Islamic Azad University, Tehran (Iran, Islamic Republic of)
2015-11-15
The main purpose of this study was to investigate the effect of welding parameters on the failure mode and stir zone characteristics of aluminum alloy 2024-T3 joined by friction stir spot welding. The welding parameters in this work are tool rotational speed, plunge depths of shoulder, and pin geometry. In accordance with the methods of previous investigations, the rotational speeds were set to 630 rpm to 2000 rpm. Two pin geometries with concave shoulder were used: triangular and cylindrical. The plunge depths of the shoulder were 0.3, 0.5 and 0.7 mm. The shoulder diameter and pin height for both geometries were 14 and 2.4 mm, respectively. The diameter of the cylindrical and triangular pins was 5 mm. Results show that the parameters mentioned earlier influence fracture mode under tension shear loading. Two different fracture modes were observed during the examinations. Low-penetration depths and low-rotational speeds lead to shear fracture, whereas high values of these factors cause the tension-shear fracture mode. Fracture of the lower sheet sometimes occurs at high rotational speeds.
Transformational plane geometry
Umble, Ronald N
2014-01-01
Axioms of Euclidean Plane Geometry The Existence and Incidence Postulates The Distance and Ruler Postulates The Plane Separation Postulate The Protractor Postulate The Side-Angle-Side Postulate and the Euclidean Parallel Postulate Theorems of Euclidean Plane Geometry The Exterior Angle Theorem Triangle Congruence Theorems The Alternate Interior Angles Theorem and the Angle Sum Theorem Similar Triangles Introduction to Transformations, Isometries, and Similarities Transformations Isometries and SimilaritiesAppendix: Proof of Surjectivity Translations, Rotations, and Reflections Translations Rotations Reflections Appendix: Geometer's Sketchpad Commands Required by Exploratory Activities Compositions of Translations, Rotations, and Reflections The Three Points Theorem Rotations as Compositions of Two Reflections Translations as Compositions of Two Halfturns or Two Reflections The Angle Addition Theorem Glide Reflections Classification of Isometries The Fundamental Theorem and Congruence Classification of Isometr...
Visscher, F.; Schaaf, van der J.; Nijhuis, T.A.; Schouten, J.C.
2013-01-01
This review-perspective paper describes the current state-of-the-art in the field of rotating reactors. The paper has a focus on rotating reactor technology with applications at lab scale, pilot scale and industrial scale. Rotating reactors are classified and discussed according to their geometry:
Molecular motion in restricted geometries
Indian Academy of Sciences (India)
Molecular dynamics in restricted geometries is known to exhibit anomalous behaviour. Diffusion, translational or rotational, of molecules is altered significantly on confinement in restricted geometries. Quasielastic neutron scattering (QENS) offers a unique possibility of studying molecular motion in such systems. Both time ...
Iversen, Birger
1992-01-01
Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics
van den Broek, P.M.
1984-01-01
The aim of this paper is to give a detailed exposition of the relation between the geometry of twistor space and the geometry of Minkowski space. The paper has a didactical purpose; no use has been made of differential geometry and cohomology.
A nonsingular rotating black hole
International Nuclear Information System (INIS)
Ghosh, Sushant G.
2015-01-01
The spacetime singularities in classical general relativity are inevitable, as predicated by the celebrated singularity theorems. However, it is a general belief that singularities do not exist in Nature and that they are the limitations of the general relativity. In the absence of a welldefined quantum gravity, models of regular black holes have been studied. We employ a probability distribution inspired mass function m(r) to replace the Kerr black hole mass M to represent a nonsingular rotating black hole that is identified asymptotically (r >> k, k > 0 constant) exactly as the Kerr-Newman black hole, and as the Kerr black hole when k = 0. The radiating counterpart renders a nonsingular generalization of Carmeli's spacetime as well as Vaidya's spacetime, in the appropriate limits. The exponential correction factor changing the geometry of the classical black hole to remove the curvature singularity can also be motivated by quantum arguments. The regular rotating spacetime can also be understood as a black hole of general relativity coupled to nonlinear electrodynamics. (orig.)
Rodger, Alison
1995-01-01
Molecular Geometry discusses topics relevant to the arrangement of atoms. The book is comprised of seven chapters that tackle several areas of molecular geometry. Chapter 1 reviews the definition and determination of molecular geometry, while Chapter 2 discusses the unified view of stereochemistry and stereochemical changes. Chapter 3 covers the geometry of molecules of second row atoms, and Chapter 4 deals with the main group elements beyond the second row. The book also talks about the complexes of transition metals and f-block elements, and then covers the organometallic compounds and trans
Frydel, Derek; Rice, Stuart A
2007-12-01
We report a hydrodynamic analysis of the long-time behavior of the linear and angular velocity autocorrelation functions of an isolated colloid particle constrained to have quasi-two-dimensional motion, and compare the predicted behavior with the results of lattice-Boltzmann simulations. Our analysis uses the singularity method to characterize unsteady linear motion of an incompressible fluid. For bounded fluids we construct an image system with a discrete set of fundamental solutions of the Stokes equation from which we extract the long-time decay of the velocity. For the case that there are free slip boundary conditions at walls separated by H particle diameters, the time evolution of the parallel linear velocity and the perpendicular rotational velocity following impulsive excitation both correspond to the time evolution of a two-dimensional (2D) fluid with effective density rho_(2D)=rhoH. For the case that there are no slip boundary conditions at the walls, the same types of motion correspond to 2D fluid motions with a coefficient of friction xi=pi(2)nu/H(2) modulo a prefactor of order 1, with nu the kinematic viscosity. The linear particle motion perpendicular to the walls also experiences an effective frictional force, but the time dependence is proportional to t(-2) , which cannot be related to either pure 3D or pure 2D fluid motion. Our incompressible fluid model predicts correct self-diffusion constants but it does not capture all of the effects of the fluid confinement on the particle motion. In particular, the linear motion of a particle perpendicular to the walls is influenced by coupling between the density flux and the velocity field, which leads to damped velocity oscillations whose frequency is proportional to c_(s)/H , with c_(s) the velocity of sound. For particle motion parallel to no slip walls there is a slowing down of a density flux that spreads diffusively, which generates a long-time decay proportional to t(-1) .
International Nuclear Information System (INIS)
Robinson, I.; Trautman, A.
1988-01-01
The geometry of classical physics is Lorentzian; but weaker geometries are often more appropriate: null geodesics and electromagnetic fields, for example, are well known to be objects of conformal geometry. To deal with a single null congruence, or with the radiative electromagnetic fields associated with it, even less is needed: flag geometry for the first, optical geometry, with which this paper is chiefly concerned, for the second. The authors establish a natural one-to-one correspondence between optical geometries, considered locally, and three-dimensional Cauchy-Riemann structures. A number of Lorentzian geometries are shown to be equivalent from the optical point of view. For example the Goedel universe, the Taub-NUT metric and Hauser's twisting null solution have an optical geometry isomorphic to the one underlying the Robinson congruence in Minkowski space. The authors present general results on the problem of lifting a CR structure to a Lorentz manifold and, in particular, to Minkowski space; and exhibit the relevance of the deviation form to this problem
Photonic mesophases from cut rod rotators
Energy Technology Data Exchange (ETDEWEB)
Stelson, Angela C.; Liddell Watson, Chekesha M., E-mail: cml66@cornell.edu [Materials Science and Engineering, Cornell University, Ithaca, New York 14853 (United States); Avendano, Carlos [Chemical Engineering and Analytical Science, The University of Manchester, Manchester M13 9PL (United Kingdom)
2016-01-14
The photonic band properties of random rotator mesophases are calculated using supercell methods applied to cut rods on a hexagonal lattice. Inspired by the thermodynamic mesophase for anisotropic building blocks, we vary the shape factor of cut fraction for the randomly oriented basis. We find large, stable bandgaps with high gap isotropy in the inverted and direct structures as a function of cut fraction, dielectric contrast, and filling fraction. Bandgap sizes up to 34.5% are maximized at high dielectric contrast for rods separated in a matrix. The bandgaps open at dielectric contrasts as low as 2.0 for the transverse magnetic polarization and 2.25 for the transverse electric polarization. Additionally, the type of scattering that promotes the bandgap is correlated with the effect of disorder on bandgap size. Slow light properties are investigated in waveguide geometry and slowdown factors up to 5 × 10{sup 4} are found.
Pottmann, Helmut; Eigensatz, Michael; Vaxman, Amir; Wallner, Johannes
2014-01-01
Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.
Pottmann, Helmut
2014-11-26
Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.
Maor, Eli
2014-01-01
If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by acclaimed math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configur
Doutsi, Effrosyni; Fillatre, Lionel; Antonini, Marc; Gaulmin, Julien
2018-07-01
This paper introduces a novel filter, which is inspired by the human retina. The human retina consists of three different layers: the Outer Plexiform Layer (OPL), the inner plexiform layer, and the ganglionic layer. Our inspiration is the linear transform which takes place in the OPL and has been mathematically described by the neuroscientific model "virtual retina." This model is the cornerstone to derive the non-separable spatio-temporal OPL retina-inspired filter, briefly renamed retina-inspired filter, studied in this paper. This filter is connected to the dynamic behavior of the retina, which enables the retina to increase the sharpness of the visual stimulus during filtering before its transmission to the brain. We establish that this retina-inspired transform forms a group of spatio-temporal Weighted Difference of Gaussian (WDoG) filters when it is applied to a still image visible for a given time. We analyze the spatial frequency bandwidth of the retina-inspired filter with respect to time. It is shown that the WDoG spectrum varies from a lowpass filter to a bandpass filter. Therefore, while time increases, the retina-inspired filter enables to extract different kinds of information from the input image. Finally, we discuss the benefits of using the retina-inspired filter in image processing applications such as edge detection and compression.
Wagner, Tom
2010-01-01
The ceremonial copper and iron bells at the Smithsonian's National Museum of African Art were the author's inspiration for an interdisciplinary unit with a focus on the contributions various cultures make toward the richness of a community. The author of this article describes an Edo bell-inspired ceramic project incorporating slab-building…
DEFF Research Database (Denmark)
Vagnby, Bo
2008-01-01
Danish housing policy needs a dose of renewed social concern - and could find new inspiration in Britain's housing and urban planning policies, says Bo Vagnby. Udgivelsesdato: November......Danish housing policy needs a dose of renewed social concern - and could find new inspiration in Britain's housing and urban planning policies, says Bo Vagnby. Udgivelsesdato: November...
Kemnitz, Arnfried
Der Grundgedanke der Analytischen Geometrie besteht darin, dass geometrische Untersuchungen mit rechnerischen Mitteln geführt werden. Geometrische Objekte werden dabei durch Gleichungen beschrieben und mit algebraischen Methoden untersucht.
Lefschetz, Solomon
2005-01-01
An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.
Ay, Nihat; Lê, Hông Vân; Schwachhöfer, Lorenz
2017-01-01
The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, inf...
International Nuclear Information System (INIS)
Jonsson, Rickard; Westman, Hans
2006-01-01
We show that by employing the standard projected curvature as a measure of spatial curvature, we can make a certain generalization of optical geometry (Abramowicz M A and Lasota J-P 1997 Class. Quantum Grav. A 14 23-30). This generalization applies to any spacetime that admits a hypersurface orthogonal shearfree congruence of worldlines. This is a somewhat larger class of spacetimes than the conformally static spacetimes assumed in standard optical geometry. In the generalized optical geometry, which in the generic case is time dependent, photons move with unit speed along spatial geodesics and the sideways force experienced by a particle following a spatially straight line is independent of the velocity. Also gyroscopes moving along spatial geodesics do not precess (relative to the forward direction). Gyroscopes that follow a curved spatial trajectory precess according to a very simple law of three-rotation. We also present an inertial force formalism in coordinate representation for this generalization. Furthermore, we show that by employing a new sense of spatial curvature (Jonsson R 2006 Class. Quantum Grav. 23 1)) closely connected to Fermat's principle, we can make a more extensive generalization of optical geometry that applies to arbitrary spacetimes. In general this optical geometry will be time dependent, but still geodesic photons move with unit speed and follow lines that are spatially straight in the new sense. Also, the sideways experienced (comoving) force on a test particle following a line that is straight in the new sense will be independent of the velocity
Burdette, A C
1971-01-01
Analytic Geometry covers several fundamental aspects of analytic geometry needed for advanced subjects, including calculus.This book is composed of 12 chapters that review the principles, concepts, and analytic proofs of geometric theorems, families of lines, the normal equation of the line, and related matters. Other chapters highlight the application of graphing, foci, directrices, eccentricity, and conic-related topics. The remaining chapters deal with the concept polar and rectangular coordinates, surfaces and curves, and planes.This book will prove useful to undergraduate trigonometric st
Berger, Marcel
2010-01-01
Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces,
Robinson, Gilbert de B
2011-01-01
This brief undergraduate-level text by a prominent Cambridge-educated mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement for Gilbert de B. Robinson's text, which is the result of several years of teaching and learning the most effective methods from discussions with students. Topics include lines and planes, determinants and linear equations, matrices, groups and linear transformations, and vectors and vector spaces. Additional subjects range from conics and quadrics to homogeneous coordinates and projective geom
Connes, Alain
1994-01-01
This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.Key Features* First full treatment of the subject and its applications* Written by the pioneer of this field* Broad applications in mathemat
CERN Bulletin
2010-01-01
Particle physicists thrive on information. They first create information by performing experiments or elaborating theoretical conjectures and then they share it through publications and various web tools. The INSPIRE service, just released, will bring state of the art information retrieval to the fingertips of researchers. Keeping track of the information shared within the particle physics community has long been the task of libraries at the larger labs, such as CERN, DESY, Fermilab and SLAC, as well as the focus of indispensible services like arXiv and those of the Particle Data Group. In 2007, many providers of information in the field came together for a summit at SLAC to see how physics information resources could be enhanced, and the INSPIRE project emerged from that meeting. The vision behind INSPIRE was built by a survey launched by the four labs to evaluate the real needs of the community. INSPIRE responds to these directives from the community by combining the most successful aspe...
Câmara, Daniel
2015-01-01
Bio-inspired techniques are based on principles, or models, of biological systems. In general, natural systems present remarkable capabilities of resilience and adaptability. In this book, we explore how bio-inspired methods can solve different problems linked to computer networks. Future networks are expected to be autonomous, scalable and adaptive. During millions of years of evolution, nature has developed a number of different systems that present these and other characteristics required for the next generation networks. Indeed, a series of bio-inspired methods have been successfully used to solve the most diverse problems linked to computer networks. This book presents some of these techniques from a theoretical and practical point of view. Discusses the key concepts of bio-inspired networking to aid you in finding efficient networking solutions Delivers examples of techniques both in theoretical concepts and practical applications Helps you apply nature's dynamic resource and task management to your co...
Indian Academy of Sciences (India)
mathematicians are trained to use very precise language, and so find it hard to simplify and state .... thing. If you take a plane on which there are two such triangles which enjoy the above ... within this geometry to simplify things if needed.
Geometry -----------~--------------RESONANCE
Indian Academy of Sciences (India)
Parallel: A pair of lines in a plane is said to be parallel if they do not meet. Mathematicians were at war ... Subsequently, Poincare, Klein, Beltrami and others refined non-. Euclidean geometry. ... plane divides the plane into two half planes and.
Variable geometry Darrieus wind machine
Pytlinski, J. T.; Serrano, D.
1983-08-01
A variable geometry Darrieus wind machine is proposed. The lower attachment of the blades to the rotor can move freely up and down the axle allowing the blades of change shape during rotation. Experimental data for a 17 m. diameter Darrieus rotor and a theoretical model for multiple streamtube performance prediction were used to develop a computer simulation program for studying parameters that affect the machine's performance. This new variable geometry concept is described and interrelated with multiple streamtube theory through aerodynamic parameters. The computer simulation study shows that governor behavior of a Darrieus turbine can not be attained by a standard turbine operating within normally occurring rotational velocity limits. A second generation variable geometry Darrieus wind turbine which uses a telescopic blade is proposed as a potential improvement on the studied concept.
Petersen, Peter
2016-01-01
Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups. Important revisions to the third edition include: a substantial addition of unique and enriching exercises scattered throughout the text; inclusion of an increased number of coordinate calculations of connection and curvature; addition of general formulas for curvature on Lie Groups and submersions; integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger; incorporation of several recent results about manifolds with posit...
International Nuclear Information System (INIS)
Strominger, A.
1990-01-01
A special manifold is an allowed target manifold for the vector multiplets of D=4, N=2 supergravity. These manifolds are of interest for string theory because the moduli spaces of Calabi-Yau threefolds and c=9, (2,2) conformal field theories are special. Previous work has given a local, coordinate-dependent characterization of special geometry. A global description of special geometries is given herein, and their properties are studied. A special manifold M of complex dimension n is characterized by the existence of a holomorphic Sp(2n+2,R)xGL(1,C) vector bundle over M with a nowhere-vanishing holomorphic section Ω. The Kaehler potential on M is the logarithm of the Sp(2n+2,R) invariant norm of Ω. (orig.)
General Geometry and Geometry of Electromagnetism
Shahverdiyev, Shervgi S.
2002-01-01
It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is geometry underlying Electromagnetism. Action for electromagnetic field and Maxwell equations are derived from curvature function of geometry underlying Electromagnetism. And it is shown that equation of motion for a particle interacting with electromagnetic...
Ciarlet, Philippe G
2007-01-01
This book gives the basic notions of differential geometry, such as the metric tensor, the Riemann curvature tensor, the fundamental forms of a surface, covariant derivatives, and the fundamental theorem of surface theory in a selfcontained and accessible manner. Although the field is often considered a classical one, it has recently been rejuvenated, thanks to the manifold applications where it plays an essential role. The book presents some important applications to shells, such as the theory of linearly and nonlinearly elastic shells, the implementation of numerical methods for shells, and
Inspirations in medical genetics.
Asadollahi, Reza
2016-02-01
There are abundant instances in the history of genetics and medical genetics to illustrate how curiosity, charisma of mentors, nature, art, the saving of lives and many other matters have inspired great discoveries. These achievements from deciphering genetic concepts to characterizing genetic disorders have been crucial for management of the patients. There remains, however, a long pathway ahead. © The Author(s) 2014.
Tank, Kristina; Moore, Tamara; Strnat, Meg
2015-01-01
This article describes the final lesson within a seven-day STEM and literacy unit that is part of the Picture STEM curriculum (pictureSTEM. org) and uses engineering to integrate science and mathematics learning in a meaningful way (Tank and Moore 2013). For this engineering challenge, students used nature as a source of inspiration for designs to…
Rice, Nicole
2012-01-01
The house paintings of the South African Ndebele people are more than just an attempt to improve the aesthetics of a community; they are a source of identity and significance for Ndebele women. In this article, the author describes an art project wherein students use the tradition of Ndebele house painting as inspiration for creating their own…
Wormholes immersed in rotating matter
Directory of Open Access Journals (Sweden)
Christian Hoffmann
2018-03-01
Full Text Available We demonstrate that rotating matter sets the throat of an Ellis wormhole into rotation, allowing for wormholes which possess full reflection symmetry with respect to the two asymptotically flat spacetime regions. We analyze the properties of this new type of rotating wormholes and show that the wormhole geometry can change from a single throat to a double throat configuration. We further discuss the ergoregions and the lightring structure of these wormholes.
Data specifications for INSPIRE
Portele, Clemens; Woolf, Andrew; Cox, Simon
2010-05-01
In Europe a major recent development has been the entering in force of the INSPIRE Directive in May 2007, establishing an infrastructure for spatial information in Europe to support Community environmental policies, and policies or activities which may have an impact on the environment. INSPIRE is based on the infrastructures for spatial information established and operated by the 27 Member States of the European Union. The Directive addresses 34 spatial data themes needed for environmental applications, with key components specified through technical implementing rules. This makes INSPIRE a unique example of a legislative "regional" approach. One of the requirements of the INSPIRE Directive is to make existing spatial data sets with relevance for one of the spatial data themes available in an interoperable way, i.e. where the spatial data from different sources in Europe can be combined to a coherent result. Since INSPIRE covers a wide range of spatial data themes, the first step has been the development of a modelling framework that provides a common foundation for all themes. This framework is largely based on the ISO 19100 series of standards. The use of common generic spatial modelling concepts across all themes is an important enabler for interoperability. As a second step, data specifications for the first set of themes has been developed based on the modelling framework. The themes include addresses, transport networks, protected sites, hydrography, administrative areas and others. The data specifications were developed by selected experts nominated by stakeholders from all over Europe. For each theme a working group was established in early 2008 working on their specific theme and collaborating with the other working groups on cross-theme issues. After a public review of the draft specifications starting in December 2008, an open testing process and thorough comment resolution process, the draft technical implementing rules for these themes have been
2012-01-01
The motto of the 2012 Olympic and Paralympic Games is ‘Inspire a generation’ so it was particularly pleasing to see science, the LHC and Higgs bosons featuring so strongly in the opening ceremony of the Paralympics last week. It’s a sign of just how far our field has come that such a high-profile event featured particle physics so strongly, and we can certainly add our support to that motto. If the legacy of London 2012 is a generation inspired by science as well as sport, then the games will have more than fulfilled their mission. Particle physics has truly inspiring stories to tell, going well beyond Higgs and the LHC, and the entire community has played its part in bringing the excitement of frontier research in particle physics to a wide audience. Nevertheless, we cannot rest on our laurels: maintaining the kind of enthusiasm for science we witnessed at the Paralympic opening ceremony will require constant vigilance, and creative thinking about ways to rea...
Perceptually-Inspired Computing
Directory of Open Access Journals (Sweden)
Ming Lin
2015-08-01
Full Text Available Human sensory systems allow individuals to see, hear, touch, and interact with the surrounding physical environment. Understanding human perception and its limit enables us to better exploit the psychophysics of human perceptual systems to design more efficient, adaptive algorithms and develop perceptually-inspired computational models. In this talk, I will survey some of recent efforts on perceptually-inspired computing with applications to crowd simulation and multimodal interaction. In particular, I will present data-driven personality modeling based on the results of user studies, example-guided physics-based sound synthesis using auditory perception, as well as perceptually-inspired simplification for multimodal interaction. These perceptually guided principles can be used to accelerating multi-modal interaction and visual computing, thereby creating more natural human-computer interaction and providing more immersive experiences. I will also present their use in interactive applications for entertainment, such as video games, computer animation, and shared social experience. I will conclude by discussing possible future research directions.
Dayside merging and cusp geometry
International Nuclear Information System (INIS)
Crooker, N.U.
1979-01-01
Geometrical considerations are presented to show that dayside magnetic merging when constrained to act only where the fields are antiparallel results in lines of merging that converge at the polar cusps. An important consequence of this geometry is that no accelerated flows are predicted across the dayside magnetopause. Acceleration owing to merging acts in opposition to the magnetosheath flow at the merging point and produces the variably directed, slower-than-magnetosheath flows observed in the entry layer. Another consequence of the merging geometry is that much of the time closed field lines constitute the subsolar region of the magnetopause. The manner in which the polar cap convection patterns predicted by the proposed geometry change as the interplanetary field is rotated through 360 0 provides a unifying description of how the observed single circular vortex and the crescent-shaped double vortex patterns mutually evolve under the influence of a single operating principle
International Nuclear Information System (INIS)
Ambruş, Victor E.; Winstanley, Elizabeth
2014-01-01
We revisit the definition of rotating thermal states for scalar and fermion fields in unbounded Minkowski space–time. For scalar fields such states are ill-defined everywhere, but for fermion fields an appropriate definition of the vacuum gives thermal states regular inside the speed-of-light surface. For a massless fermion field, we derive analytic expressions for the thermal expectation values of the fermion current and stress–energy tensor. These expressions may provide qualitative insights into the behaviour of thermal rotating states on more complex space–time geometries
DEFF Research Database (Denmark)
Meier, Ninna
2016-01-01
What academics or books have inspired you in your writing and research, or helped to make sense of the world around you? In this feature essay, Ninna Meier returns to her experience of reading Hannah Arendt as she sought to understand work and how it relates to value production in capitalist...... economies. Meier recounts how Arendt’s book On Revolution (1963) forged connective threads between the ‘smallest parts’ and the ‘largest wholes’ and showed how academic work is never fully relegated to the past, but can return in new iterations across time....
Childs, Peter R N
2010-01-01
Rotating flow is critically important across a wide range of scientific, engineering and product applications, providing design and modeling capability for diverse products such as jet engines, pumps and vacuum cleaners, as well as geophysical flows. Developed over the course of 20 years' research into rotating fluids and associated heat transfer at the University of Sussex Thermo-Fluid Mechanics Research Centre (TFMRC), Rotating Flow is an indispensable reference and resource for all those working within the gas turbine and rotating machinery industries. Traditional fluid and flow dynamics titles offer the essential background but generally include very sparse coverage of rotating flows-which is where this book comes in. Beginning with an accessible introduction to rotating flow, recognized expert Peter Childs takes you through fundamental equations, vorticity and vortices, rotating disc flow, flow around rotating cylinders and flow in rotating cavities, with an introduction to atmospheric and oceanic circul...
Lee, William H K.
2016-01-01
Rotational seismology is an emerging study of all aspects of rotational motions induced by earthquakes, explosions, and ambient vibrations. It is of interest to several disciplines, including seismology, earthquake engineering, geodesy, and earth-based detection of Einstein’s gravitation waves.Rotational effects of seismic waves, together with rotations caused by soil–structure interaction, have been observed for centuries (e.g., rotated chimneys, monuments, and tombstones). Figure 1a shows the rotated monument to George Inglis observed after the 1897 Great Shillong earthquake. This monument had the form of an obelisk rising over 19 metres high from a 4 metre base. During the earthquake, the top part broke off and the remnant of some 6 metres rotated about 15° relative to the base. The study of rotational seismology began only recently when sensitive rotational sensors became available due to advances in aeronautical and astronomical instrumentations.
Combining Bio-inspired Sensing with Bio-inspired Locomotion
DEFF Research Database (Denmark)
Shaikh, Danish; Hallam, John; Christensen-Dalsgaard, Jakob
In this paper we present a preliminary Braitenberg vehicle–like approach to combine bio-inspired audition with bio-inspired quadruped locomotion in simulation. Locomotion gaits of the salamander–like robot Salamandra robotica are modified by a lizard’s peripheral auditory system model that modula......In this paper we present a preliminary Braitenberg vehicle–like approach to combine bio-inspired audition with bio-inspired quadruped locomotion in simulation. Locomotion gaits of the salamander–like robot Salamandra robotica are modified by a lizard’s peripheral auditory system model...
Anaïs Vernède
2011-01-01
On Tuesday 18 January 2011, artist Pipilotti Rist came to CERN to find out how science could provide her with a source of inspiration for her art and perhaps to get ideas for future work. Pipilotti, who is an eclectic artist always on the lookout for an original source of inspiration, is almost as passionate about physics as she is about art. Ever Is Over All, 1997, audio video installation by Pipilotti Rist. View of the installation at the National Museum for Foreign Art, Sofia, Bulgaria. © Pipilotti Rist. Courtesy the artist and Hauser & Wirth. Photo by Angel Tzvetanov. Swiss video-maker Pipilotti Rist (her real name is Elisabeth Charlotte Rist), who is well-known in the international art world for her highly colourful videos and creations, visited CERN for the first time on Tuesday 18 January 2011. Her visit represented a trip down memory lane, since she originally studied physics before becoming interested in pursuing a career as an artist and going on to de...
Silva, Alessandro
1993-01-01
The papers in this wide-ranging collection report on the results of investigations from a number of linked disciplines, including complex algebraic geometry, complex analytic geometry of manifolds and spaces, and complex differential geometry.
Eisenhart, Luther Pfahler
2005-01-01
This concise text by a prominent mathematician deals chiefly with manifolds dominated by the geometry of paths. Topics include asymmetric and symmetric connections, the projective geometry of paths, and the geometry of sub-spaces. 1927 edition.
International Nuclear Information System (INIS)
Gurevich, L.Eh.; Gliner, Eh.B.
1978-01-01
Problems of investigating the Universe space-time geometry are described on a popular level. Immediate space-time geometries, corresponding to three cosmologic models are considered. Space-time geometry of a closed model is the spherical Riemann geonetry, of an open model - is the Lobachevskij geometry; and of a plane model - is the Euclidean geometry. The Universe real geometry in the contemporary epoch of development is based on the data testifying to the fact that the Universe is infinitely expanding
KEMAJUAN BELAJAR SISWA PADA GEOMETRI TRANSFORMASI MENGGUNAKAN AKTIVITAS REFLEKSI GEOMETRI
Directory of Open Access Journals (Sweden)
Irkham Ulil Albab
2014-10-01
, observations, and field notes. The findings of the study showed that this instructional design could stimulate students to provide reflection characteristics and other transformation geometry informally, to classify them in the transformation isometry in the second level, and to find the reflection supporting line in the more formal level. In addition, the reflection supporting line was used by the students to draw the reflection image and the mirroring pattern and to understand the rotation and translation shapes as a combination of reflection at the highest level. Keyword: geometric transformation, rotation, translation, and HLT
International Nuclear Information System (INIS)
Rosquist, K.
1980-01-01
Global rotation in cosmological models is defined on an observational basis. A theorem is proved saying that, for rigid motion, the global rotation is equal to the ordinary local vorticity. The global rotation is calculated in the space-time homogeneous class III models, with Godel's model as a special case. It is shown that, with the exception of Godel's model, the rotation in these models becomes infinite for finite affine parameter values. In some directions the rotation changes sign and becomes infinite in a direction opposite to the local vorticity. The points of infinite rotation are identified as conjugate points along the null geodesics. The physical interpretation of the infinite rotation is discussed, and a comparison with the behaviour of the area distance at conjugate points is given. (author)
Time-dependent, Bianchi II, rotating universe
International Nuclear Information System (INIS)
Reboucas, M.J.
1981-01-01
An exact cosmological solution of Einstein's equations which has time-dependent rotation is presented. The t-constant sections are of Bianchi type II. The source of this geometry is a fluid which has not been thermalized. (Author) [pt
Microflyers: inspiration from nature
Sirohi, Jayant
2013-04-01
Over the past decade, there has been considerable interest in miniaturizing aircraft to create a class of extremely small, robotic vehicles with a gross mass on the order of tens of grams and a dimension on the order of tens of centimeters. These are collectively refered to as micro aerial vehicles (MAVs) or microflyers. Because the size of microflyers is on the same order as that of small birds and large insects, engineers are turning to nature for inspiration. Bioinspired concepts make use of structural or aerodynamic mechanisms that are observed in insects and birds, such as elastic energy storage and unsteady aerodynamics. Biomimetic concepts attempt to replicate the form and function of natural flyers, such as flapping-wing propulsion and external appearance. This paper reviews recent developments in the area of man-made microflyers. The design space for microflyers will be described, along with fundamental physical limits to miniaturization. Key aerodynamic phenomena at the scale of microflyers will be highlighted. Because the focus is on bioinspiration and biomimetics, scaled-down versions of conventional aircraft, such as fixed wing micro air vehicles and microhelicopters will not be addressed. A few representative bioinspired and biomimetic microflyer concepts developed by researchers will be described in detail. Finally, some of the sensing mechanisms used by natural flyers that are being implemented in man-made microflyers will be discussed.
Inspiration, anyone? (Editorial
Directory of Open Access Journals (Sweden)
Lindsay Glynn
2006-09-01
Full Text Available I have to admit that writing an editorial for this issue was a struggle. Trying to sit down and write when the sun was shining outside and most of my colleagues were on vacation was, to say the least, difficult. Add to that research projects and conferences…let’s just say that I found myself less than inspired. A pitiful plea for ideas to a colleague resulted in the reintroduction to a few recent evidence based papers and resources which inspired further searching and reading. Though I generally find myself surrounded (more like buried in research papers and EBLIP literature, somehow I had missed the great strides that have been made of late in the world of evidence based library and information practice. I realize now that I am inspired by the researchers, authors and innovators who are putting EBLIP on the proverbial map. My biggest beef with library literature in general has been the plethora of articles highlighting what we should be doing. Take a close look at the evidence based practitioners in the information professions: these are some of the people who are actively practicing what has been preached for the past few years. Take, for example, the about‐to‐be released Libraries using Evidence Toolkit by Northern Sydney Central Coast Health and The University of Newcastle, Australia (see their announcement in this issue. An impressive advisory group is responsible for maintaining the currency and relevancy of the site as well as promoting the site and acting as a steering committee for related projects. This group is certainly doing more than “talking the talk”: they took their experience at the 3rd International Evidence Based Librarianship Conference and did something with the information they obtained by implementing solutions that worked in their environment. The result? The creation of a collection of tools for all of us to use. This toolkit is just what EBLIP needs: a portal to resources aimed at supporting the information
2004-01-01
Art students inspired by CERN will be returning to show their work 9 to 16 October in Building 500, outside the Auditorium. Seventeen art students from around Europe visited CERN last January for a week of introductions to particle physics and astrophysics, and discussions with CERN scientists about their projects. A CERN scientist "adopted"each artist so they could ask questions during and after the visit. Now the seeds planted during their visit have come to fruition in a show using many media and exploring varied concepts, such as how people experience the online world, the sheer scale of CERN's equipment, and the abstractness of the entities scientists are looking for. "The work is so varied, people are going to love some pieces and detest others," says Andrew Charalambous, the project coordinator from University College London who is also curating the exhibition. "It's contemporary modern art, and that's sometimes difficult to take in." For more information on this thought-provoking show, see: htt...
International Nuclear Information System (INIS)
Posch, C
2012-01-01
Nature still outperforms the most powerful computers in routine functions involving perception, sensing and actuation like vision, audition, and motion control, and is, most strikingly, orders of magnitude more energy-efficient than its artificial competitors. The reasons for the superior performance of biological systems are subject to diverse investigations, but it is clear that the form of hardware and the style of computation in nervous systems are fundamentally different from what is used in artificial synchronous information processing systems. Very generally speaking, biological neural systems rely on a large number of relatively simple, slow and unreliable processing elements and obtain performance and robustness from a massively parallel principle of operation and a high level of redundancy where the failure of single elements usually does not induce any observable system performance degradation. In the late 1980's, Carver Mead demonstrated that silicon VLSI technology can be employed in implementing ''neuromorphic'' circuits that mimic neural functions and fabricating building blocks that work like their biological role models. Neuromorphic systems, as the biological systems they model, are adaptive, fault-tolerant and scalable, and process information using energy-efficient, asynchronous, event-driven methods. In this paper, some basics of neuromorphic electronic engineering and its impact on recent developments in optical sensing and artificial vision are presented. It is demonstrated that bio-inspired vision systems have the potential to outperform conventional, frame-based vision acquisition and processing systems in many application fields and to establish new benchmarks in terms of redundancy suppression/data compression, dynamic range, temporal resolution and power efficiency to realize advanced functionality like 3D vision, object tracking, motor control, visual feedback loops, etc. in real-time. It is argued that future artificial vision systems
Lekner, John
2008-01-01
Any free-particle wavepacket solution of Schrodinger's equation can be converted by differentiations to wavepackets rotating about the original direction of motion. The angular momentum component along the motion associated with this rotation is an integral multiple of [h-bar]. It is an "intrinsic" angular momentum: independent of origin and…
International Nuclear Information System (INIS)
Noe, C.
1984-01-01
Products to dry are introduced inside a rotating tube placed in an oven, the cross section of the tube is an arc of spiral. During clockwise rotation of the tube products are maintained inside and mixed, during anticlockwise products are removed. Application is made to drying of radioactive wastes [fr
Nature-inspired optimization algorithms
Yang, Xin-She
2014-01-01
Nature-Inspired Optimization Algorithms provides a systematic introduction to all major nature-inspired algorithms for optimization. The book's unified approach, balancing algorithm introduction, theoretical background and practical implementation, complements extensive literature with well-chosen case studies to illustrate how these algorithms work. Topics include particle swarm optimization, ant and bee algorithms, simulated annealing, cuckoo search, firefly algorithm, bat algorithm, flower algorithm, harmony search, algorithm analysis, constraint handling, hybrid methods, parameter tuning
Fenyvesi, Kristof; Houghton, Tony; Diego-Mantecón, José Manuel; Crilly, Elizabeth; Oldknow, Adrian; Lavicza, Zsolt; Blanco, Teresa F.
2017-01-01
Abstract The goal of the Kids Inspiring Kids in STEAM (KIKS) project was to raise students' awareness towards the multi- and transdisciplinary connections between the STEAM subjects (Science, Technology, Engineering, Arts & Mathematics), and make the learning about topics and phenomena from these fields more enjoyable. In order to achieve these goals, KIKS project has popularized the STEAM-concept by projects based on the students inspiring other students-approach and by utilizing new tec...
Smart Nacre-inspired Nanocomposites.
Peng, Jingsong; Cheng, Qunfeng
2018-03-15
Nacre-inspired nanocomposites with excellent mechanical properties have achieved remarkable attention in the past decades. The high performance of nacre-inspired nanocomposites is a good basis for the further application of smart devices. Recently, some smart nanocomposites inspired by nacre have demonstrated good mechanical properties as well as effective and stable stimuli-responsive functions. In this Concept, we summarize the recent development of smart nacre-inspired nanocomposites, including 1D fibers, 2D films and 3D bulk nanocomposites, in response to temperature, moisture, light, strain, and so on. We show that diverse smart nanocomposites could be designed by combining various conventional fabrication methods of nacre-inspired nanocomposites with responsive building blocks and interface interactions. The nacre-inspired strategy is versatile for different kinds of smart nanocomposites in extensive applications, such as strain sensors, displays, artificial muscles, robotics, and so on, and may act as an effective roadmap for designing smart nanocomposites in the future. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Detection strategies for extreme mass ratio inspirals
International Nuclear Information System (INIS)
Cornish, Neil J
2011-01-01
The capture of compact stellar remnants by galactic black holes provides a unique laboratory for exploring the near-horizon geometry of the Kerr spacetime, or possible departures from general relativity if the central cores prove not to be black holes. The gravitational radiation produced by these extreme mass ratio inspirals (EMRIs) encodes a detailed map of the black hole geometry, and the detection and characterization of these signals is a major scientific goal for the LISA mission. The waveforms produced are very complex, and the signals need to be coherently tracked for tens of thousands of cycles to produce a detection, making EMRI signals one of the most challenging data analysis problems in all of gravitational wave astronomy. Estimates for the number of templates required to perform an exhaustive grid-based matched-filter search for these signals are astronomically large, and far out of reach of current computational resources. Here I describe an alternative approach that employs a hybrid between genetic algorithms and Markov chain Monte Carlo techniques, along with several time-saving techniques for computing the likelihood function. This approach has proven effective at the blind extraction of relatively weak EMRI signals from simulated LISA data sets.
Meyer, Walter J
2006-01-01
Meyer''s Geometry and Its Applications, Second Edition, combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes in many chapters. The Second Edition of Geometry and Its Applications is a significant text for any college or university that focuses on geometry''s usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers.* Realistic applications integrated throughout the text, including (but not limited to): - Symmetries of artistic patterns- Physics- Robotics- Computer vision- Computer graphics- Stability of architectural structures- Molecular biology- Medicine- Pattern recognition* Historical notes included in many chapters...
Indian Academy of Sciences (India)
algebraic geometry but also in related fields like number theory. ... every vector bundle on the affine space is trivial. (equivalently ... les on a compact Riemann surface to unitary rep- ... tial geometry and topology and was generalised in.
International Nuclear Information System (INIS)
Sloane, Peter
2007-01-01
We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)
Energy Technology Data Exchange (ETDEWEB)
Sloane, Peter [Department of Mathematics, King' s College, University of London, Strand, London WC2R 2LS (United Kingdom)
2007-09-15
We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)
Physicists Get INSPIREd: INSPIRE Project and Grid Applications
International Nuclear Information System (INIS)
Klem, Jukka; Iwaszkiewicz, Jan
2011-01-01
INSPIRE is the new high-energy physics scientific information system developed by CERN, DESY, Fermilab and SLAC. INSPIRE combines the curated and trusted contents of SPIRES database with Invenio digital library technology. INSPIRE contains the entire HEP literature with about one million records and in addition to becoming the reference HEP scientific information platform, it aims to provide new kinds of data mining services and metrics to assess the impact of articles and authors. Grid and cloud computing provide new opportunities to offer better services in areas that require large CPU and storage resources including document Optical Character Recognition (OCR) processing, full-text indexing of articles and improved metrics. D4Science-II is a European project that develops and operates an e-Infrastructure supporting Virtual Research Environments (VREs). It develops an enabling technology (gCube) which implements a mechanism for facilitating the interoperation of its e-Infrastructure with other autonomously running data e-Infrastructures. As a result, this creates the core of an e-Infrastructure ecosystem. INSPIRE is one of the e-Infrastructures participating in D4Science-II project. In the context of the D4Science-II project, the INSPIRE e-Infrastructure makes available some of its resources and services to other members of the resulting ecosystem. Moreover, it benefits from the ecosystem via a dedicated Virtual Organization giving access to an array of resources ranging from computing and storage resources of grid infrastructures to data and services.
Geometry Design, Principles and Assembly of Micromotors
Directory of Open Access Journals (Sweden)
Huanpo Ning
2018-02-01
Full Text Available Discovery of bio-inspired, self-propelled and externally-powered nano-/micro-motors, rotors and engines (micromachines is considered a potentially revolutionary paradigm in nanoscience. Nature knows how to combine different elements together in a fluidic state for intelligent design of nano-/micro-machines, which operate by pumping, stirring, and diffusion of their internal components. Taking inspirations from nature, scientists endeavor to develop the best materials, geometries, and conditions for self-propelled motion, and to better understand their mechanisms of motion and interactions. Today, microfluidic technology offers considerable advantages for the next generation of biomimetic particles, droplets and capsules. This review summarizes recent achievements in the field of nano-/micromotors, and methods of their external control and collective behaviors, which may stimulate new ideas for a broad range of applications.
LHC Phenomenology and Cosmology of String-Inspired Intersecting D-Brane Models
Anchordoqui, Luis A.; Goldberg, Haim; Huang, Xing; Lust, Dieter; Taylor, Tomasz R.; Vlcek, Brian
2012-01-01
We discuss the phenomenology and cosmology of a Standard-like Model inspired by string theory, in which the gauge fields are localized on D-branes wrapping certain compact cycles on an underlying geometry, whose intersection can give rise to chiral fermions. The energy scale associated with string physics is assumed to be near the Planck mass. To develop our program in the simplest way, we work within the construct of a minimal model with gauge-extended sector U (3)_B \\times Sp (1)_L \\times U (1)_{I_R} \\times U (1)_L. The resulting U (1) content gauges the baryon number B, the lepton number L, and a third additional abelian charge I_R which acts as the third isospin component of an SU(2)_R. All mixing angles and gauge couplings are fixed by rotation of the U(1) gauge fields to a basis diagonal in hypercharge Y and in an anomaly free linear combination of I_R and B-L. The anomalous $Z'$ gauge boson obtains a string scale St\\"uckelberg mass via a 4D version of the Green-Schwarz mechanism. To keep the realizatio...
Geometry essentials for dummies
Ryan, Mark
2011-01-01
Just the critical concepts you need to score high in geometry This practical, friendly guide focuses on critical concepts taught in a typical geometry course, from the properties of triangles, parallelograms, circles, and cylinders, to the skills and strategies you need to write geometry proofs. Geometry Essentials For Dummies is perfect for cramming or doing homework, or as a reference for parents helping kids study for exams. Get down to the basics - get a handle on the basics of geometry, from lines, segments, and angles, to vertices, altitudes, and diagonals Conque
Arithmetic noncommutative geometry
Marcolli, Matilde
2005-01-01
Arithmetic noncommutative geometry denotes the use of ideas and tools from the field of noncommutative geometry, to address questions and reinterpret in a new perspective results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at archimedean places of arithmetic surfaces and varieties. The main reason why noncommutative geometry can be expected to say something about topics of arithmetic interest lies in the fact that it provides the right framework in which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry, such as moduli spaces (of which modular curves are the simplest case) or arithmetic varieties (completed by suitable "fibers at infinity"), by adding boundaries...
Centrifugal particle confinement in mirror geometry
White, Roscoe; Hassam, Adil; Brizard, Alain
2018-01-01
The use of supersonic rotation of a plasma in mirror geometry has distinct advantages for thermonuclear fusion. The device is steady state, there are no disruptions, the loss cone is almost closed, sheared rotation stabilizes magnetohydrodynamic instabilities as well as plasma turbulence, there are no runaway electrons, and the coil configuration is simple. In this work, we examine the effect of rotation on mirror confinement using a full cyclotron orbit code. The full cyclotron simulations give a much more complete description of the particle energy distribution and losses than the use of guiding center equations. Both collisionless loss as a function of rotation and the effect of collisions are investigated. Although the cross field diffusion is classical, we find that the local rotating Maxwellian is increased to higher energy, increasing the fusion rate and also enhancing the radial diffusion. We find a loss channel not envisioned with a guiding center treatment, but a design can be chosen that can satisfy the Lawson criterion for ions. Of course, the rotation has a minimal effect on the alpha particle birth distribution, so there is initially loss through the usual loss cone, just as in a mirror with no rotation. However after this loss, the alphas slow down on the electrons with little pitch angle scattering until reaching low energy, so over half of the initial alpha energy is transferred to the electrons. The important problem of energy confinement, with losses primarily through the electron channel, is not addressed in this work. We also discuss the use of rotating mirror geometry to produce an ion thruster.
Paradigms for biologically inspired design
DEFF Research Database (Denmark)
Lenau, T. A.; Metzea, A.-L.; Hesselberg, T.
2018-01-01
engineering, medical engineering, nanotechnology, photonics,environmental protection and agriculture. However, a major obstacle for the wider use of biologically inspired design isthe knowledge barrier that exist between the application engineers that have insight into how to design suitable productsand......Biologically inspired design is attracting increasing interest since it offers access to a huge biological repository of wellproven design principles that can be used for developing new and innovative products. Biological phenomena can inspireproduct innovation in as diverse areas as mechanical...... the biologists with detailed knowledge and experience in understanding how biological organisms function in theirenvironment. The biologically inspired design process can therefore be approached using different design paradigmsdepending on the dominant opportunities, challenges and knowledge characteristics...
DEFF Research Database (Denmark)
Ejersbo, Lisser Rye
2015-01-01
NY-times har en ugentlig klumme med gode råd. For nogle uger siden var ugens inspiration henvendt til lærere/undervisere og drejede sig om, hvordan man skaber taletid til alle uden at have favoritter og overse de mere stille elever.......NY-times har en ugentlig klumme med gode råd. For nogle uger siden var ugens inspiration henvendt til lærere/undervisere og drejede sig om, hvordan man skaber taletid til alle uden at have favoritter og overse de mere stille elever....
Geometry and light the science of invisibility
Leonhardt, Ulf
2010-01-01
The science of invisibility combines two of physics' greatest concepts: Einstein's general relativity and Maxwell's principles of electromagnetism. Recent years have witnessed major breakthroughs in the area, and the authors of this volume - Ulf Leonhardt and Thomas Philbin of Scotland's University of St. Andrews - have been active in the transformation of invisibility from fiction into science. Their work on designing invisibility devices is based on modern metamaterials, inspired by Fermat's principle, analogies between mechanics and optics, and the geometry of curved space. Suitable for gra
Grasso, Frank W; Setlur, Pradeep
2007-12-01
Octopus arms house 200-300 independently controlled suckers that can alternately afford an octopus fine manipulation of small objects and produce high adhesion forces on virtually any non-porous surface. Octopuses use their suckers to grasp, rotate and reposition soft objects (e.g., octopus eggs) without damaging them and to provide strong, reversible adhesion forces to anchor the octopus to hard substrates (e.g., rock) during wave surge. The biological 'design' of the sucker system is understood to be divided anatomically into three functional groups: the infundibulum that produces a surface seal that conforms to arbitrary surface geometry; the acetabulum that generates negative pressures for adhesion; and the extrinsic muscles that allow adhered surfaces to be rotated relative to the arm. The effector underlying these abilities is the muscular hydrostat. Guided by sensory input, the thousands of muscle fibers within the muscular hydrostats of the sucker act in coordination to provide stiffness or force when and where needed. The mechanical malleability of octopus suckers, the interdigitated arrangement of their muscle fibers and the flexible interconnections of its parts make direct studies of their control challenging. We developed a dynamic simulator (ABSAMS) that models the general functioning of muscular hydrostat systems built from assemblies of biologically constrained muscular hydrostat models. We report here on simulation studies of octopus-inspired and artificial suckers implemented in this system. These simulations reproduce aspects of octopus sucker performance and squid tentacle extension. Simulations run with these models using parameters from man-made actuators and materials can serve as tools for designing soft robotic implementations of man-made artificial suckers and soft manipulators.
5000 years of geometry mathematics in history and culture
Scriba, Christoph J
2015-01-01
The present volume provides a fascinating overview of geometrical ideas and perceptions from the earliest cultures to the mathematical and artistic concepts of the 20th century. It is the English translation of the 3rd edition of the well-received German book “5000 Jahre Geometrie,” in which geometry is presented as a chain of developments in cultural history and their interaction with architecture, the visual arts, philosophy, science, and engineering. Geometry originated in the ancient cultures along the Indus and Nile Rivers and in Mesopotamia, experiencing its first “Golden Age” in Ancient Greece. Inspired by the Greek mathematics, a new germ of geometry blossomed in the Islamic civilizations. Through the Oriental influence on Spain, this knowledge later spread to Western Europe. Here, as part of the medieval Quadrivium, the understanding of geometry was deepened, leading to a revival during the Renaissance. Together with parallel achievements in India, China, Japan and the ancient American cultur...
International Nuclear Information System (INIS)
Tangedahl, M.J.; Stone, C.R.
1992-01-01
This paper reports that recent changes in the oil and gas industry and ongoing developments in horizontal and underbalanced drilling necessitated development of a better rotating head. A new device called the rotating blowout preventer (RBOP) was developed by Seal-Tech. It is designed to replace the conventional rotating control head on top of BOP stacks and allows drilling operations to continue even on live (underbalanced) wells. Its low wear characteristics and high working pressure (1,500 psi) allow drilling rig crews to drill safely in slightly underbalanced conditions or handle severe well control problems during the time required to actuate other BOPs in the stack. Drilling with a RBOP allows wellbores to be completely closed in tat the drill floor rather than open as with conventional BOPs
Bárány, Imre; Vilcu, Costin
2016-01-01
This volume presents easy-to-understand yet surprising properties obtained using topological, geometric and graph theoretic tools in the areas covered by the Geometry Conference that took place in Mulhouse, France from September 7–11, 2014 in honour of Tudor Zamfirescu on the occasion of his 70th anniversary. The contributions address subjects in convexity and discrete geometry, in distance geometry or with geometrical flavor in combinatorics, graph theory or non-linear analysis. Written by top experts, these papers highlight the close connections between these fields, as well as ties to other domains of geometry and their reciprocal influence. They offer an overview on recent developments in geometry and its border with discrete mathematics, and provide answers to several open questions. The volume addresses a large audience in mathematics, including researchers and graduate students interested in geometry and geometrical problems.
Dickey, Jean O.
1995-01-01
The study of the Earth's rotation in space (encompassing Universal Time (UT1), length of day, polar motion, and the phenomena of precession and nutation) addresses the complex nature of Earth orientation changes, the mechanisms of excitation of these changes and their geophysical implications in a broad variety of areas. In the absence of internal sources of energy or interactions with astronomical objects, the Earth would move as a rigid body with its various parts (the crust, mantle, inner and outer cores, atmosphere and oceans) rotating together at a constant fixed rate. In reality, the world is considerably more complicated, as is schematically illustrated. The rotation rate of the Earth's crust is not constant, but exhibits complicated fluctuations in speed amounting to several parts in 10(exp 8) [corresponding to a variation of several milliseconds (ms) in the Length Of the Day (LOD) and about one part in 10(exp 6) in the orientation of the rotation axis relative to the solid Earth's axis of figure (polar motion). These changes occur over a broad spectrum of time scales, ranging from hours to centuries and longer, reflecting the fact that they are produced by a wide variety of geophysical and astronomical processes. Geodetic observations of Earth rotation changes thus provide insights into the geophysical processes illustrated, which are often difficult to obtain by other means. In addition, these measurements are required for engineering purposes. Theoretical studies of Earth rotation variations are based on the application of Euler's dynamical equations to the problem of finding the response of slightly deformable solid Earth to variety of surface and internal stresses.
In Search of Scientific Inspiration.
2017-01-12
In the ever-expanding sea of scientific advances, how do you find inspiration for your own study? Cell editor Jiaying Tan talked with Mark Lemmon and Joseph (Yossi) Schlessinger about the importance of fueling your research creativity with the conceptual excitement and technical advance from the broad scientific field. An excerpt of the conversation appears below. Copyright © 2017. Published by Elsevier Inc.
INSPIRED High School Computing Academies
Doerschuk, Peggy; Liu, Jiangjiang; Mann, Judith
2011-01-01
If we are to attract more women and minorities to computing we must engage students at an early age. As part of its mission to increase participation of women and underrepresented minorities in computing, the Increasing Student Participation in Research Development Program (INSPIRED) conducts computing academies for high school students. The…
Inspiration: One Percent and Rising
Walling, Donovan R.
2009-01-01
Inventor Thomas Edison once famously declared, "Genius is one percent inspiration and ninety-nine percent perspiration." If that's the case, then the students the author witnessed at the International Student Media Festival (ISMF) last November in Orlando, Florida, are geniuses and more. The students in the ISMF pre-conference workshop…
DEFF Research Database (Denmark)
Thanh Tung, Truong; Dao, Trong Tuan; Grifell Junyent, Marta
2018-01-01
The fungal plasma membrane H+-ATPase (Pma1p) is a potential target for the discovery of new antifungal agents. Surprisingly, no structure-activity relationship studies for small molecules targeting Pma1p have been reported. Herein, we disclose a LEGO-inspired fragment assembly strategy for design...
Inspiration til fremtidens naturfaglige uddannelser
DEFF Research Database (Denmark)
Busch, Henrik; Troelsen, Rie; Horst, Sebastian
uddannelsesniveauer • at den naturfaglige uddannelseskultur styrkes • at lærerkompetencerne styrkes. Rapportens 2. bind - den selvstændige publikation Inspiration til fremtidens naturfaglige uddannelser • En antologi indeholder en række essays om væsentlige problemstillinger for naturfagene. Der er tidligere udsendt...
Plateau's problem an invitation to varifold geometry
Frederick J Almgren, Jr
2001-01-01
There have been many wonderful developments in the theory of minimal surfaces and geometric measure theory in the past 25 to 30 years. Many of the researchers who have produced these excellent results were inspired by this little book--or by Fred Almgren himself. The book is indeed a delightful invitation to the world of variational geometry. A central topic is Plateau's Problem, which is concerned with surfaces that model the behavior of soap films. When trying to resolve the problem, however, one soon finds that smooth surfaces are insufficient: Varifolds are needed. With varifolds, one can obtain geometrically meaningful solutions without having to know in advance all their possible singularities. This new tool makes possible much exciting new analysis and many new results. Plateau's problem and varifolds live in the world of geometric measure theory, where differential geometry and measure theory combine to solve problems which have variational aspects. The author's hope in writing this book was to encour...
Algorithms in Algebraic Geometry
Dickenstein, Alicia; Sommese, Andrew J
2008-01-01
In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its
O'Leary, Michael
2010-01-01
Guides readers through the development of geometry and basic proof writing using a historical approach to the topic. In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfull
Fundamental concepts of geometry
Meserve, Bruce E
1983-01-01
Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.
Developments in special geometry
International Nuclear Information System (INIS)
Mohaupt, Thomas; Vaughan, Owen
2012-01-01
We review the special geometry of N = 2 supersymmetric vector and hypermultiplets with emphasis on recent developments and applications. A new formulation of the local c-map based on the Hesse potential and special real coordinates is presented. Other recent developments include the Euclidean version of special geometry, and generalizations of special geometry to non-supersymmetric theories. As applications we discuss the proof that the local r-map and c-map preserve geodesic completeness, and the construction of four- and five-dimensional static solutions through dimensional reduction over time. The shared features of the real, complex and quaternionic version of special geometry are stressed throughout.
UNDERSTANDING THE GEOMETRY OF ASTROPHYSICAL MAGNETIC FIELDS
Energy Technology Data Exchange (ETDEWEB)
Broderick, Avery E [Canadian Institute for Theoretical Astrophysics, 60 St. George St., Toronto, ON M5S 3H8 (Canada); Blandford, Roger D., E-mail: aeb@cita.utoronto.c [Kavli Institute for Particle Astrophysics and Cosmology, 2575 Sand Hill Rd., Menlo Park, CA 94309 (United States)
2010-08-01
Faraday rotation measurements have provided an invaluable technique for probing the properties of astrophysical magnetized plasmas. Unfortunately, typical observations provide information only about the density-weighted average of the magnetic field component parallel to the line of sight. As a result, the magnetic field geometry along the line of sight, and in many cases even the location of the rotating material, is poorly constrained. Frequently, interpretations of Faraday rotation observations are dependent upon underlying models of the magnetic field being probed (e.g., uniform, turbulent, equipartition). However, we show that at sufficiently low frequencies, specifically below roughly 13(RM/1 rad m{sup -2}){sup 1/4}(B/1 G){sup 1/2} MHz, the character of Faraday rotation changes, entering what we term the 'super-adiabatic regime' in which the rotation measure (RM) is proportional to the integrated absolute value of the line-of-sight component of the field. As a consequence, comparing RMs at high frequencies with those in this new regime provides direct information about the geometry of the magnetic field along the line of sight. Furthermore, the frequency defining the transition to this new regime, {nu}{sub SA}, depends directly upon the local electron density and magnetic field strength where the magnetic field is perpendicular to the line of sight, allowing the unambiguous distinction between Faraday rotation within and in front of the emission region. Typical values of {nu}{sub SA} range from 10 kHz (below the ionospheric cutoff, but above the heliospheric cutoff) to 10 GHz, depending upon the details of the Faraday rotating environment. In particular, for resolved active galactic nuclei, including the black holes at the center of the Milky Way (Sgr A*) and M81, {nu}{sub SA} ranges from roughly 10 MHz to 10 GHz, and thus can be probed via existing and up-coming ground-based radio observatories.
UNDERSTANDING THE GEOMETRY OF ASTROPHYSICAL MAGNETIC FIELDS
International Nuclear Information System (INIS)
Broderick, Avery E.; Blandford, Roger D.
2010-01-01
Faraday rotation measurements have provided an invaluable technique for probing the properties of astrophysical magnetized plasmas. Unfortunately, typical observations provide information only about the density-weighted average of the magnetic field component parallel to the line of sight. As a result, the magnetic field geometry along the line of sight, and in many cases even the location of the rotating material, is poorly constrained. Frequently, interpretations of Faraday rotation observations are dependent upon underlying models of the magnetic field being probed (e.g., uniform, turbulent, equipartition). However, we show that at sufficiently low frequencies, specifically below roughly 13(RM/1 rad m -2 ) 1/4 (B/1 G) 1/2 MHz, the character of Faraday rotation changes, entering what we term the 'super-adiabatic regime' in which the rotation measure (RM) is proportional to the integrated absolute value of the line-of-sight component of the field. As a consequence, comparing RMs at high frequencies with those in this new regime provides direct information about the geometry of the magnetic field along the line of sight. Furthermore, the frequency defining the transition to this new regime, ν SA , depends directly upon the local electron density and magnetic field strength where the magnetic field is perpendicular to the line of sight, allowing the unambiguous distinction between Faraday rotation within and in front of the emission region. Typical values of ν SA range from 10 kHz (below the ionospheric cutoff, but above the heliospheric cutoff) to 10 GHz, depending upon the details of the Faraday rotating environment. In particular, for resolved active galactic nuclei, including the black holes at the center of the Milky Way (Sgr A*) and M81, ν SA ranges from roughly 10 MHz to 10 GHz, and thus can be probed via existing and up-coming ground-based radio observatories.
A Tony Thomas-Inspired Guide to INSPIRE
Energy Technology Data Exchange (ETDEWEB)
O' Connell, Heath B.; /Fermilab
2010-04-01
The SPIRES database was created in the late 1960s to catalogue the high energy physics preprints received by the SLAC Library. In the early 1990s it became the first database on the web and the first website outside of Europe. Although indispensible to the HEP community, its aging software infrastructure is becoming a serious liability. In a joint project involving CERN, DESY, Fermilab and SLAC, a new database, INSPIRE, is being created to replace SPIRES using CERN's modern, open-source Invenio database software. INSPIRE will maintain the content and functionality of SPIRES plus many new features. I describe this evolution from the birth of SPIRES to the current day, noting that the career of Tony Thomas spans this timeline.
A Tony Thomas-Inspired Guide to INSPIRE
International Nuclear Information System (INIS)
O'Connell, Heath B.
2010-01-01
The SPIRES database was created in the late 1960s to catalogue the high energy physics preprints received by the SLAC Library. In the early 1990s it became the first database on the web and the first website outside of Europe. Although indispensible to the HEP community, its aging software infrastructure is becoming a serious liability. In a joint project involving CERN, DESY, Fermilab and SLAC, a new database, INSPIRE, is being created to replace SPIRES using CERN's modern, open-source Invenio database software. INSPIRE will maintain the content and functionality of SPIRES plus many new features. I describe this evolution from the birth of SPIRES to the current day, noting that the career of Tony Thomas spans this timeline.
Norsk inspiration til uddannelse og job
DEFF Research Database (Denmark)
Skovhus, Randi Boelskifte; Thomsen, Rie; Buhl, Rita
2017-01-01
Anmeldelse af bog om det norske fag Utdanningsvalg - inspiration til arbejde med uddannelse og job......Anmeldelse af bog om det norske fag Utdanningsvalg - inspiration til arbejde med uddannelse og job...
Geometry of multihadron production
Energy Technology Data Exchange (ETDEWEB)
Bjorken, J.D.
1994-10-01
This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions.
1996-01-01
Designs and Finite Geometries brings together in one place important contributions and up-to-date research results in this important area of mathematics. Designs and Finite Geometries serves as an excellent reference, providing insight into some of the most important research issues in the field.
Geometry of multihadron production
International Nuclear Information System (INIS)
Bjorken, J.D.
1994-10-01
This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions
Morris, Barbara H.
2004-01-01
This article describes a geometry project that used the beauty of stained-glass-window designs to teach middle school students about geometric figures and concepts. Three honors prealgebra teachers and a middle school mathematics gifted intervention specialist created a geometry project that covered the curriculum and also assessed students'…
Ships - inspiring objects in architecture
Marczak, Elzbieta
2017-10-01
Sea-going vessels have for centuries fascinated people, not only those who happen to work at sea, but first and foremost, those who have never set foot aboard a ship. The environment in which ships operate is reminiscent of freedom and countless adventures, but also of hard and interesting maritime working life. The famous words of Pompey: “Navigare necesseest, vivere non estnecesse” (sailing is necessary, living - is not necessary), which he pronounced on a stormy sea voyage, arouse curiosity and excitement, inviting one to test the truth of this saying personally. It is often the case, however, that sea-faring remains within the realm of dreams, while the fascination with ships demonstrates itself through a transposition of naval features onto land constructions. In such cases, ship-inspired motifs bring alive dreams and yearnings as well as reflect tastes. Tourism is one of the indicators of people’s standard of living and a measure of a society’s civilisation. Maritime tourism has been developing rapidly in recent decades. A sea cruise offers an insight into life at sea. Still, most people derive their knowledge of passenger vessels and their furnishings from the mass media. Passenger vessels, also known as “floating cities,” are described as majestic and grand, while their on-board facilities as luxurious, comfortable, exclusive and inaccessible to common people on land. Freight vessels, on the other hand, are described as enormous objects which dwarf the human being into insignificance. This article presents the results of research intended to answer the following questions: what makes ships a source of inspiration for land architecture? To what extent and by what means do architects draw on ships in their design work? In what places can we find structures inspired by ships? What ships inspire architects? This article presents examples of buildings, whose design was inspired by the architecture and structural details of sea vessels. An analysis of
Energy Technology Data Exchange (ETDEWEB)
Grotz, Andreas
2011-10-07
In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.
Methods of information geometry
Amari, Shun-Ichi
2000-01-01
Information geometry provides the mathematical sciences with a new framework of analysis. It has emerged from the investigation of the natural differential geometric structure on manifolds of probability distributions, which consists of a Riemannian metric defined by the Fisher information and a one-parameter family of affine connections called the \\alpha-connections. The duality between the \\alpha-connection and the (-\\alpha)-connection together with the metric play an essential role in this geometry. This kind of duality, having emerged from manifolds of probability distributions, is ubiquitous, appearing in a variety of problems which might have no explicit relation to probability theory. Through the duality, it is possible to analyze various fundamental problems in a unified perspective. The first half of this book is devoted to a comprehensive introduction to the mathematical foundation of information geometry, including preliminaries from differential geometry, the geometry of manifolds or probability d...
International Nuclear Information System (INIS)
Grotz, Andreas
2011-01-01
In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.
Supersymmetric geometries of IIA supergravity III
International Nuclear Information System (INIS)
Gran, Ulf; Papadopoulos, George; Schultz, Christian von
2016-01-01
We find that (massive) IIA backgrounds that admit a G 2 ⋉ℝ 8 invariant Killing spinor must exhibit a null Killing vector field which leaves the Killing spinor invariant and that the rotation of the Killing vector field satisfies a certain g 2 instanton condition. This result together with those in http://dx.doi.org/10.1007/JHEP05(2014)024 and http://dx.doi.org/10.1007/JHEP12(2015)113 complete the classification of geometries of all (massive) IIA backgrounds that preserve one supersymmetry. We also explore the geometry of a class of backgrounds which admit a G 2 ⋉ℝ 8 invariant Killing spinor and where in addition an appropriate 1-form bilinear vanishes. In all cases, we express the fluxes of the theory in terms of the geometry.
Geometry on the space of geometries
International Nuclear Information System (INIS)
Christodoulakis, T.; Zanelli, J.
1988-06-01
We discuss the geometric structure of the configuration space of pure gravity. This is an infinite dimensional manifold, M, where each point represents one spatial geometry g ij (x). The metric on M is dictated by geometrodynamics, and from it, the Christoffel symbols and Riemann tensor can be found. A ''free geometry'' tracing a geodesic on the manifold describes the time evolution of space in the strong gravity limit. In a regularization previously introduced by the authors, it is found that M does not have the same dimensionality, D, everywhere, and that D is not a scalar, although it is covariantly constant. In this regularization, it is seen that the path integral measure can be absorbed in a renormalization of the cosmological constant. (author). 19 refs
Social insects inspire human design
Holbrook, C. Tate; Clark, Rebecca M.; Moore, Dani; Overson, Rick P.; Penick, Clint A.; Smith, Adrian A.
2010-01-01
The international conference ‘Social Biomimicry: Insect Societies and Human Design’, hosted by Arizona State University, USA, 18–20 February 2010, explored how the collective behaviour and nest architecture of social insects can inspire innovative and effective solutions to human design challenges. It brought together biologists, designers, engineers, computer scientists, architects and businesspeople, with the dual aims of enriching biology and advancing biomimetic design. PMID:20392721
Biology-Inspired Autonomous Control
2011-08-31
insect brain, allow these animals to fly with damaged wings, order of body mass payloads (e.g., foraging bees with a load of pollen , blood satiated...The research focus addressed two broad, complementary research areas : autonomous systems concepts inspired by the behavior and neurobiology...UL 46 19b. TELEPHONE NUMBER (include area code) 850 883-1887 Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std. Z39.18 iii Table of
Complex and symplectic geometry
Medori, Costantino; Tomassini, Adriano
2017-01-01
This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.
Kulczycki, Stefan
2008-01-01
This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry.Starting with fundamental assumptions, the author examines the theorems of Hjelmslev, mapping a plane into a circle, the angle of parallelism and area of a polygon, regular polygons, straight lines and planes in space, and the horosphere. Further development of the theory covers hyperbolic functions, the geometry of suff
Conformal symmetry for rotating D-branes
International Nuclear Information System (INIS)
Cao Liming; Matsuo, Yoshinori; Tsukioka, Takuya; Yoo, Chul-Moon
2009-01-01
We apply the Kerr/CFT correspondence to the rotating black p-brane solutions. These solutions give the simplest examples from string theory point of view. Their near horizon geometries have structures of AdS, even though black p-brane solutions do not have AdS-like structures in the non-rotating case. The microscopic entropy which can be calculated via the Cardy formula exactly agrees with Bekenstein-Hawking entropy.
Roe, John
2003-01-01
Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This point of view is effective because it is often true that the relevant geometric properties of metric spaces are determined by their coarse geometry. Two examples of important uses of coarse geometry are Gromov's beautiful notion of a hyperbolic group and Mostow's proof of his famous rigidity theorem. The first few chapters of the book provide a general perspective on coarse structures. Even when only metric coarse structures are in view, the abstract framework brings the same simplification as does the passage from epsilons and deltas to open sets when speaking of continuity. The middle section reviews notions of negative curvature and rigidity. Modern interest in large scale geometry derives in large part from Mostow's rigidity theorem and from Gromov's subsequent 'large scale' rendition of the crucial properties of n...
Lectures on Symplectic Geometry
Silva, Ana Cannas
2001-01-01
The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and cl...
Kollár, János
1997-01-01
This volume contains the lectures presented at the third Regional Geometry Institute at Park City in 1993. The lectures provide an introduction to the subject, complex algebraic geometry, making the book suitable as a text for second- and third-year graduate students. The book deals with topics in algebraic geometry where one can reach the level of current research while starting with the basics. Topics covered include the theory of surfaces from the viewpoint of recent higher-dimensional developments, providing an excellent introduction to more advanced topics such as the minimal model program. Also included is an introduction to Hodge theory and intersection homology based on the simple topological ideas of Lefschetz and an overview of the recent interactions between algebraic geometry and theoretical physics, which involve mirror symmetry and string theory.
DEFF Research Database (Denmark)
Kokkendorff, Simon Lyngby
2002-01-01
The subject of this Ph.D.-thesis is somewhere in between continuous and discrete geometry. Chapter 2 treats the geometry of finite point sets in semi-Riemannian hyperquadrics,using a matrix whose entries are a trigonometric function of relative distances in a given point set. The distance...... to the geometry of a simplex in a semi-Riemannian hyperquadric. In chapter 3 we study which finite metric spaces that are realizable in a hyperbolic space in the limit where curvature goes to -∞. We show that such spaces are the so called leaf spaces, the set of degree 1 vertices of weighted trees. We also...... establish results on the limiting geometry of such an isometrically realized leaf space simplex in hyperbolic space, when curvature goes to -∞. Chapter 4 discusses negative type of metric spaces. We give a measure theoretic treatment of this concept and related invariants. The theory developed...
Busemann, Herbert
2005-01-01
A comprehensive approach to qualitative problems in intrinsic differential geometry, this text examines Desarguesian spaces, perpendiculars and parallels, covering spaces, the influence of the sign of the curvature on geodesics, more. 1955 edition. Includes 66 figures.
Tabachnikov, Serge
2005-01-01
Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off the boundary or, equivalently, the behavior of rays of light in a domain with ideally reflecting boundary. From the point of view of differential geometry, the billiard flow is the geodesic flow on a manifold with boundary. This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics. The topics covered include variational principles of billiard motion, symplectic geometry of rays of light and integral geometry, existence and nonexistence of caustics, optical properties of conics and quadrics and completely integrable billiards, periodic billiard trajectories, polygonal billiards, mechanisms of chaos in billiard dynamics, and the lesser-known subject of dual (or outer) billiards. The book is based on an advanced undergraduate topics course (but contains more material than can be realistically taught in one semester). Although the minimum prerequisit...
Introduction to tropical geometry
Maclagan, Diane
2015-01-01
Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of t...
Rudiments of algebraic geometry
Jenner, WE
2017-01-01
Aimed at advanced undergraduate students of mathematics, this concise text covers the basics of algebraic geometry. Topics include affine spaces, projective spaces, rational curves, algebraic sets with group structure, more. 1963 edition.
Implosions and hypertoric geometry
DEFF Research Database (Denmark)
Dancer, A.; Kirwan, F.; Swann, A.
2013-01-01
The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion.......The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion....
Intermediate algebra & analytic geometry
Gondin, William R
1967-01-01
Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, system
Ceresole, Anna; Gnecchi, Alessandra; Marrani, Alessio
2013-01-01
We analyze some properties of the four dimensional supergravity theories which originate from five dimensions upon reduction. They generalize to N>2 extended supersymmetries the d-geometries with cubic prepotentials, familiar from N=2 special K\\"ahler geometry. We emphasize the role of a suitable parametrization of the scalar fields and the corresponding triangular symplectic basis. We also consider applications to the first order flow equations for non-BPS extremal black holes.
International Nuclear Information System (INIS)
Osborne, I; Brownson, E; Eulisse, G; Jones, C D; Sexton-Kennedy, E; Lange, D J
2014-01-01
CMS faces real challenges with upgrade of the CMS detector through 2020 and beyond. One of the challenges, from the software point of view, is managing upgrade simulations with the same software release as the 2013 scenario. We present the CMS geometry description software model, its integration with the CMS event setup and core software. The CMS geometry configuration and selection is implemented in Python. The tools collect the Python configuration fragments into a script used in CMS workflow. This flexible and automated geometry configuration allows choosing either transient or persistent version of the same scenario and specific version of the same scenario. We describe how the geometries are integrated and validated, and how we define and handle different geometry scenarios in simulation and reconstruction. We discuss how to transparently manage multiple incompatible geometries in the same software release. Several examples are shown based on current implementation assuring consistent choice of scenario conditions. The consequences and implications for multiple/different code algorithms are discussed.
Software Geometry in Simulations
Alion, Tyler; Viren, Brett; Junk, Tom
2015-04-01
The Long Baseline Neutrino Experiment (LBNE) involves many detectors. The experiment's near detector (ND) facility, may ultimately involve several detectors. The far detector (FD) will be significantly larger than any other Liquid Argon (LAr) detector yet constructed; many prototype detectors are being constructed and studied to motivate a plethora of proposed FD designs. Whether it be a constructed prototype or a proposed ND/FD design, every design must be simulated and analyzed. This presents a considerable challenge to LBNE software experts; each detector geometry must be described to the simulation software in an efficient way which allows for multiple authors to easily collaborate. Furthermore, different geometry versions must be tracked throughout their use. We present a framework called General Geometry Description (GGD), written and developed by LBNE software collaborators for managing software to generate geometries. Though GGD is flexible enough to be used by any experiment working with detectors, we present it's first use in generating Geometry Description Markup Language (GDML) files to interface with LArSoft, a framework of detector simulations, event reconstruction, and data analyses written for all LAr technology users at Fermilab. Brett is the other of the framework discussed here, the General Geometry Description (GGD).
Introduction to combinatorial geometry
International Nuclear Information System (INIS)
Gabriel, T.A.; Emmett, M.B.
1985-01-01
The combinatorial geometry package as used in many three-dimensional multimedia Monte Carlo radiation transport codes, such as HETC, MORSE, and EGS, is becoming the preferred way to describe simple and complicated systems. Just about any system can be modeled using the package with relatively few input statements. This can be contrasted against the older style geometry packages in which the required input statements could be large even for relatively simple systems. However, with advancements come some difficulties. The users of combinatorial geometry must be able to visualize more, and, in some instances, all of the system at a time. Errors can be introduced into the modeling which, though slight, and at times hard to detect, can have devastating effects on the calculated results. As with all modeling packages, the best way to learn the combinatorial geometry is to use it, first on a simple system then on more complicated systems. The basic technique for the description of the geometry consists of defining the location and shape of the various zones in terms of the intersections and unions of geometric bodies. The geometric bodies which are generally included in most combinatorial geometry packages are: (1) box, (2) right parallelepiped, (3) sphere, (4) right circular cylinder, (5) right elliptic cylinder, (6) ellipsoid, (7) truncated right cone, (8) right angle wedge, and (9) arbitrary polyhedron. The data necessary to describe each of these bodies are given. As can be easily noted, there are some subsets included for simplicity
Evaluation of a cone beam computed tomography geometry for image guided small animal irradiation
International Nuclear Information System (INIS)
Yang, Yidong; Armour, Michael; Wang, Ken Kang-Hsin; Gandhi, Nishant; Wong, John; Iordachita, Iulian; Siewerdsen, Jeffrey
2015-01-01
The conventional imaging geometry for small animal cone beam computed tomography (CBCT) is that a detector panel rotates around the head-to-tail axis of an imaged animal (‘tubular’ geometry). Another unusual but possible imaging geometry is that the detector panel rotates around the anterior-to-posterior axis of the animal (‘pancake’ geometry). The small animal radiation research platform developed at Johns Hopkins University employs the pancake geometry where a prone-positioned animal is rotated horizontally between an x-ray source and detector panel. This study is to assess the CBCT image quality in the pancake geometry and investigate potential methods for improvement. We compared CBCT images acquired in the pancake geometry with those acquired in the tubular geometry when the phantom/animal was placed upright simulating the conventional CBCT geometry. Results showed signal-to-noise and contrast-to-noise ratios in the pancake geometry were reduced in comparison to the tubular geometry at the same dose level. But the overall spatial resolution within the transverse plane of the imaged cylinder/animal was better in the pancake geometry. A modest exposure increase to two folds in the pancake geometry can improve image quality to a level close to the tubular geometry. Image quality can also be improved by inclining the animal, which reduces streak artifacts caused by bony structures. The major factor resulting in the inferior image quality in the pancake geometry is the elevated beam attenuation along the long axis of the phantom/animal and consequently increased scatter-to-primary ratio in that orientation. Not withstanding, the image quality in the pancake-geometry CBCT is adequate to support image guided animal positioning, while providing unique advantages of non-coplanar and multiple mice irradiation. This study also provides useful knowledge about the image quality in the two very different imaging geometries, i.e. pancake and tubular geometry
Evaluation of a cone beam computed tomography geometry for image guided small animal irradiation.
Yang, Yidong; Armour, Michael; Wang, Ken Kang-Hsin; Gandhi, Nishant; Iordachita, Iulian; Siewerdsen, Jeffrey; Wong, John
2015-07-07
The conventional imaging geometry for small animal cone beam computed tomography (CBCT) is that a detector panel rotates around the head-to-tail axis of an imaged animal ('tubular' geometry). Another unusual but possible imaging geometry is that the detector panel rotates around the anterior-to-posterior axis of the animal ('pancake' geometry). The small animal radiation research platform developed at Johns Hopkins University employs the pancake geometry where a prone-positioned animal is rotated horizontally between an x-ray source and detector panel. This study is to assess the CBCT image quality in the pancake geometry and investigate potential methods for improvement. We compared CBCT images acquired in the pancake geometry with those acquired in the tubular geometry when the phantom/animal was placed upright simulating the conventional CBCT geometry. Results showed signal-to-noise and contrast-to-noise ratios in the pancake geometry were reduced in comparison to the tubular geometry at the same dose level. But the overall spatial resolution within the transverse plane of the imaged cylinder/animal was better in the pancake geometry. A modest exposure increase to two folds in the pancake geometry can improve image quality to a level close to the tubular geometry. Image quality can also be improved by inclining the animal, which reduces streak artifacts caused by bony structures. The major factor resulting in the inferior image quality in the pancake geometry is the elevated beam attenuation along the long axis of the phantom/animal and consequently increased scatter-to-primary ratio in that orientation. Not withstanding, the image quality in the pancake-geometry CBCT is adequate to support image guided animal positioning, while providing unique advantages of non-coplanar and multiple mice irradiation. This study also provides useful knowledge about the image quality in the two very different imaging geometries, i.e. pancake and tubular geometry, respectively.
Global aspects of complex geometry
Catanese, Fabrizio; Huckleberry, Alan T
2006-01-01
Present an overview of developments in Complex Geometry. This book covers topics that range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kahler geometry, and group actions to Hodge theory and characteristic p-geometry.
Stancu, Cristina
2017-04-01
Using space as context to inspire science education tapps into the excitement of generations of discovering the unknown resulting in unprecedented public participation. Educators are finding exciting and age appropiate materials for their class that explore science, technology, engineering and mathematics. Possible misconceptions are highlighted so that teachers may plan lessons to facilitate correct conceptual understanding. With a range of hands-on learning experiences, Web materials and online ,opportunities for students, educators are invited to take a closer look to actual science missions. This session leverages resources, materials and expertise to address a wide range of traditional and nontraditional audiences while providing consistent messages and information on various space agencies programs.
Natural photonics for industrial inspiration.
Parker, Andrew R
2009-05-13
There are two considerations for optical biomimetics: the diversity of submicrometre architectures found in the natural world, and the industrial manufacture of these. A review exists on the latter subject, where current engineering methods are considered along with those of the natural cells. Here, on the other hand, I will provide a modern review of the different categories of reflectors and antireflectors found in animals, including their optical characterization. The purpose of this is to inspire designers within the $2 billion annual optics industry.
Neuroscience-Inspired Artificial Intelligence.
Hassabis, Demis; Kumaran, Dharshan; Summerfield, Christopher; Botvinick, Matthew
2017-07-19
The fields of neuroscience and artificial intelligence (AI) have a long and intertwined history. In more recent times, however, communication and collaboration between the two fields has become less commonplace. In this article, we argue that better understanding biological brains could play a vital role in building intelligent machines. We survey historical interactions between the AI and neuroscience fields and emphasize current advances in AI that have been inspired by the study of neural computation in humans and other animals. We conclude by highlighting shared themes that may be key for advancing future research in both fields. Copyright © 2017. Published by Elsevier Inc.
Sources of hyperbolic geometry
Stillwell, John
1996-01-01
This book presents, for the first time in English, the papers of Beltrami, Klein, and Poincaré that brought hyperbolic geometry into the mainstream of mathematics. A recognition of Beltrami comparable to that given the pioneering works of Bolyai and Lobachevsky seems long overdue-not only because Beltrami rescued hyperbolic geometry from oblivion by proving it to be logically consistent, but because he gave it a concrete meaning (a model) that made hyperbolic geometry part of ordinary mathematics. The models subsequently discovered by Klein and Poincaré brought hyperbolic geometry even further down to earth and paved the way for the current explosion of activity in low-dimensional geometry and topology. By placing the works of these three mathematicians side by side and providing commentaries, this book gives the student, historian, or professional geometer a bird's-eye view of one of the great episodes in mathematics. The unified setting and historical context reveal the insights of Beltrami, Klein, and Po...
Hu, Hui; Ning, Zhe
2016-11-01
Due to the auto-rotating trait of maple seeds during falling down process, flow characteristics of rotating maple seeds have been studied by many researchers in recent years. In the present study, an experimental investigation was performed to explore maple-seed-inspired UAV propellers for improved aerodynamic and aeroacoustic performances. Inspired by the auto-rotating trait of maple seeds, the shape of a maple seed is leveraged for the planform design of UAV propellers. The aerodynamic and aeroacoustic performances of the maple-seed-inspired propellers are examined in great details, in comparison with a commercially available UAV propeller purchased on the market (i.e., a baseline propeller). During the experiments, in addition to measuring the aerodynamic forces generated by the maple-seed-inspired propellers and the baseline propeller, a high-resolution Particle Image Velocimetry (PIV) system was used to quantify the unsteady flow structures in the wakes of the propellers. The aeroacoustic characteristics of the propellers are also evaluated by leveraging an anechoic chamber available at the Aerospace Engineering Department of Iowa State University. The research work is supported by National Science Foundation under Award Numbers of OSIE-1064235.
Computational synthetic geometry
Bokowski, Jürgen
1989-01-01
Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to stud...
Discrete and computational geometry
Devadoss, Satyan L
2011-01-01
Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also fe...
Ochiai, T.; Nacher, J. C.
2011-09-01
Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.
2002-01-01
Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Com...
Zheng, Fangyang
2002-01-01
The theory of complex manifolds overlaps with several branches of mathematics, including differential geometry, algebraic geometry, several complex variables, global analysis, topology, algebraic number theory, and mathematical physics. Complex manifolds provide a rich class of geometric objects, for example the (common) zero locus of any generic set of complex polynomials is always a complex manifold. Yet complex manifolds behave differently than generic smooth manifolds; they are more coherent and fragile. The rich yet restrictive character of complex manifolds makes them a special and interesting object of study. This book is a self-contained graduate textbook that discusses the differential geometric aspects of complex manifolds. The first part contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. The second part discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles, and gives a brief account of the surface classifi...
Kornyshev, Alexei A.
2010-10-01
The conference 'From DNA-Inspired Physics to Physics-Inspired Biology' (1-5 June 2009, International Center for Theoretical Physics, Trieste, Italy) that myself and two former presidents of the American Biophysical Society—Wilma Olson (Rutgers University) and Adrian Parsegian (NIH), with the support of an ICTP team (Ralf Gebauer (Local Organizer) and Doreen Sauleek (Conference Secretary)), have organized was intended to establish stronger links between the biology and physics communities on the DNA front. The relationships between them were never easy. In 1997, Adrian published a paper in Physics Today ('Harness the Hubris') summarizing his thoughts about the main obstacles for a successful collaboration. The bottom line of that article was that physicists must seriously learn biology before exploring it and even having an interpreter, a friend or co-worker, who will be cooperating with you and translating the problems of biology into a physical language, may not be enough. He started his story with a joke about a physicist asking a biologist: 'I want to study the brain. Tell me something about it!' Biologist: 'First, the brain consists of two parts, and..' Physicist: 'Stop. You have told me too much.' Adrian listed a few direct avenues where physicists' contributions may be particularly welcome. This gentle and elegantly written paper caused, however, a stormy reaction from Bob Austin (Princeton), published together with Adrian's notes, accusing Adrian of forbidding physicists to attack big questions in biology straightaway. Twelve years have passed and many new developments have taken place in the biologist-physicist interaction. This was something I addressed in my opening conference speech, with my position lying somewhere inbetween Parsegian's and Austin's, which is briefly outlined here. I will first recall certain precepts or 'dogmas' that fly in the air like Valkyries, poisoning those relationships. Since the early seventies when I was a first year Ph
Yale, Paul B
2012-01-01
This book is an introduction to the geometry of Euclidean, affine, and projective spaces with special emphasis on the important groups of symmetries of these spaces. The two major objectives of the text are to introduce the main ideas of affine and projective spaces and to develop facility in handling transformations and groups of transformations. Since there are many good texts on affine and projective planes, the author has concentrated on the n-dimensional cases.Designed to be used in advanced undergraduate mathematics or physics courses, the book focuses on ""practical geometry,"" emphasi
Flexible intuitions of Euclidean geometry in an Amazonian indigene group
Izard, Véronique; Pica, Pierre; Spelke, Elizabeth S.; Dehaene, Stanislas
2011-01-01
Kant argued that Euclidean geometry is synthesized on the basis of an a priori intuition of space. This proposal inspired much behavioral research probing whether spatial navigation in humans and animals conforms to the predictions of Euclidean geometry. However, Euclidean geometry also includes concepts that transcend the perceptible, such as objects that are infinitely small or infinitely large, or statements of necessity and impossibility. We tested the hypothesis that certain aspects of nonperceptible Euclidian geometry map onto intuitions of space that are present in all humans, even in the absence of formal mathematical education. Our tests probed intuitions of points, lines, and surfaces in participants from an indigene group in the Amazon, the Mundurucu, as well as adults and age-matched children controls from the United States and France and younger US children without education in geometry. The responses of Mundurucu adults and children converged with that of mathematically educated adults and children and revealed an intuitive understanding of essential properties of Euclidean geometry. For instance, on a surface described to them as perfectly planar, the Mundurucu's estimations of the internal angles of triangles added up to ∼180 degrees, and when asked explicitly, they stated that there exists one single parallel line to any given line through a given point. These intuitions were also partially in place in the group of younger US participants. We conclude that, during childhood, humans develop geometrical intuitions that spontaneously accord with the principles of Euclidean geometry, even in the absence of training in mathematics. PMID:21606377
Guard Cell and Tropomyosin Inspired Chemical Sensor
Directory of Open Access Journals (Sweden)
Jacquelyn K.S. Nagel
2013-10-01
Full Text Available Sensors are an integral part of many engineered products and systems. Biological inspiration has the potential to improve current sensor designs as well as inspire innovative ones. This paper presents the design of an innovative, biologically-inspired chemical sensor that performs “up-front” processing through mechanical means. Inspiration from the physiology (function of the guard cell coupled with the morphology (form and physiology of tropomyosin resulted in two concept variants for the chemical sensor. Applications of the sensor design include environmental monitoring of harmful gases, and a non-invasive approach to detect illnesses including diabetes, liver disease, and cancer on the breath.
INSPIRE 2012 da Istanbul a Firenze
Directory of Open Access Journals (Sweden)
Mauro Salvemini
2012-09-01
Full Text Available DURING THE CONFERENCE HELD IN ISTANBUL IN 2012 INSPIRE THE NEWS THAT MOST IMPRESSED ITALIANS PRESENT, EVEN THOSE IN THE PUBLIC ADMINISTRATION , WAS THAT THE NEXT INSPIRE CONFERENCE WILL TAKE PLACE IN FLORENCEDurante la conferenza INSPIRE 2012 svoltasi ad Istanbul la notizia che ha maggiormente colpito gli italiani presenti, anche quelli della pubblica amministrazione , è stata che la prossima Conferenza INSPIRE si svolgerà a Firenze dal 23 al 27 giugno 2013.
INSPIRE 2012 da Istanbul a Firenze
Directory of Open Access Journals (Sweden)
Mauro Salvemini
2012-09-01
Full Text Available DURING THE CONFERENCE HELD IN ISTANBUL IN 2012 INSPIRE THE NEWS THAT MOST IMPRESSED ITALIANS PRESENT, EVEN THOSE IN THE PUBLIC ADMINISTRATION , WAS THAT THE NEXT INSPIRE CONFERENCE WILL TAKE PLACE IN FLORENCE Durante la conferenza INSPIRE 2012 svoltasi ad Istanbul la notizia che ha maggiormente colpito gli italiani presenti, anche quelli della pubblica amministrazione , è stata che la prossima Conferenza INSPIRE si svolgerà a Firenze dal 23 al 27 giugno 2013.
Classification of pulmonary emphysema from chest CT scans using integral geometry descriptors
van Rikxoort, E. M.; Goldin, J. G.; Galperin-Aizenberg, M.; Brown, M. S.
2011-03-01
To gain insight into the underlying pathways of emphysema and monitor the effect of treatment, methods to quantify and phenotype the different types of emphysema from chest CT scans are of crucial importance. Current standard measures rely on density thresholds for individual voxels, which is influenced by inspiration level and does not take into account the spatial relationship between voxels. Measures based on texture analysis do take the interrelation between voxels into account and therefore might be useful for distinguishing different types of emphysema. In this study, we propose to use Minkowski functionals combined with rotation invariant Gaussian features to distinguish between healthy and emphysematous tissue and classify three different types of emphysema. Minkowski functionals characterize binary images in terms of geometry and topology. In 3D, four Minkowski functionals are defined. By varying the threshold and size of neighborhood around a voxel, a set of Minkowski functionals can be defined for each voxel. Ten chest CT scans with 1810 annotated regions were used to train the method. A set of 108 features was calculated for each training sample from which 10 features were selected to be most informative. A linear discriminant classifier was trained to classify each voxel in the lungs into a subtype of emphysema or normal lung. The method was applied to an independent test set of 30 chest CT scans with varying amounts and types of emphysema with 4347 annotated regions of interest. The method is shown to perform well, with an overall accuracy of 95%.
Surface geometry of 5D black holes and black rings
International Nuclear Information System (INIS)
Frolov, Valeri P.; Goswami, Rituparno
2007-01-01
We discuss geometrical properties of the horizon surface of five-dimensional rotating black holes and black rings. Geometrical invariants characterizing these 3D geometries are calculated. We obtain a global embedding of the 5D rotating black horizon surface into a flat space. We also describe the Kaluza-Klein reduction of the black ring solution (along the direction of its rotation) which, though it is nakedly singular, relates this solution to the 4D metric of a static black hole distorted by the presence of external scalar (dilaton) and vector ('electromagnetic') fields. The properties of the reduced black hole horizon and its embedding in E 3 are briefly discussed
Towards relativistic quantum geometry
Energy Technology Data Exchange (ETDEWEB)
Ridao, Luis Santiago [Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina); Bellini, Mauricio, E-mail: mbellini@mdp.edu.ar [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata (Argentina); Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina)
2015-12-17
We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner–Nordström black-hole is studied.
Multiplicity in difference geometry
Tomasic, Ivan
2011-01-01
We prove a first principle of preservation of multiplicity in difference geometry, paving the way for the development of a more general intersection theory. In particular, the fibres of a \\sigma-finite morphism between difference curves are all of the same size, when counted with correct multiplicities.
Spacetime and Euclidean geometry
Brill, Dieter; Jacobson, Ted
2006-04-01
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.
International Nuclear Information System (INIS)
Konopleva, N.P.
2009-01-01
The basic ideas of description methods of physical fields and elementary particle interactions are discussed. One of such ideas is the conception of space-time geometry. In this connection experimental measurement methods are analyzed. It is shown that measure procedures are the origin of geometrical axioms. The connection between space symmetry properties and the conservation laws is considered
Wares, Arsalan; Elstak, Iwan
2017-01-01
The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and algebra. The activity can be used as a context for illustrating how algebra…
MacKeown, P. K.
1984-01-01
Clarifies two concepts of gravity--those of a fictitious force and those of how space and time may have geometry. Reviews the position of Newton's theory of gravity in the context of special relativity and considers why gravity (as distinct from electromagnetics) lends itself to Einstein's revolutionary interpretation. (JN)
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm
2011-01-01
This paper applies I.M. Gelfand's distinction between adequate and non-adequate use of mathematical language in different contexts to the newly opened window of model-based measurements of intracellular dynamics. The specifics of geometry and dynamics on the mesoscale of cell physiology are elabo...
Diophantine geometry an introduction
Hindry, Marc
2000-01-01
This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.
Sliding vane geometry turbines
Sun, Harold Huimin; Zhang, Jizhong; Hu, Liangjun; Hanna, Dave R
2014-12-30
Various systems and methods are described for a variable geometry turbine. In one example, a turbine nozzle comprises a central axis and a nozzle vane. The nozzle vane includes a stationary vane and a sliding vane. The sliding vane is positioned to slide in a direction substantially tangent to an inner circumference of the turbine nozzle and in contact with the stationary vane.
Boyer, Carl B
2012-01-01
Designed as an integrated survey of the development of analytic geometry, this study presents the concepts and contributions from before the Alexandrian Age through the eras of the great French mathematicians Fermat and Descartes, and on through Newton and Euler to the "Golden Age," from 1789 to 1850.
Coxeter, HSM
1965-01-01
This textbook introduces non-Euclidean geometry, and the third edition adds a new chapter, including a description of the two families of 'mid-lines' between two given lines and an elementary derivation of the basic formulae of spherical trigonometry and hyperbolic trigonometry, and other new material.
International Nuclear Information System (INIS)
Ezin, J.P.
1988-08-01
The lectures given at the ''5th Symposium of Mathematics in Abidjan: Differential Geometry and Mechanics'' are presented. They are divided into four chapters: Riemannian metric on a differential manifold, curvature tensor fields on a Riemannian manifold, some classical functionals on Riemannian manifolds and questions. 11 refs
Hartshorne, Robin
2000-01-01
In recent years, I have been teaching a junior-senior-level course on the classi cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa rately. The remainder of the book is an exploration of questions that arise natu rally from this reading, together with their modern answers. To shore up the foundations we use Hilbert's axioms. The Cartesian plane over a field provides an analytic model of the theory, and conversely, we see that one can introduce coordinates into an abstract geometry. The theory of area is analyzed by cutting figures into triangles. The algebra of field extensions provides a method for deciding which geometrical constructions are possible. The investigation of the parallel postulate leads to the various non-Euclidean geometries. And ...
[Nikola Tesla: flashes of inspiration].
Villarejo-Galende, Albero; Herrero-San Martín, Alejandro
2013-01-16
Nikola Tesla (1856-1943) was one of the greatest inventors in history and a key player in the revolution that led to the large-scale use of electricity. He also made important contributions to such diverse fields as x-rays, remote control, radio, the theory of consciousness or electromagnetism. In his honour, the international unit of magnetic induction was named after him. Yet, his fame is scarce in comparison with that of other inventors of the time, such as Edison, with whom he had several heated arguments. He was a rather odd, reserved person who lived for his inventions, the ideas for which came to him in moments of inspiration. In his autobiography he relates these flashes with a number of neuropsychiatric manifestations, which can be seen to include migraine auras, synaesthesiae, obsessions and compulsions.
Collide@CERN: sharing inspiration
Katarina Anthony
2012-01-01
Late last year, Julius von Bismarck was appointed to be CERN's first "artist in residence" after winning the Collide@CERN Digital Arts award. He’ll be spending two months at CERN starting this March but, to get a flavour of what’s in store, he visited the Organization last week for a crash course in its inspiring activities. Julius von Bismarck, taking a closer look... When we arrive to interview German artist Julius von Bismarck, he’s being given a presentation about antiprotons’ ability to kill cancer cells. The whiteboard in the room contains graphs and equations that might easily send a non-scientist running, yet as Julius puts it, “if I weren’t interested, I’d be asleep”. Given his numerous questions, he must have been fascinated. “This ‘introduction’ week has been exhilarating,” says Julius. “I’ve been able to interact ...
Switchable bio-inspired adhesives
Kroner, Elmar
2015-03-01
Geckos have astonishing climbing abilities. They can adhere to almost any surface and can run on walls and even stick to ceilings. The extraordinary adhesion performance is caused by a combination of a complex surface pattern on their toes and the biomechanics of its movement. These biological dry adhesives have been intensely investigated during recent years because of the unique combination of adhesive properties. They provide high adhesion, allow for easy detachment, can be removed residue-free, and have self-cleaning properties. Many aspects have been successfully mimicked, leading to artificial, bio-inspired, patterned dry adhesives, and were addressed and in some aspects they even outperform the adhesion capabilities of geckos. However, designing artificial patterned adhesion systems with switchable adhesion remains a big challenge; the gecko's adhesion system is based on a complex hierarchical surface structure and on advanced biomechanics, which are both difficult to mimic. In this paper, two approaches are presented to achieve switchable adhesion. The first approach is based on a patterned polydimethylsiloxane (PDMS) polymer, where adhesion can be switched on and off by applying a low and a high compressive preload. The switch in adhesion is caused by a reversible mechanical instability of the adhesive silicone structures. The second approach is based on a composite material consisting of a Nickel- Titanium (NiTi) shape memory alloy and a patterned adhesive PDMS layer. The NiTi alloy is trained to change its surface topography as a function of temperature, which results in a change of the contact area and of alignment of the adhesive pattern towards a substrate, leading to switchable adhesion. These examples show that the unique properties of bio-inspired adhesives can be greatly improved by new concepts such as mechanical instability or by the use of active materials which react to external stimuli.
Topology, Geometry, and Mechanics of Z -Plasty
Matsumoto, Elisabetta A.; Liang, Haiyi; Mahadevan, L.
2018-02-01
Reconstructive surgeries often use topological manipulation of tissue to minimize postoperative scarring. The most common version of this, Z -plasty, involves modifying a straight line cut into a Z shape, followed by a rotational transposition of the resulting triangular pedicle flaps, and a final restitching of the wound. This locally reorients the anisotropic stress field and reduces the potential for scarring. We analyze the planar geometry and mechanics of the Z -plasty to quantify the rotation of the overall stress field and the local forces on the restitched cut using theory, simulations, and simple physical Z -plasty experiments with foam sheets that corroborate each other. Our study rationalizes the most typical surgical choice of this angle, and opens the way for a range of surgical decisions by characterizing the stresses along the cut.
Geometry of Theory Space and RG Flows
Kar, Sayan
The space of couplings of a given theory is the arena of interest in this article. Equipped with a metric ansatz akin to the Fisher information matrix in the space of parameters in statistics (similar metrics in physics are the Zamolodchikov metric or the O'Connor-Stephens metric) we investigate the geometry of theory space through a study of specific examples. We then look into renormalisation group flows in theory space and make an attempt to characterise such flows via its isotropic expansion, rotation and shear. Consequences arising from the evolution equation for the isotropic expansion are discussed. We conclude by pointing out generalisations and pose some open questions.
Theory of gearing kinematics, geometry, and synthesis
Radzevich, Stephen P
2012-01-01
The first book of its kind, Theory of Gearing: Kinematics, Geometry, and Synthesis systematically develops a scientific theory of gearing that makes it possible to synthesize novel gears with the desired performance. Written by a leading gearing expert who holds more than 200 patents, it presents a modern methodology for gear design. The proposed theory is based on a key postulate: all the design parameters for an optimal gear pair for a particular application can be derived from (a) a given configuration of the rotation vectors of the driving and driven shafts and (b) the power transmitted by
Business Inspiration: Small Business Leadership in Recovery?
Rae, David; Price, Liz; Bosworth, Gary; Parkinson, Paul
2012-01-01
Business Inspiration was a short, action-centred leadership and innovation development programme designed for owners and managers of smaller firms to address business survival and repositioning needs arising from the UK's economic downturn. The article examines the design and delivery of Business Inspiration and the impact of the programme on…
Inspiration til undervisning på museer
DEFF Research Database (Denmark)
Hyllested, Trine Elisabeth
2015-01-01
collection and arrangement of knowledge meant to give a general view of, to inspire and to develop teaching at museums in Denmark......collection and arrangement of knowledge meant to give a general view of, to inspire and to develop teaching at museums in Denmark...
Flow produced in a conical container by a rotating endwall
International Nuclear Information System (INIS)
Escudier, M.P.; O'Leary, J.; Poole, R.J.
2007-01-01
Numerical calculations have been carried out for flow in a truncated cone generated by rotation of one endwall. For both convergent (radius increasing with approach to the rotating endwall) and divergent geometries, vortex breakdown is suppressed beyond a certain angle of inclination of the sidewall. At the same time Moffat eddies of increasing strength and extent appear in the corner between the sidewall and the non-rotating endwall. For the divergent geometry, a zone of recirculation appears on the sidewall and eventually merges with the Moffat eddies. The flow phenomena identified from streamline patterns are consistent with the calculated variation of pressure around the periphery of the computational domain
International Nuclear Information System (INIS)
Krishnan, Chethan
2011-01-01
Recent developments suggest that the near-region of rotating black holes behaves like a CFT. To understand this better, I propose to study quantum fields in this region. An instructive approach for this might be to put a large black hole in AdS and to think of the entire geometry as a toy model for the 'near-region'. Quantum field theory on rotating black holes in AdS can be well-defined (unlike in flat space), if fields are quantized in the co-rotating-with-the-horizon frame. First, some generalities of constructing Hartle-Hawking Green functions in this approach are discussed. Then as a specific example where the details are easy to handle, I turn to 2+1 dimensions (BTZ), write down the Green functions explicitly starting with the co-rotating frame, and observe some structural similarities they have with the Kerr-CFT scattering amplitudes. Finally, in BTZ, there is also an alternate construction for the Green functions: we can start from the covering AdS 3 space and use the method of images. Using a 19th century integral formula, I show the equality between the boundary correlators arising via the two constructions.
... 25560729 . Read More Frozen shoulder Rotator cuff problems Rotator cuff repair Shoulder arthroscopy Shoulder CT scan Shoulder MRI scan Shoulder pain Patient Instructions Rotator cuff - self-care Shoulder surgery - discharge Using your ...
Multivariate calculus and geometry
Dineen, Seán
2014-01-01
Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook has successfully followed this programme. It additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.
Multilevel geometry optimization
Rodgers, Jocelyn M.; Fast, Patton L.; Truhlar, Donald G.
2000-02-01
Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol.
Multilevel geometry optimization
Energy Technology Data Exchange (ETDEWEB)
Rodgers, Jocelyn M. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Fast, Patton L. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Truhlar, Donald G. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States)
2000-02-15
Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol. (c) 2000 American Institute of Physics.
Krauss, Lawrence M.; Turner, Michael S.
1999-01-01
The recognition that the cosmological constant may be non-zero forces us to re-evaluate standard notions about the connection between geometry and the fate of our Universe. An open Universe can recollapse, and a closed Universe can expand forever. As a corollary, we point out that there is no set of cosmological observations we can perform that will unambiguously allow us to determine what the ultimate destiny of the Universe will be.
DEFF Research Database (Denmark)
Tamke, Martin; Ramsgaard Thomsen, Mette; Riiber Nielsen, Jacob
2009-01-01
The versatility of wood constructions and traditional wood joints for the production of non standard elements was in focus of a design based research. Herein we established a seamless process from digital design to fabrication. A first research phase centered on the development of a robust...... parametric model and a generic design language a later explored the possibilities to construct complex shaped geometries with self registering joints on modern wood crafting machines. The research was carried out as collaboration with industrial partners....
International Nuclear Information System (INIS)
Lepora, N.; Kibble, T.
1999-01-01
We analyse symmetry breaking in the Weinberg-Salam model paying particular attention to the underlying geometry of the theory. In this context we find two natural metrics upon the vacuum manifold: an isotropic metric associated with the scalar sector, and a squashed metric associated with the gauge sector. Physically, the interplay between these metrics gives rise to many of the non-perturbative features of Weinberg-Salam theory. (author)
International Nuclear Information System (INIS)
Hull, C.M.
1993-01-01
The geometric structure of theories with gauge fields of spins two and higher should involve a higher spin generalisation of Riemannian geometry. Such geometries are discussed and the case of W ∝ -gravity is analysed in detail. While the gauge group for gravity in d dimensions is the diffeomorphism group of the space-time, the gauge group for a certain W-gravity theory (which is W ∝ -gravity in the case d=2) is the group of symplectic diffeomorphisms of the cotangent bundle of the space-time. Gauge transformations for W-gravity gauge fields are given by requiring the invariance of a generalised line element. Densities exist and can be constructed from the line element (generalising √detg μν ) only if d=1 or d=2, so that only for d=1,2 can actions be constructed. These two cases and the corresponding W-gravity actions are considered in detail. In d=2, the gauge group is effectively only a subgroup of the symplectic diffeomorphisms group. Some of the constraints that arise for d=2 are similar to equations arising in the study of self-dual four-dimensional geometries and can be analysed using twistor methods, allowing contact to be made with other formulations of W-gravity. While the twistor transform for self-dual spaces with one Killing vector reduces to a Legendre transform, that for two Killing vectors gives a generalisation of the Legendre transform. (orig.)
Integral geometry and valuations
Solanes, Gil
2014-01-01
Valuations are finitely additive functionals on the space of convex bodies. Their study has become a central subject in convexity theory, with fundamental applications to integral geometry. In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a self-contained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, is devoted to the theory of convex valuations, with emphasis on the latest developments. A special focus is put on the new fundamental structures of the space of valuations discovered after Alesker's irreducibility theorem. Moreover, the author describes the newly developed theory of valuations on manifolds. In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló, based on the notions and tools presented...
CBM RICH geometry optimization
Energy Technology Data Exchange (ETDEWEB)
Mahmoud, Tariq; Hoehne, Claudia [II. Physikalisches Institut, Giessen Univ. (Germany); Collaboration: CBM-Collaboration
2016-07-01
The Compressed Baryonic Matter (CBM) experiment at the future FAIR complex will investigate the phase diagram of strongly interacting matter at high baryon density and moderate temperatures in A+A collisions from 2-11 AGeV (SIS100) beam energy. The main electron identification detector in the CBM experiment will be a RICH detector with a CO{sub 2} gaseous-radiator, focusing spherical glass mirrors, and MAPMT photo-detectors being placed on a PMT-plane. The RICH detector is located directly behind the CBM dipole magnet. As the final magnet geometry is now available, some changes in the RICH geometry become necessary. In order to guarantee a magnetic field of 1 mT at maximum in the PMT plane for effective operation of the MAPMTs, two measures have to be taken: The PMT plane is moved outwards of the stray field by tilting the mirrors by 10 degrees and shielding boxes have been designed. In this contribution the results of the geometry optimization procedure are presented.
Introducing geometry concept based on history of Islamic geometry
Maarif, S.; Wahyudin; Raditya, A.; Perbowo, K. S.
2018-01-01
Geometry is one of the areas of mathematics interesting to discuss. Geometry also has a long history in mathematical developments. Therefore, it is important integrated historical development of geometry in the classroom to increase’ knowledge of how mathematicians earlier finding and constructing a geometric concept. Introduction geometrical concept can be started by introducing the Muslim mathematician who invented these concepts so that students can understand in detail how a concept of geometry can be found. However, the history of mathematics development, especially history of Islamic geometry today is less popular in the world of education in Indonesia. There are several concepts discovered by Muslim mathematicians that should be appreciated by the students in learning geometry. Great ideas of mathematicians Muslim can be used as study materials to supplement religious character values taught by Muslim mathematicians. Additionally, by integrating the history of geometry in teaching geometry are expected to improve motivation and geometrical understanding concept.
Biologically-inspired soft exosuit.
Asbeck, Alan T; Dyer, Robert J; Larusson, Arnar F; Walsh, Conor J
2013-06-01
In this paper, we present the design and evaluation of a novel soft cable-driven exosuit that can apply forces to the body to assist walking. Unlike traditional exoskeletons which contain rigid framing elements, the soft exosuit is worn like clothing, yet can generate moments at the ankle and hip with magnitudes of 18% and 30% of those naturally generated by the body during walking, respectively. Our design uses geared motors to pull on Bowden cables connected to the suit near the ankle. The suit has the advantages over a traditional exoskeleton in that the wearer's joints are unconstrained by external rigid structures, and the worn part of the suit is extremely light, which minimizes the suit's unintentional interference with the body's natural biomechanics. However, a soft suit presents challenges related to actuation force transfer and control, since the body is compliant and cannot support large pressures comfortably. We discuss the design of the suit and actuation system, including principles by which soft suits can transfer force to the body effectively and the biological inspiration for the design. For a soft exosuit, an important design parameter is the combined effective stiffness of the suit and its interface to the wearer. We characterize the exosuit's effective stiffness, and present preliminary results from it generating assistive torques to a subject during walking. We envision such an exosuit having broad applicability for assisting healthy individuals as well as those with muscle weakness.
Deyhle, Hans; Bunk, Oliver; Buser, Stefan; Krastl, Gabriel; Zitzmann, Nicola U.; Ilgenstein, Bernd; Beckmann, Felix; Pfeiffer, Franz; Weiger, Roland; Müller, Bert
2009-08-01
Human teeth are anisotropic composites. Dentin as the core material of the tooth consists of nanometer-sized calcium phosphate crystallites embedded in collagen fiber networks. It shows its anisotropy on the micrometer scale by its well-oriented microtubules. The detailed three-dimensional nanostructure of the hard tissues namely dentin and enamel, however, is not understood, although numerous studies on the anisotropic mechanical properties have been performed and evaluated to explain the tooth function including the enamel-dentin junction acting as effective crack barrier. Small angle X-ray scattering (SAXS) with a spatial resolution in the 10 μm range allows determining the size and orientation of the constituents on the nanometer scale with reasonable precision. So far, only some dental materials, i.e. the fiber reinforced posts exhibit anisotropic properties related to the micrometer-size glass fibers. Dental fillings, composed of nanostructures oriented similar to the natural hard tissues of teeth, however, do not exist at all. The current X-ray-based investigations of extracted human teeth provide evidence for oriented micro- and nanostructures in dentin and enamel. These fundamental quantitative findings result in profound knowledge to develop biologically inspired dental fillings with superior resistance to thermal and mechanical shocks.
Fracture Mechanics: Inspirations from Nature
Directory of Open Access Journals (Sweden)
David Taylor
2014-10-01
Full Text Available In Nature there are many examples of materials performing structural functions. Nature requires materials which are stiff and strong to provide support against various forces, including self-weight, the dynamic forces involved in movement, and external loads such as wind or the actions of a predator. These materials and structures have evolved over millions of years; the science of Biomimetics seeks to understand Nature and, as a result, to find inspiration for the creation of better engineering solutions. There has been relatively little fundamental research work in this area from a fracture mechanics point of view. Natural materials are quite brittle and, as a result, they have evolved several interesting strategies for preventing failure by crack propagation. Fatigue is also a major problem for many animals and plants. In this paper, several examples will be given of recent work in the Bioengineering Research Centre at Trinity College Dublin, investigating fracture and fatigue in such diverse materials as bamboo, the legs and wings of insects, and living cells.
Anaïs Schaeffer
2012-01-01
During the Frankfurt book fair last October, the CERN stand drew quite the crowd. Director-General Rolf Heuer was there to promote CERN’s mission and the "LHC: the Large Hadron Collider" book. He met a lot of visitors and for one of them there was also a nice follow-up… Marcus and his father visiting the LINAC facility. Fifteen year-old Marcus lives in Lauterecken near Frankfurt. The popular book fair last autumn was for him a nice opportunity to get in touch with the CERN environment. Inspired by the stand and what the CERN people were describing, he started to ask more and more questions… So many, that Rolf Heuer decided to invite him to come to CERN and find out some of the answers for himself. A few weeks later, while recovering from an exciting visit to the ATLAS underground cavern and other CERN installations with a cup of tea in Restaurant 1, Marcus shared his enthusiasm about the Organization: “When I was younger, my moth...
Two lectures on D-geometry and noncommutative geometry
International Nuclear Information System (INIS)
Douglas, M.R.
1999-01-01
This is a write-up of lectures given at the 1998 Spring School at the Abdus Salam ICTP. We give a conceptual introduction to D-geometry, the study of geometry as seen by D-branes in string theory, and to noncommutative geometry as it has appeared in D-brane and Matrix theory physics. (author)
Geometry and self-righting of turtles.
Domokos, Gábor; Várkonyi, Péter L
2008-01-07
Terrestrial animals with rigid shells face imminent danger when turned upside down. A rich variety of righting strategies of beetle and turtle species have been described, but the exact role of the shell's geometry in righting is so far unknown. These strategies are often based on active mechanisms, e.g. most beetles self-right via motion of their legs or wings; flat, aquatic turtles use their muscular neck to flip back. On the other hand, highly domed, terrestrial turtles with short limbs and necks have virtually no active control: here shape itself may serve as a fundamental tool. Based on field data gathered on a broad spectrum of aquatic and terrestrial turtle species we develop a geometric model of the shell. Inspired by recent mathematical results, we demonstrate that a simple mechanical classification of the model is closely linked to the animals' righting strategy. Specifically, we show that the exact geometry of highly domed terrestrial species is close to optimal for self-righting, and the shell's shape is the predominant factor of their ability to flip back. Our study illustrates how evolution solved a far-from-trivial geometrical problem and equipped some turtles with monostatic shells: beautiful forms, which rarely appear in nature otherwise.
Accretion onto a noncommutative-inspired Schwarzschild black hole
Gangopadhyay, Sunandan; Paik, Biplab; Mandal, Rituparna
2018-05-01
In this paper, we investigate the problem of ordinary baryonic matter accretion onto the noncommutative (NC) geometry-inspired Schwarzschild black hole. The fundamental equations governing the spherically symmetric steady state matter accretion are deduced. These equations are seen to be modified due to the presence of noncommutativity. The matter accretion rate is computed and is found to increase rapidly with the increase in strength of the NC parameter. The sonic radius reduces while the sound speed at the sonic point increases with the increase in the strength of noncommutativity. The profile of the thermal environment is finally investigated below the sonic radius and at the event horizon and is found to be affected by noncommutativity.
Flectofin: a hingeless flapping mechanism inspired by nature
International Nuclear Information System (INIS)
Lienhard, J; Schleicher, S; Knippers, J; Poppinga, S; Masselter, T; Milwich, M; Speck, T
2011-01-01
This paper presents a novel biomimetic approach to the kinematics of deployable systems for architectural purposes. Elastic deformation of the entire structure replaces the need for local hinges. This change becomes possible by using fibre-reinforced polymers (FRP) such as glass fibre reinforced polymer (GFRP) that can combine high tensile strength with low bending stiffness, thus offering a large range of calibrated elastic deformations. The employment of elasticity within a structure facilitates not only the generation of complex geometries, but also takes the design space a step further by creating elastic kinetic structures, here referred to as pliable structures. In this paper, the authors give an insight into the abstraction strategies used to derive elastic kinetics from plants, which show a clear interrelation of form, actuation and kinematics. Thereby, the focus will be on form-finding and simulation methods which have been adopted to generate a biomimetic principle which is patented under the name Flectofin®. This bio inspired hingeless flapping device is inspired by the valvular pollination mechanism that was derived and abstracted from the kinematics found in the Bird-Of-Paradise flower (Strelitzia reginae, Strelitziaceae).
Flectofin: a hingeless flapping mechanism inspired by nature.
Lienhard, J; Schleicher, S; Poppinga, S; Masselter, T; Milwich, M; Speck, T; Knippers, J
2011-12-01
This paper presents a novel biomimetic approach to the kinematics of deployable systems for architectural purposes. Elastic deformation of the entire structure replaces the need for local hinges. This change becomes possible by using fibre-reinforced polymers (FRP) such as glass fibre reinforced polymer (GFRP) that can combine high tensile strength with low bending stiffness, thus offering a large range of calibrated elastic deformations. The employment of elasticity within a structure facilitates not only the generation of complex geometries, but also takes the design space a step further by creating elastic kinetic structures, here referred to as pliable structures. In this paper, the authors give an insight into the abstraction strategies used to derive elastic kinetics from plants, which show a clear interrelation of form, actuation and kinematics. Thereby, the focus will be on form-finding and simulation methods which have been adopted to generate a biomimetic principle which is patented under the name Flectofin®. This bio inspired hingeless flapping device is inspired by the valvular pollination mechanism that was derived and abstracted from the kinematics found in the Bird-Of-Paradise flower (Strelitzia reginae, Strelitziaceae).
Equilibrium of current driven rotating liquid metal
International Nuclear Information System (INIS)
Velikhov, E.P.; Ivanov, A.A.; Zakharov, S.V.; Zakharov, V.S.; Livadny, A.O.; Serebrennikov, K.S.
2006-01-01
In view of great importance of magneto-rotational instability (MRI) as a fundamental mechanism for angular momentum transfer in magnetized stellar accretion disks, several research centers are involved in experimental study of MRI under laboratory conditions. The idea of the experiment is to investigate the rotation dynamics of well conducting liquid (liquid metal) between two cylinders in axial magnetic field. In this Letter, an experimental scheme with immovable cylinders and fluid rotation driven by radial current is considered. The analytical solution of a stationary flow was found taking into account the external current. Results of axially symmetric numerical simulations of current driven fluid dynamics in experimental setup geometry are presented. The analytical solution and numerical simulations show that the current driven fluid rotation in axial magnetic field provides the axially homogeneous velocity profile suitable for MRI study in classical statement
Bio-inspired computation in telecommunications
Yang, Xin-She; Ting, TO
2015-01-01
Bio-inspired computation, especially those based on swarm intelligence, has become increasingly popular in the last decade. Bio-Inspired Computation in Telecommunications reviews the latest developments in bio-inspired computation from both theory and application as they relate to telecommunications and image processing, providing a complete resource that analyzes and discusses the latest and future trends in research directions. Written by recognized experts, this is a must-have guide for researchers, telecommunication engineers, computer scientists and PhD students.
Directory of Open Access Journals (Sweden)
Mauro Salvemini
2010-03-01
Full Text Available INPIRE's maturityThe INSPIRE Conference 2010 took place from 23 to 25 June 2010 in Kraków, Poland. On 22 June pre-conference workshops have been organized. The theme of this year’s edition has been "INSPIRE as a Framework for Cooperation".The INSPIRE Conference has been organised through a series of plenary sessions addressing common policy issues, and parallel sessions focusing in particular on applications and implementations of SDIs, research issues and new and evolvingtechnologies and applications and poster presentations.
DEFF Research Database (Denmark)
Pawlowski, F; Jorgensen, P; Olsen, Jeppe
2002-01-01
A detailed study is carried out of the accuracy of molecular equilibrium geometries obtained from least-squares fits involving experimental rotational constants B(0) and sums of ab initio vibration-rotation interaction constants alpha(r)(B). The vibration-rotation interaction constants have been...... calculated for 18 single-configuration dominated molecules containing hydrogen and first-row atoms at various standard levels of ab initio theory. Comparisons with the experimental data and tests for the internal consistency of the calculations show that the equilibrium structures generated using Hartree......-Fock vibration-rotation interaction constants have an accuracy similar to that obtained by a direct minimization of the CCSD(T) energy. The most accurate vibration-rotation interaction constants are those calculated at the CCSD(T)/cc-pVQZ level. The equilibrium bond distances determined from these interaction...
International Nuclear Information System (INIS)
Hook, D W
2008-01-01
A geometric framework for quantum mechanics arose during the mid 1970s when authors such as Cantoni explored the notion of generalized transition probabilities, and Kibble promoted the idea that the space of pure quantum states provides a natural quantum mechanical analogue for classical phase space. This central idea can be seen easily since the projection of Schroedinger's equation from a Hilbert space into the space of pure spaces is a set of Hamilton's equations. Over the intervening years considerable work has been carried out by a variety of authors and a mature description of quantum mechanics in geometric terms has emerged with many applications. This current offering would seem ideally placed to review the last thirty years of progress and relate this to the most recent work in quantum entanglement. Bengtsson and Zyczkowski's beautifully illustrated volume, Geometry of Quantum States (referred to as GQS from now on) attempts to cover considerable ground in its 466 pages. Its topics range from colour theory in Chapter 1 to quantum entanglement in Chapter 15-to say that this is a whirlwind tour is, perhaps, no understatement. The use of the work 'introduction' in the subtitle of GQS, might suggest to the reader that this work be viewed as a textbook and I think that this interpretation would be incorrect. The authors have chosen to present a survey of different topics with the specific aim to introduce entanglement in geometric terms-the book is not intended as a pedagogical introduction to the geometric approach to quantum mechanics. Each of the fifteen chapters is a short, and mostly self-contained, essay on a particular aspect or application of geometry in the context of quantum mechanics with entanglement being addressed specifically in the final chapter. The chapters fall into three classifications: those concerned with the mathematical background, those which discuss quantum theory and the foundational aspects of the geometric framework, and
Functional integration over geometries
International Nuclear Information System (INIS)
Mottola, E.
1995-01-01
The geometric construction of the functional integral over coset spaces M/G is reviewed. The inner product on the cotangent space of infinitesimal deformations of M defines an invariant distance and volume form, or functional integration measure on the full configuration space. Then, by a simple change of coordinates parameterizing the gauge fiber G, the functional measure on the coset space M/G is deduced. This change of integration variables leads to a Jacobian which is entirely equivalent to the Faddeev--Popov determinant of the more traditional gauge fixed approach in non-abelian gauge theory. If the general construction is applied to the case where G is the group of coordinate reparameterizations of spacetime, the continuum functional integral over geometries, i.e. metrics modulo coordinate reparameterizations may be defined. The invariant functional integration measure is used to derive the trace anomaly and effective action for the conformal part of the metric in two and four dimensional spacetime. In two dimensions this approach generates the Polyakov--Liouville action of closed bosonic non-critical string theory. In four dimensions the corresponding effective action leads to novel conclusions on the importance of quantum effects in gravity in the far infrared, and in particular, a dramatic modification of the classical Einstein theory at cosmological distance scales, signaled first by the quantum instability of classical de Sitter spacetime. Finite volume scaling relations for the functional integral of quantum gravity in two and four dimensions are derived, and comparison with the discretized dynamical triangulation approach to the integration over geometries are discussed. Outstanding unsolved problems in both the continuum definition and the simplicial approach to the functional integral over geometries are highlighted
Dooner, David B
2012-01-01
Building on the first edition published in 1995 this new edition of Kinematic Geometry of Gearing has been extensively revised and updated with new and original material. This includes the methodology for general tooth forms, radius of torsure', cylinder of osculation, and cylindroid of torsure; the author has also completely reworked the '3 laws of gearing', the first law re-written to better parallel the existing 'Law of Gearing" as pioneered by Leonard Euler, expanded from Euler's original law to encompass non-circular gears and hypoid gears, the 2nd law of gearing describing a unique relat
Flegg, H Graham
2001-01-01
This excellent introduction to topology eases first-year math students and general readers into the subject by surveying its concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology. The first three chapters focus on congruence classes defined by transformations in real Euclidean space. As the number of permitted transformations increases, these classes become larger, and their common topological properties become intuitively clear. Chapters 4-12 give a largely intuitive presentation of selected topics.
Torsional heterotic geometries
International Nuclear Information System (INIS)
Becker, Katrin; Sethi, Savdeep
2009-01-01
We construct new examples of torsional heterotic backgrounds using duality with orientifold flux compactifications. We explain how duality provides a perturbative solution to the type I/heterotic string Bianchi identity. The choice of connection used in the Bianchi identity plays an important role in the construction. We propose the existence of a much larger landscape of compact torsional geometries using string duality. Finally, we present some quantum exact metrics that correspond to NS5-branes placed on an elliptic space. These metrics describe how torus isometries are broken by NS flux.
Geometrie verstehen: statisch - kinematisch
Kroll, Ekkehard
Dem Allgemeinen steht begrifflich das Besondere gegenüber. In diesem Sinne sind allgemeine Überlegungen zum Verstehen von Mathematik zu ergänzen durch Untersuchungen hinsichtlich des Verstehens der einzelnen mathematischen Disziplinen, insbesondere der Geometrie. Hier haben viele Schülerinnen und Schüler Probleme. Diese rühren hauptsächlich daher, dass eine fertige geometrische Konstruktion in ihrer statischen Präsentation auf Papier nicht mehr die einzelnen Konstruktionsschritte erkennen lässt; zum Nachvollzug müssen sie daher ergänzend in einer Konstruktionsbeschreibung festgehalten werden.
Kendig, Keith
2015-01-01
Designed to make learning introductory algebraic geometry as easy as possible, this text is intended for advanced undergraduates and graduate students who have taken a one-year course in algebra and are familiar with complex analysis. This newly updated second edition enhances the original treatment's extensive use of concrete examples and exercises with numerous figures that have been specially redrawn in Adobe Illustrator. An introductory chapter that focuses on examples of curves is followed by a more rigorous and careful look at plane curves. Subsequent chapters explore commutative ring th
Abhyankar, Shreeram Shankar
1964-01-01
This book provides, for use in a graduate course or for self-study by graduate students, a well-motivated treatment of several topics, especially the following: (1) algebraic treatment of several complex variables; (2) geometric approach to algebraic geometry via analytic sets; (3) survey of local algebra; (4) survey of sheaf theory. The book has been written in the spirit of Weierstrass. Power series play the dominant role. The treatment, being algebraic, is not restricted to complex numbers, but remains valid over any complete-valued field. This makes it applicable to situations arising from
Akopyan, A V
2007-01-01
The book is devoted to the properties of conics (plane curves of second degree) that can be formulated and proved using only elementary geometry. Starting with the well-known optical properties of conics, the authors move to less trivial results, both classical and contemporary. In particular, the chapter on projective properties of conics contains a detailed analysis of the polar correspondence, pencils of conics, and the Poncelet theorem. In the chapter on metric properties of conics the authors discuss, in particular, inscribed conics, normals to conics, and the Poncelet theorem for confoca
2015-01-01
This stimulating volume offers a broad collection of the principles of geometry and trigonometry and contains colorful diagrams to bring mathematical principles to life. Subjects are enriched by references to famous mathematicians and their ideas, and the stories are presented in a very comprehensible way. Readers investigate the relationships of points, lines, surfaces, and solids. They study construction methods for drawing figures, a wealth of facts about these figures, and above all, methods to prove the facts. They learn about triangle measure for circular motion, sine and cosine, tangent
REA, The Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Geometry I includes methods of proof, points, lines, planes, angles, congruent angles and line segments, triangles, parallelism, quadrilaterals, geometric inequalities, and geometric
Ring wormholes via duality rotations
Directory of Open Access Journals (Sweden)
Gary W. Gibbons
2016-09-01
Full Text Available We apply duality rotations and complex transformations to the Schwarzschild metric to obtain wormhole geometries with two asymptotically flat regions connected by a throat. In the simplest case these are the well-known wormholes supported by phantom scalar field. Further duality rotations remove the scalar field to yield less well known vacuum metrics of the oblate Zipoy–Voorhees–Weyl class, which describe ring wormholes. The ring encircles the wormhole throat and can have any radius, whereas its tension is always negative and should be less than −c4/4G. If the tension reaches the maximal value, the geometry becomes exactly flat, but the topology remains non-trivial and corresponds to two copies of Minkowski space glued together along the disk encircled by the ring. The geodesics are straight lines, and those which traverse the ring get to the other universe. The ring therefore literally produces a hole in space. Such wormholes could perhaps be created by negative energies concentrated in toroidal volumes, for example by vacuum fluctuations.
Graded geometry and Poisson reduction
Cattaneo, A S; Zambon, M
2009-01-01
The main result of [2] extends the Marsden-Ratiu reduction theorem [4] in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry necessary for the proof in [2]. Further, we provide an alternative algebraic proof for the main result. ©2009 American Institute of Physics
International Nuclear Information System (INIS)
Bohr, A.
1977-01-01
History is surveyed of the development of the theory of rotational states in nuclei. The situation in the 40's when ideas formed of the collective states of a nucleus is evoked. The general rotation theory and the relation between the single-particle and rotational motion are briefly discussed. Future prospects of the rotation theory development are indicated. (I.W.)
International Nuclear Information System (INIS)
Bohr, A.
1976-01-01
Nuclear structure theories are reviewed concerned with nuclei rotational motion. The development of the deformed nucleus model facilitated a discovery of rotational spectra of nuclei. Comprehensive verification of the rotational scheme and a successful classification of corresponding spectra stimulated investigations of the rotational movement dynamics. Values of nuclear moments of inertia proved to fall between two marginal values corresponding to rotation of a solid and hydrodynamic pattern of an unrotating flow, respectively. The discovery of governing role of the deformation and a degree of a symmetry violence for determining rotational degrees of freedon is pointed out to pave the way for generalization of the rotational spectra
Biologically inspired toys using artificial muscles
Bar-Cohen, Y.
2001-01-01
Recent developments in electroactive polymers, so-called artificial muscles, could one day be used to make bionics possible. Meanwhile, as this technology evolves novel mechanisms are expected to emerge that are biologically inspired.
Innovative Didactics in an International Internship - inspiration
DEFF Research Database (Denmark)
Lembcke, Steen; Skibsted, Else Bengaard; Mølgaard, Niels
An inspiration handbook for the international team from the teacher education programme in VIA. Aimed to assist internship supervisors and students during international internships in regards to innovation, social entrepreneurship and development of the international teacher. Introduces why and how...
Biologically Inspired Technology Using Electroactive Polymers (EAP)
Bar-Cohen, Yoseph
2006-01-01
Evolution allowed nature to introduce highly effective biological mechanisms that are incredible inspiration for innovation. Humans have always made efforts to imitate nature's inventions and we are increasingly making advances that it becomes significantly easier to imitate, copy, and adapt biological methods, processes and systems. This brought us to the ability to create technology that is far beyond the simple mimicking of nature. Having better tools to understand and to implement nature's principles we are now equipped like never before to be inspired by nature and to employ our tools in far superior ways. Effectively, by bio-inspiration we can have a better view and value of nature capability while studying its models to learn what can be extracted, copied or adapted. Using electroactive polymers (EAP) as artificial muscles is adding an important element to the development of biologically inspired technologies.
Inspirational Catalogue of Master Thesis Proposals 2015
DEFF Research Database (Denmark)
Thorndahl, Søren
2015-01-01
This catalog presents different topics for master thesis projects. It is important to emphasize that the project descriptions only serves as an inspiration and that you always can discuss with the potential supervisors the specific contents of a project.......This catalog presents different topics for master thesis projects. It is important to emphasize that the project descriptions only serves as an inspiration and that you always can discuss with the potential supervisors the specific contents of a project....
Nature as inspiration for leisure education
ŠPIRHANZLOVÁ, Andrea
2017-01-01
The thesis deals with the organization of leisure activities where the main tool and inspiration is nature. The theoretical part defines basic concepts of pedagogy of free time and points to the possibility of using nature as an inspiration not only for creating content components of leisure activities, but also as the environment in which the pedagogical - educational process of activities takes place. The practical part contains specific pedagogical - educational activity whose essence is b...
Low torque hydrodynamic lip geometry for rotary seals
Dietle, Lannie L.; Schroeder, John E.
2015-07-21
A hydrodynamically lubricating geometry for the generally circular dynamic sealing lip of rotary seals that are employed to partition a lubricant from an environment. The dynamic sealing lip is provided for establishing compressed sealing engagement with a relatively rotatable surface, and for wedging a film of lubricating fluid into the interface between the dynamic sealing lip and the relatively rotatable surface in response to relative rotation that may occur in the clockwise or the counter-clockwise direction. A wave form incorporating an elongated dimple provides the gradual convergence, efficient impingement angle, and gradual interfacial contact pressure rise that are conducive to efficient hydrodynamic wedging. Skewed elevated contact pressure zones produced by compression edge effects provide for controlled lubricant movement within the dynamic sealing interface between the seal and the relatively rotatable surface, producing enhanced lubrication and low running torque.
INSPIRE from the JRC Point of View
Directory of Open Access Journals (Sweden)
Vlado Cetl
2012-12-01
Full Text Available This paper summarises some recent developments in INSPIRE implementation from the JRC (Joint Research Centre point of view. The INSPIRE process started around 11 years ago and today, clear results and benefits can be seen. Spatial data are more accessible and shared more frequently between countries and at the European level. In addition to this, efficient, unified coordination and collaboration between different stakeholders and participants has been achieved, which is another great success. The JRC, as a scientific think-tank of the European Commission, has played a very important role in this process from the very beginning. This role is in line with its mission, which is to provide customer-driven scientific and technical support for the conception, development, implementation and monitoring of European Union (EU policies. The JRC acts as the overall technical coordinator of INSPIRE, but it also carries out the activities necessary to support the coherent implementation of INSPIRE, by helping member states in the implementation process. Experiences drawn from collaboration and negotiation in each country and at the European level will be of great importance in the revision of the INSPIRE Directive, which is envisaged for 2014. Keywords: spatial data infrastructure (SDI; INSPIRE; development; Joint Research Centre (JRC
Bending, force recovery, and D-cones in origami inspired model geometries
Eldar, Theresa; Rozairo, Damith; Croll, Andrew B.
The need for materials with advanced functionality has driven a considerable amount of modern materials science. One idea that has gained significant traction is combining of the ideas Origami and Kirigami with existing materials to build in advanced functionality. In most origami damage is induced in order to trap areas of high curvature in desirable locations in a material. However, the long term and dynamic consequences of local failure are largely unknown. In order to gauge the complex interplay of material properties, relaxation and failure in a set of model thin films, a series of bending and force recovery experiments were carried out. We focus on three materials; polydimethylsiloxane (PDMS), polycarbonate (PC), and polystyrene (PS) chosen for their varying responses to stress. We first measured the load bearing capacity of a single bend in each material, examining the force recovery of bends at various curvatures. Next we examined a doubly folded system in which a single developable cone was created in a similar manner. While the D-cone clearly has massive local consequences for each system, it plays an insignificant role in the system's overall behavior. Finally, we considered higher order combinations of d-cones, ridges and bends. AFOSR under the Young Investigator Program (FA9550-15-1-0168).
Quasinormal Modes of a Noncommutative-Geometry-Inspired Schwarzschild Black Hole
Liang, Jun
2018-01-01
Not Available Supported by the Natural Science Foundation of Education Department of Shannxi Province under Grant No 15JK1077, and the Doctorial Scientific Research Starting Fund of Shannxi University of Science and Technology under Grant No BJ12-02.
Design of a dynamic sensor inspired by bat ears
International Nuclear Information System (INIS)
Müller, Rolf; Pannala, Mittu; Praveen K Reddy, O; Meymand, Sajjad Z
2012-01-01
In bats, the outer ear shapes act as beamforming baffles that create a spatial sensitivity pattern for the reception of the biosonar signals. Whereas technical receivers for wave-based signals usually have rigid geometries, the outer ears of some bat species, such as horseshoe bats, can undergo non-rigid deformations as a result of muscular actuation. It is hypothesized that these deformations provide the animals with a mechanism to adapt their spatial hearing sensitivity on short, sub-second time scales. This biological approach could be of interest to engineering as an inspiration for the design of beamforming devices that combine flexibility with parsimonious implementation. To explore this possibility, a biomimetic dynamic baffle was designed based on a simple shape overall geometry based on an average bat ear. This shape was augmented with three different biomimetic local shape features, a ridge on its exposed surface as well as a flap and an incision along its rim. Dynamic non-rigid deformations of the shape were accomplished through a simple actuation mechanism based on linear actuation inserted at a single point. Despite its simplicity, the prototype device was able to reproduce the dynamic functional characteristics that have been predicted for its biological paragon in a qualitative fashion. (paper)
Bochnak, Jacek; Roy, Marie-Françoise
1998-01-01
This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. The careful and clearly written account covers both basic concepts and up-to-date research topics. It may be used as text for a graduate course. The present edition is a substantially revised and expanded English version of the book "Géometrie algébrique réelle" originally published in French, in 1987, as Volume 12 of ERGEBNISSE. Since the publication of the French version the theory has made advances in several directions. Many of these are included in this English version. Thus the English book may be regarded as a completely new treatment of the subject.
Critique of information geometry
International Nuclear Information System (INIS)
Skilling, John
2014-01-01
As applied to probability, information geometry fails because probability distributions do not form a metric space. Probability theory rests on a compelling foundation of elementary symmetries, which also support information (aka minus entropy, Kullback-Leibler) H(p;q) as the unique measure of divergence from source probability distribution q to destination p. Because the only compatible connective H is from≠to asymmetric, H(p;q)≠H(q;p), there can be no compatible geometrical distance (which would necessarily be from=to symmetric). Hence there is no distance relationship compatible with the structure of probability theory. Metrics g and densities sqrt(det(g)) interpreted as prior probabilities follow from the definition of distance, and must fail likewise. Various metrics and corresponding priors have been proposed, Fisher's being the most popular, but all must behave unacceptably. This is illustrated with simple counter-examples
International Nuclear Information System (INIS)
Correa, Diego H.; Silva, Guillermo A.
2008-01-01
We discuss how geometrical and topological aspects of certain (1/2)-BPS type IIB geometries are captured by their dual operators in N = 4 Super Yang-Mills theory. The type IIB solutions are characterized by arbitrary droplet pictures in a plane and we consider, in particular, axially symmetric droplets. The 1-loop anomalous dimension of the dual gauge theory operators probed with single traces is described by some bosonic lattice Hamiltonians. These Hamiltonians are shown to encode the topology of the droplets. In appropriate BMN limits, the Hamiltonians spectrum reproduces the spectrum of near-BPS string excitations propagating along each of the individual edges of the droplet. We also study semiclassical regimes for the Hamiltonians. For droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents
Emergent geometry of membranes
Energy Technology Data Exchange (ETDEWEB)
Badyn, Mathias Hudoba de; Karczmarek, Joanna L.; Sabella-Garnier, Philippe; Yeh, Ken Huai-Che [Department of Physics and Astronomy, University of British Columbia,6224 Agricultural Road, Vancouver (Canada)
2015-11-13
In work http://dx.doi.org/10.1103/PhysRevD.86.086001, a surface embedded in flat ℝ{sup 3} is associated to any three hermitian matrices. We study this emergent surface when the matrices are large, by constructing coherent states corresponding to points in the emergent geometry. We find the original matrices determine not only shape of the emergent surface, but also a unique Poisson structure. We prove that commutators of matrix operators correspond to Poisson brackets. Through our construction, we can realize arbitrary noncommutative membranes: for example, we examine a round sphere with a non-spherically symmetric Poisson structure. We also give a natural construction for a noncommutative torus embedded in ℝ{sup 3}. Finally, we make remarks about area and find matrix equations for minimal area surfaces.
Geometry through history Euclidean, hyperbolic, and projective geometries
Dillon, Meighan I
2018-01-01
Presented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid’s system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work. Students cultivate skills applicable to much of modern mathematics through sections that integrate concepts like projective and hyperbolic geometry with representative proof-based exercises. For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the...
On organizing principles of discrete differential geometry. Geometry of spheres
International Nuclear Information System (INIS)
Bobenko, Alexander I; Suris, Yury B
2007-01-01
Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. This survey contains a discussion of the following two fundamental discretization principles: the transformation group principle (smooth geometric objects and their discretizations are invariant with respect to the same transformation group) and the consistency principle (discretizations of smooth parametrized geometries can be extended to multidimensional consistent nets). The main concrete geometric problem treated here is discretization of curvature-line parametrized surfaces in Lie geometry. Systematic use of the discretization principles leads to a discretization of curvature-line parametrization which unifies circular and conical nets.
Higher geometry an introduction to advanced methods in analytic geometry
Woods, Frederick S
2005-01-01
For students of mathematics with a sound background in analytic geometry and some knowledge of determinants, this volume has long been among the best available expositions of advanced work on projective and algebraic geometry. Developed from Professor Woods' lectures at the Massachusetts Institute of Technology, it bridges the gap between intermediate studies in the field and highly specialized works.With exceptional thoroughness, it presents the most important general concepts and methods of advanced algebraic geometry (as distinguished from differential geometry). It offers a thorough study
Rotationally invariant correlation filtering
International Nuclear Information System (INIS)
Schils, G.F.; Sweeney, D.W.
1985-01-01
A method is presented for analyzing and designing optical correlation filters that have tailored rotational invariance properties. The concept of a correlation of an image with a rotation of itself is introduced. A unified theory of rotation-invariant filtering is then formulated. The unified approach describes matched filters (with no rotation invariance) and circular-harmonic filters (with full rotation invariance) as special cases. The continuum of intermediate cases is described in terms of a cyclic convolution operation over angle. The angular filtering approach allows an exact choice for the continuous trade-off between loss of the correlation energy (or specificity regarding the image) and the amount of rotational invariance desired
An introduction to incidence geometry
De Bruyn, Bart
2016-01-01
This book gives an introduction to the field of Incidence Geometry by discussing the basic families of point-line geometries and introducing some of the mathematical techniques that are essential for their study. The families of geometries covered in this book include among others the generalized polygons, near polygons, polar spaces, dual polar spaces and designs. Also the various relationships between these geometries are investigated. Ovals and ovoids of projective spaces are studied and some applications to particular geometries will be given. A separate chapter introduces the necessary mathematical tools and techniques from graph theory. This chapter itself can be regarded as a self-contained introduction to strongly regular and distance-regular graphs. This book is essentially self-contained, only assuming the knowledge of basic notions from (linear) algebra and projective and affine geometry. Almost all theorems are accompanied with proofs and a list of exercises with full solutions is given at the end...
International Nuclear Information System (INIS)
Buescher, R.
2005-01-01
Casimir interactions are interactions induced by quantum vacuum fluctuations and thermal fluctuations of the electromagnetic field. Using a path integral quantization for the gauge field, an effective Gaussian action will be derived which is the starting point to compute Casimir forces between macroscopic objects analytically and numerically. No assumptions about the independence of the material and shape dependent contributions to the interaction are made. We study the limit of flat surfaces in further detail and obtain a concise derivation of Lifshitz' theory of molecular forces. For the case of ideally conducting boundaries, the Gaussian action will be calculated explicitly. Both limiting cases are also discussed within the framework of a scalar field quantization approach, which is applicable for translationally invariant geometries. We develop a non-perturbative approach to calculate the Casimir interaction from the Gaussian action for periodically deformed and ideally conducting objects numerically. The obtained results reveal two different scaling regimes for the Casimir force as a function of the distance between the objects, their deformation wavelength and -amplitude. The results confirm that the interaction is non-additive, especially in the presence of strong geometric deformations. Furthermore, the numerical approach is extended to calculate lateral Casimir forces. The results are consistent with the results of the proximity-force approximation for large deformation wavelengths. A qualitatively different behaviour between the normal and lateral force is revealed. We also establish a relation between the boundary induced change of the of the density of states for the scalar Helmholtz equation and the Casimir interaction using the path integral method. For statically deformed boundaries, this relation can be expressed as a novel trace formula, which is formally similar to the so-called Krein-Friedel-Lloyd formula. While the latter formula describes the
Planetary Image Geometry Library
Deen, Robert C.; Pariser, Oleg
2010-01-01
The Planetary Image Geometry (PIG) library is a multi-mission library used for projecting images (EDRs, or Experiment Data Records) and managing their geometry for in-situ missions. A collection of models describes cameras and their articulation, allowing application programs such as mosaickers, terrain generators, and pointing correction tools to be written in a multi-mission manner, without any knowledge of parameters specific to the supported missions. Camera model objects allow transformation of image coordinates to and from view vectors in XYZ space. Pointing models, specific to each mission, describe how to orient the camera models based on telemetry or other information. Surface models describe the surface in general terms. Coordinate system objects manage the various coordinate systems involved in most missions. File objects manage access to metadata (labels, including telemetry information) in the input EDRs and RDRs (Reduced Data Records). Label models manage metadata information in output files. Site objects keep track of different locations where the spacecraft might be at a given time. Radiometry models allow correction of radiometry for an image. Mission objects contain basic mission parameters. Pointing adjustment ("nav") files allow pointing to be corrected. The object-oriented structure (C++) makes it easy to subclass just the pieces of the library that are truly mission-specific. Typically, this involves just the pointing model and coordinate systems, and parts of the file model. Once the library was developed (initially for Mars Polar Lander, MPL), adding new missions ranged from two days to a few months, resulting in significant cost savings as compared to rewriting all the application programs for each mission. Currently supported missions include Mars Pathfinder (MPF), MPL, Mars Exploration Rover (MER), Phoenix, and Mars Science Lab (MSL). Applications based on this library create the majority of operational image RDRs for those missions. A
Initiation to global Finslerian geometry
Akbar-Zadeh, Hassan
2006-01-01
After a brief description of the evolution of thinking on Finslerian geometry starting from Riemann, Finsler, Berwald and Elie Cartan, the book gives a clear and precise treatment of this geometry. The first three chapters develop the basic notions and methods, introduced by the author, to reach the global problems in Finslerian Geometry. The next five chapters are independent of each other, and deal with among others the geometry of generalized Einstein manifolds, the classification of Finslerian manifolds of constant sectional curvatures. They also give a treatment of isometric, affine, p
Directory of Open Access Journals (Sweden)
Šárka Nedomová
2013-01-01
Full Text Available Precise quantification of the profile of egg can provide a powerful tool for the analysis of egg shape for various biological problems. A new approach to the geometry of a Ostrich’s egg profile is presented here using an analysing the egg’s digital photo by edge detection techniques. The obtained points on the eggshell counter are fitted by the Fourier series. The obtained equations describing an egg profile have been used to calculate radii of curvature. The radii of the curvature at the important point of the egg profile (sharp end, blunt end and maximum thickness are independent on the egg shape index. The exact values of the egg surface and the egg volume have been obtained. These quantities are also independent on the egg shape index. These quantities can be successively estimated on the basis of simplified equations which are expressed in terms of the egg length, L¸ and its width, B. The surface area of the eggshells also exhibits good correlation with the egg long circumference length. Some limitations of the most used procedures have been also shown.
Nonperturbative quantum geometries
International Nuclear Information System (INIS)
Jacobson, T.; California Univ., Santa Barbara; Smolin, L.; California Univ., Santa Barbara
1988-01-01
Using the self-dual representation of quantum general relativity, based on Ashtekar's new phase space variables, we present an infinite dimensional family of quantum states of the gravitational field which are exactly annihilated by the hamiltonian constraint. These states are constructed from Wilson loops for Ashtekar's connection (which is the spatial part of the left handed spin connection). We propose a new regularization procedure which allows us to evaluate the action of the hamiltonian constraint on these states. Infinite linear combinations of these states which are formally annihilated by the diffeomorphism constraints as well are also described. These are explicit examples of physical states of the gravitational field - and for the compact case are exact zero eigenstates of the hamiltonian of quantum general relativity. Several different approaches to constructing diffeomorphism invariant states in the self dual representation are also described. The physical interpretation of the states described here is discussed. However, as we do not yet know the physical inner product, any interpretation is at this stage speculative. Nevertheless, this work suggests that quantum geometry at Planck scales might be much simpler when explored in terms of the parallel transport of left-handed spinors than when explored in terms of the three metric. (orig.)
Bhatia, Rajendra
2013-01-01
This book is an outcome of the Indo-French Workshop on Matrix Information Geometries (MIG): Applications in Sensor and Cognitive Systems Engineering, which was held in Ecole Polytechnique and Thales Research and Technology Center, Palaiseau, France, in February 23-25, 2011. The workshop was generously funded by the Indo-French Centre for the Promotion of Advanced Research (IFCPAR). During the event, 22 renowned invited french or indian speakers gave lectures on their areas of expertise within the field of matrix analysis or processing. From these talks, a total of 17 original contribution or state-of-the-art chapters have been assembled in this volume. All articles were thoroughly peer-reviewed and improved, according to the suggestions of the international referees. The 17 contributions presented are organized in three parts: (1) State-of-the-art surveys & original matrix theory work, (2) Advanced matrix theory for radar processing, and (3) Matrix-based signal processing applications.
Variable gearing in a biologically inspired pneumatic actuator array
International Nuclear Information System (INIS)
Azizi, Emanuel; Roberts, Thomas J
2013-01-01
A fundamental feature of pennate muscles is that muscle fibers are oriented at an angle to the line of action and rotate as they shorten, becoming more oblique throughout a contraction. This change in fiber orientation (pennation angle) can amplify the shortening velocity of a fiber and increase output velocity of the muscle. The velocity advantage resulting from dynamic changes in pennation angle can be characterized as a gear ratio (muscle velocity/fiber velocity). A recent study has shown that a pennate muscle's gear ratio varies automatically depending on the load such that a muscle operates with a high gear during rapid contractions and low gear during forceful contractions. We examined whether this variable gearing behavior can be replicated in a pennate array of artificial muscles. We used McKibben type pneumatic actuators, which shorten in tension when filled with compressed gas. Similar to muscle fibers, the actuators expand radially during shortening, a feature thought to be a critical part of the variable gearing mechanism in pennate muscles. We arranged McKibben actuators in an array oriented to mimic a pennate muscle, and quantified the system's gear ratio during contraction against a range of loads. Video was used to measure the gear ratio during each contraction. We find that similar to pennate muscles, the gear ratio decreases significantly with increasing load and that variable gearing results from load-dependent variation in the amount of actuator rotation. These results support the idea that variable gearing in pennate muscles is mediated by difference is fiber rotation and the direction of muscle bulging. The behavior of our artificial muscle array also highlights the potential benefits of bio-inspired architectures in artificial muscle arrays, including the ability to vary force and speed automatically in response to variable loading conditions. (paper)
Variable gearing in a biologically inspired pneumatic actuator array.
Azizi, Emanuel; Roberts, Thomas J
2013-06-01
A fundamental feature of pennate muscles is that muscle fibers are oriented at an angle to the line of action and rotate as they shorten, becoming more oblique throughout a contraction. This change in fiber orientation (pennation angle) can amplify the shortening velocity of a fiber and increase output velocity of the muscle. The velocity advantage resulting from dynamic changes in pennation angle can be characterized as a gear ratio (muscle velocity/fiber velocity). A recent study has shown that a pennate muscle's gear ratio varies automatically depending on the load such that a muscle operates with a high gear during rapid contractions and low gear during forceful contractions. We examined whether this variable gearing behavior can be replicated in a pennate array of artificial muscles. We used McKibben type pneumatic actuators, which shorten in tension when filled with compressed gas. Similar to muscle fibers, the actuators expand radially during shortening, a feature thought to be a critical part of the variable gearing mechanism in pennate muscles. We arranged McKibben actuators in an array oriented to mimic a pennate muscle, and quantified the system's gear ratio during contraction against a range of loads. Video was used to measure the gear ratio during each contraction. We find that similar to pennate muscles, the gear ratio decreases significantly with increasing load and that variable gearing results from load-dependent variation in the amount of actuator rotation. These results support the idea that variable gearing in pennate muscles is mediated by difference is fiber rotation and the direction of muscle bulging. The behavior of our artificial muscle array also highlights the potential benefits of bio-inspired architectures in artificial muscle arrays, including the ability to vary force and speed automatically in response to variable loading conditions.
VARIABLE GEARING IN A BIOLOGICALLY-INSPIRED PNEUMATIC ACTUATOR ARRAY
Azizi, Emanuel; Roberts, Thomas J.
2013-01-01
A fundamental feature of pennate muscles is that muscle fibers are oriented at an angle to the line of action and rotate as they shorten, becoming more oblique throughout a contraction. This change in fiber orientation (pennation angle) can amplify the shortening velocity of a fiber and increase output velocity of the muscle. The velocity advantage resulting from dynamic changes in pennation angle can be characterized as a gear ratio (muscle velocity/fiber velocity). A recent study has shown that a pennate muscle’s gear ratio varies automatically depending on the load such that a muscle operates with a high gear during rapid contractions and low gear during forceful contractions. We examined whether this variable gearing behavior can be replicated in a pennate array of artificial muscles. We used McKibben type pneumatic actuators, which shorten in tension when filled with compressed gas. Similar to muscle fibers, the actuators expand radially during shortening, a feature thought to be a critical part of the variable gearing mechanism in pennate muscles. We arranged McKibben actuators in an array oriented to mimic a pennate muscle, and quantified the system’s gear ratio during contraction against a range of loads. Video was used to measure the gear ratio during each contraction. We find that similar to pennate muscles, the gear ratio decreases significantly with increasing load and that variable gearing results from load-dependent variation in the amount of actuator rotation. These results support the idea that variable gearing in pennate muscles is mediated by difference is fiber rotation and the direction of muscle bulging. The behavior of our artificial muscle array also highlights the potential benefits of bio-inspired architectures in artificial muscle arrays, including the ability to vary force and speed automatically in response to variable loading conditions. PMID:23462288
Nature-inspired computation in engineering
2016-01-01
This timely review book summarizes the state-of-the-art developments in nature-inspired optimization algorithms and their applications in engineering. Algorithms and topics include the overview and history of nature-inspired algorithms, discrete firefly algorithm, discrete cuckoo search, plant propagation algorithm, parameter-free bat algorithm, gravitational search, biogeography-based algorithm, differential evolution, particle swarm optimization and others. Applications include vehicle routing, swarming robots, discrete and combinatorial optimization, clustering of wireless sensor networks, cell formation, economic load dispatch, metamodeling, surrogated-assisted cooperative co-evolution, data fitting and reverse engineering as well as other case studies in engineering. This book will be an ideal reference for researchers, lecturers, graduates and engineers who are interested in nature-inspired computation, artificial intelligence and computational intelligence. It can also serve as a reference for relevant...
Biologically Inspired Micro-Flight Research
Raney, David L.; Waszak, Martin R.
2003-01-01
Natural fliers demonstrate a diverse array of flight capabilities, many of which are poorly understood. NASA has established a research project to explore and exploit flight technologies inspired by biological systems. One part of this project focuses on dynamic modeling and control of micro aerial vehicles that incorporate flexible wing structures inspired by natural fliers such as insects, hummingbirds and bats. With a vast number of potential civil and military applications, micro aerial vehicles represent an emerging sector of the aerospace market. This paper describes an ongoing research activity in which mechanization and control concepts for biologically inspired micro aerial vehicles are being explored. Research activities focusing on a flexible fixed- wing micro aerial vehicle design and a flapping-based micro aerial vehicle concept are presented.
Learning from nature: Nature-inspired algorithms
DEFF Research Database (Denmark)
Albeanu, Grigore; Madsen, Henrik; Popentiu-Vladicescu, Florin
2016-01-01
.), genetic and evolutionary strategies, artificial immune systems etc. Well-known examples of applications include: aircraft wing design, wind turbine design, bionic car, bullet train, optimal decisions related to traffic, appropriate strategies to survive under a well-adapted immune system etc. Based......During last decade, the nature has inspired researchers to develop new algorithms. The largest collection of nature-inspired algorithms is biology-inspired: swarm intelligence (particle swarm optimization, ant colony optimization, cuckoo search, bees' algorithm, bat algorithm, firefly algorithm etc...... on collective social behaviour of organisms, researchers have developed optimization strategies taking into account not only the individuals, but also groups and environment. However, learning from nature, new classes of approaches can be identified, tested and compared against already available algorithms...
Biologically inspired technologies in NASA's morphing project
McGowan, Anna-Maria R.; Cox, David E.; Lazos, Barry S.; Waszak, Martin R.; Raney, David L.; Siochi, Emilie J.; Pao, S. Paul
2003-07-01
For centuries, biology has provided fertile ground for hypothesis, discovery, and inspiration. Time-tested methods used in nature are being used as a basis for several research studies conducted at the NASA Langley Research Center as a part of Morphing Project, which develops and assesses breakthrough vehicle technologies. These studies range from low drag airfoil design guided by marine and avian morphologies to soaring techniques inspired by birds and the study of small flexible wing vehicles. Biology often suggests unconventional yet effective approaches such as non-planar wings, dynamic soaring, exploiting aeroelastic effects, collaborative control, flapping, and fibrous active materials. These approaches and other novel technologies for future flight vehicles are being studied in NASA's Morphing Project. This paper will discuss recent findings in the aeronautics-based, biologically-inspired research in the project.
Influence of toroidal rotation on resistive tearing modes in tokamaks
International Nuclear Information System (INIS)
Wang, S.; Ma, Z. W.
2015-01-01
Influence of toroidal equilibrium plasma rotation on m/n = 2/1 resistive tearing modes is studied numerically using a 3D toroidal MHD code (CLT). It is found that the toroidal rotation with or without shear can suppress the tearing instability and the Coriolis effect in the toroidal geometry plays a dominant role on the rotation induced stabilization. For a high viscosity plasma (τ R /τ V ≫ 1, where τ R and τ V represent resistive and viscous diffusion time, respectively), the effect of the rotation shear combined with the viscosity appears to be stabilizing. For a low viscosity plasmas (τ R /τ V ≪ 1), the rotation shear shows a destabilizing effect when the rotation is large
Influence of toroidal rotation on resistive tearing modes in tokamaks
Energy Technology Data Exchange (ETDEWEB)
Wang, S.; Ma, Z. W., E-mail: zwma@zju.edu.cn [Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou 310027 (China)
2015-12-15
Influence of toroidal equilibrium plasma rotation on m/n = 2/1 resistive tearing modes is studied numerically using a 3D toroidal MHD code (CLT). It is found that the toroidal rotation with or without shear can suppress the tearing instability and the Coriolis effect in the toroidal geometry plays a dominant role on the rotation induced stabilization. For a high viscosity plasma (τ{sub R}/τ{sub V} ≫ 1, where τ{sub R} and τ{sub V} represent resistive and viscous diffusion time, respectively), the effect of the rotation shear combined with the viscosity appears to be stabilizing. For a low viscosity plasmas (τ{sub R}/τ{sub V} ≪ 1), the rotation shear shows a destabilizing effect when the rotation is large.
Plasma rotation under a driven radial current in a tokamak
International Nuclear Information System (INIS)
Chang, C.S.
1999-01-01
The neoclassical behaviour of plasma rotation under a driven radial electrical current is studied in a tokamak geometry. An ambipolar radial electric field develops instantly in such a way that the driven current is balanced by a return current j p in the plasma. The j p x B torque pushes the plasma into a new rotation state both toroidally and poloidally. An anomalous toroidal viscosity is needed to avoid an extreme toroidal rotation speed. It is shown that the poloidal rotation relaxes to a new equilibrium speed, which is in general smaller than the E x B poloidal speed, and that the timescale for the relaxation of poloidal rotation is the same as that of toroidal rotation generation, which is usually much longer than the ion-ion collision time. (author)
Parameterization of rotational spectra
International Nuclear Information System (INIS)
Zhou Chunmei; Liu Tong
1992-01-01
The rotational spectra of the strongly deformed nuclei with low rotational frequencies and weak band mixture are analyzed. The strongly deformed nuclei are commonly encountered in the rare-earth region (e. g., 150 220). A lot of rotational band knowledge are presented
HKT geometry and de Sitter supergravity
International Nuclear Information System (INIS)
Grover, Jai; Gutowski, Jan B.; Herdeiro, Carlos A.R.; Sabra, Wafic
2009-01-01
Solutions of five-dimensional minimal de Sitter supergravity admitting Killing spinors are considered. It is shown that the 'timelike' solutions are determined in terms of a four-dimensional hyper-Kaehler torsion (HKT) manifold. If the HKT manifold is conformally hyper-Kaehler the most general solution can be obtained from a sub-class of supersymmetric solutions of minimal N=2 ungauged supergravity, by means of a simple transformation. Examples include a multi-BMPV de Sitter solution, describing multiple rotating black holes co-moving with the expansion of the universe. If the HKT manifold is not conformally hyper-Kaehler, examples admitting a tri-holomorphic Killing vector field are constructed in terms of certain solutions of three-dimensional Einstein-Weyl geometry
Hydrodynamics of compressible superfluids in confined geometries
International Nuclear Information System (INIS)
Malmi-Kakkada, Abdul N; Valls, Oriol T; Dasgupta, Chandan
2014-01-01
We present a study of the hydrodynamics of compressible superfluids in confined geometries. We use a perturbative procedure in terms of the dimensionless expansion parameter (v/v s ) 2 where v is the typical speed of the flow and v s is the speed of sound. A zero value of this parameter corresponds to the incompressible limit. We apply the procedure to two specific problems: the case of a trapped superfluid with a Gaussian profile of the local density, and that of a superfluid confined in a rotating obstructed cylinder. We find that the corrections due to finite compressibility which are, as expected, negligible for liquid He, are important but amenable to the perturbative treatment for typical ultracold atomic systems. (paper)
Rotational instabilities in field reversed configurations
International Nuclear Information System (INIS)
Santiago, M.A.M.; Tsui, K.H.; Ponciano, B.M.B.; Sakanaka, P.H.
1988-01-01
The rotational instability (n = 2 toroidal mode) in field reversed configurations (FRC) using the ideal MHD equations in cylindrical geometry is studied. These equations are solved using a realistic densite profile, and the influence of some plasma parameters on the growth rate is analysed. The model shows good qualitative results. The growth rate increases rapidly as rotational frequency goes up and the mode m = 2 dominates over the m = 1 mode. With the variation of the density profile, it is observed that the growth rate decreases as the density dip at the center fills up. Calculated value ranges from 1/2 to 1/7 of the rotational frequency Ω whereas the measured value is around Ω/50. The developed analysis is valid for larger machines. The influence of the plasma resistivity on the mode stabilization is also analysed. The resistivity, which is the fundamental factor in the formation of compact torus, tends to decrease the growth rate. (author) [pt
Inspiration in the Act of Reading
DEFF Research Database (Denmark)
Zeller, Kinga
2016-01-01
In German-language theology, Professor Ulrich H. J. Körtner’s theory of inspiration, as it relates to the Bible reader’s perspective, is well known. His attempt to gain fruitful insights from contemporary literary hermeneutics while linking them to theological concerns makes his approach a valued...... yet not uncontroversial example of a reception-aesthetics twist on the Lutheran sola Scriptura. This article presents Körtner’s hermeneutical considerations with special regard to inspiration related to the Bible reader’s perspective and shows how this approach may be related to some aspects...
GPS: Geometry, Probability, and Statistics
Field, Mike
2012-01-01
It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…
Surrogate Modeling for Geometry Optimization
DEFF Research Database (Denmark)
Rojas Larrazabal, Marielba de la Caridad; Abraham, Yonas; Holzwarth, Natalie
2009-01-01
A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used.......A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used....
Kaehler geometry and SUSY mechanics
International Nuclear Information System (INIS)
Bellucci, Stefano; Nersessian, Armen
2001-01-01
We present two examples of SUSY mechanics related with Kaehler geometry. The first system is the N = 4 supersymmetric one-dimensional sigma-model proposed in hep-th/0101065. Another system is the N = 2 SUSY mechanics whose phase space is the external algebra of an arbitrary Kaehler manifold. The relation of these models with antisymplectic geometry is discussed
A prediction for bubbling geometries
Okuda, Takuya
2007-01-01
We study the supersymmetric circular Wilson loops in N=4 Yang-Mills theory. Their vacuum expectation values are computed in the parameter region that admits smooth bubbling geometry duals. The results are a prediction for the supergravity action evaluated on the bubbling geometries for Wilson loops.
Directory of Open Access Journals (Sweden)
Stergioulas Nikolaos
2003-01-01
Full Text Available Rotating relativistic stars have been studied extensively in recent years, both theoretically and observationally, because of the information they might yield about the equation of state of matter at extremely high densities and because they are considered to be promising sources of gravitational waves. The latest theoretical understanding of rotating stars in relativity is reviewed in this updated article. The sections on the equilibrium properties and on the nonaxisymmetric instabilities in f-modes and r-modes have been updated and several new sections have been added on analytic solutions for the exterior spacetime, rotating stars in LMXBs, rotating strange stars, and on rotating stars in numerical relativity.
Numerical simulations of odorant detection by biologically inspired sensor arrays
International Nuclear Information System (INIS)
Schuech, R; Stacey, M T; Barad, M F; Koehl, M A R
2012-01-01
The antennules of many marine crustaceans enable them to rapidly locate sources of odorant in turbulent environmental flows and may provide biological inspiration for engineered plume sampling systems. A substantial gap in knowledge concerns how the physical interaction between a sensing device and the chemical filaments forming a turbulent plume affects odorant detection and filters the information content of the plume. We modeled biological arrays of chemosensory hairs as infinite arrays of odorant flux-detecting cylinders and simulated the fluid flow around and odorant flux into the hair-like sensors as they intercepted a single odorant filament. As array geometry and sampling kinematics were varied, we quantified distortion of the flux time series relative to the spatial shape of the original odorant filament as well as flux metrics that may be important to both organisms and engineered systems attempting to measure plume structure and/or identify chemical composition. The most important predictor of signal distortion is the ratio of sensor diameter to odorant filament width. Achieving high peak properties (e.g. sharpness) of the flux time series and maximizing the total number of odorant molecules detected appear to be mutually exclusive design goals. Sensor arrays inspired specifically by the spiny lobster Panulirus argus and mantis shrimp Gonodactylaceus falcatus introduce little signal distortion but these species' neural systems may not be able to resolve plume structure at the level of individual filaments via temporal properties of the odorant flux. Current chemical sensors are similarly constrained. Our results suggest either that the spatial distribution of flux across the aesthetasc array is utilized by P. argus and G. falcatus, or that such high spatiotemporal resolution is unnecessary for effective plume tracking.
Origami-inspired active structures: a synthesis and review
International Nuclear Information System (INIS)
Peraza-Hernandez, Edwin A; Hartl, Darren J; Malak Jr, Richard J; Lagoudas, Dimitris C
2014-01-01
Origami, the ancient art of paper folding, has inspired the design of engineering devices and structures for decades. The underlying principles of origami are very general, which has led to applications ranging from cardboard containers to deployable space structures. More recently, researchers have become interested in the use of active materials (i.e., those that convert various forms of energy into mechanical work) to effect the desired folding behavior. When used in a suitable geometry, active materials allow engineers to create self-folding structures. Such structures are capable of performing folding and/or unfolding operations without being kinematically manipulated by external forces or moments. This is advantageous for many applications including space systems, underwater robotics, small scale devices, and self-assembling systems. This article is a survey and analysis of prior work on active self-folding structures as well as methods and tools available for the design of folding structures in general and self-folding structures in particular. The goal is to provide researchers and practitioners with a systematic view of the state-of-the-art in this important and evolving area. Unifying structural principles for active self-folding structures are identified and used as a basis for a quantitative and qualitative comparison of numerous classes of active materials. Design considerations specific to folded structures are examined, including the issues of crease pattern identification and fold kinematics. Although few tools have been created with active materials in mind, many of them are useful in the overall design process for active self-folding structures. Finally, the article concludes with a discussion of open questions for the field of origami-inspired engineering. (topical review)
Three-Dimensional-Printing of Bio-Inspired Composites
Xiang Gu, Grace; Su, Isabelle; Sharma, Shruti; Voros, Jamie L.; Qin, Zhao; Buehler, Markus J.
2016-01-01
Optimized for millions of years, natural materials often outperform synthetic materials due to their hierarchical structures and multifunctional abilities. They usually feature a complex architecture that consists of simple building blocks. Indeed, many natural materials such as bone, nacre, hair, and spider silk, have outstanding material properties, making them applicable to engineering applications that may require both mechanical resilience and environmental compatibility. However, such natural materials are very difficult to harvest in bulk, and may be toxic in the way they occur naturally, and therefore, it is critical to use alternative methods to fabricate materials that have material functions similar to material function as their natural counterparts for large-scale applications. Recent progress in additive manufacturing, especially the ability to print multiple materials at upper micrometer resolution, has given researchers an excellent instrument to design and reconstruct natural-inspired materials. The most advanced 3D-printer can now be used to manufacture samples to emulate their geometry and material composition with high fidelity. Its capabilities, in combination with computational modeling, have provided us even more opportunities for designing, optimizing, and testing the function of composite materials, in order to achieve composites of high mechanical resilience and reliability. In this review article, we focus on the advanced material properties of several multifunctional biological materials and discuss how the advanced 3D-printing techniques can be used to mimic their architectures and functions. Lastly, we discuss the limitations of 3D-printing, suggest possible future developments, and discuss applications using bio-inspired materials as a tool in bioengineering and other fields. PMID:26747791
Three-Dimensional-Printing of Bio-Inspired Composites.
Xiang Gu, Grace; Su, Isabelle; Sharma, Shruti; Voros, Jamie L; Qin, Zhao; Buehler, Markus J
2016-02-01
Optimized for millions of years, natural materials often outperform synthetic materials due to their hierarchical structures and multifunctional abilities. They usually feature a complex architecture that consists of simple building blocks. Indeed, many natural materials such as bone, nacre, hair, and spider silk, have outstanding material properties, making them applicable to engineering applications that may require both mechanical resilience and environmental compatibility. However, such natural materials are very difficult to harvest in bulk, and may be toxic in the way they occur naturally, and therefore, it is critical to use alternative methods to fabricate materials that have material functions similar to material function as their natural counterparts for large-scale applications. Recent progress in additive manufacturing, especially the ability to print multiple materials at upper micrometer resolution, has given researchers an excellent instrument to design and reconstruct natural-inspired materials. The most advanced 3D-printer can now be used to manufacture samples to emulate their geometry and material composition with high fidelity. Its capabilities, in combination with computational modeling, have provided us even more opportunities for designing, optimizing, and testing the function of composite materials, in order to achieve composites of high mechanical resilience and reliability. In this review article, we focus on the advanced material properties of several multifunctional biological materials and discuss how the advanced 3D-printing techniques can be used to mimic their architectures and functions. Lastly, we discuss the limitations of 3D-printing, suggest possible future developments, and discuss applications using bio-inspired materials as a tool in bioengineering and other fields.
Shafarevich, Igor Rostislavovich
1994-01-01
Shafarevich Basic Algebraic Geometry 2 The second edition of Shafarevich's introduction to algebraic geometry is in two volumes. The second volume covers schemes and complex manifolds, generalisations in two different directions of the affine and projective varieties that form the material of the first volume. Two notable additions in this second edition are the section on moduli spaces and representable functors, motivated by a discussion of the Hilbert scheme, and the section on Kähler geometry. The book ends with a historical sketch discussing the origins of algebraic geometry. From the Zentralblatt review of this volume: "... one can only respectfully repeat what has been said about the first part of the book (...): a great textbook, written by one of the leading algebraic geometers and teachers himself, has been reworked and updated. As a result the author's standard textbook on algebraic geometry has become even more important and valuable. Students, teachers, and active researchers using methods of al...
Optical geometry across the horizon
International Nuclear Information System (INIS)
Jonsson, Rickard
2006-01-01
In a recent paper (Jonsson and Westman 2006 Class. Quantum Grav. 23 61), a generalization of optical geometry, assuming a non-shearing reference congruence, is discussed. Here we illustrate that this formalism can be applied to (a finite four-volume) of any spherically symmetric spacetime. In particular we apply the formalism, using a non-static reference congruence, to do optical geometry across the horizon of a static black hole. While the resulting geometry in principle is time dependent, we can choose the reference congruence in such a manner that an embedding of the geometry always looks the same. Relative to the embedded geometry the reference points are then moving. We discuss the motion of photons, inertial forces and gyroscope precession in this framework
DEFF Research Database (Denmark)
Gramkow, Claus
1999-01-01
In this article two common approaches to averaging rotations are compared to a more advanced approach based on a Riemannian metric. Very offten the barycenter of the quaternions or matrices that represent the rotations are used as an estimate of the mean. These methods neglect that rotations belo...... approximations to the Riemannian metric, and that the subsequent corrections are inherient in the least squares estimation. Keywords: averaging rotations, Riemannian metric, matrix, quaternion......In this article two common approaches to averaging rotations are compared to a more advanced approach based on a Riemannian metric. Very offten the barycenter of the quaternions or matrices that represent the rotations are used as an estimate of the mean. These methods neglect that rotations belong...
Kinds of inspiration in interaction design
DEFF Research Database (Denmark)
Halskov, Kim
2010-01-01
In this paper, we explore the role of sources of inspiration in interaction design. We identify four strategies for relating sources of inspiration to emerging ideas: selection; adaptation; translation; and combination. As our starting point, we argue that sources of inspiration are a form...... of knowledge crucial to creativity. Our research is based on empirical findings arising from the use of Inspiration Card Workshops, which are collaborative design events in which domain and technology insight are combined to create design concepts. In addition to the systematically introduced sources...... of inspiration that form part of the workshop format, a number of spontaneous sources of inspiration emerged during these workshops....
Buckling Pneumatic Linear Actuators Inspired by Muscle
Yang, Dian; Verma, Mohit Singh; So, Ju-Hee; Mosadegh, Bobak; Keplinger, Christoph; Lee, Benjamin; Khashai, Fatemeh; Lossner, Elton Garret; Suo, Zhigang; Whitesides, George McClelland
2016-01-01
The mechanical features of biological muscles are difficult to reproduce completely in synthetic systems. A new class of soft pneumatic structures (vacuum-actuated muscle-inspired pneumatic structures) is described that combines actuation by negative pressure (vacuum), with cooperative buckling of beams fabricated in a slab of elastomer, to achieve motion and demonstrate many features that are similar to that of mammalian muscle.
Inspiration and the Texts of the Bible
Directory of Open Access Journals (Sweden)
Dirk Buchner
1997-12-01
Full Text Available This article seeks to explore what the inspired text of the Old Testament was as it existed for the New Testament authors, particularly for the author of the book of Hebrews. A quick look at the facts makes. it clear that there was, at the time, more than one 'inspired' text, among these were the Septuagint and the Masoretic Text 'to name but two'. The latter eventually gained ascendancy which is why it forms the basis of our translated Old Testament today. Yet we have to ask: what do we make of that other text that was the inspired Bible to the early Church, especially to the writer of the book of Hebrews, who ignored the Masoretic text? This article will take a brief look at some suggestions for a doctrine of inspiration that keeps up with the facts of Scripture. Allied to this, the article is something of a bibliographical study of recent developments in textual research following the discovery of the Dead Sea scrolls.
Using Space to Inspire and Engage Children
Clements, Allan
2015-01-01
The European Space Education Resources Office (ESERO-UK) is a project of the European Space Agency (ESA) and national partners including the Department for Education (DfE), The UK Space Agency (UKSA) and the Science and Technology Facilities Council (STFC). The key objective of the project is to promote space as an exciting inspirational context…
Inspired by Athletes, Myths, and Poets
Melvin, Samantha
2010-01-01
Tales of love and hate, of athleticism, heroism, devotion to gods and goddesses that influenced myth and culture are a way of sharing ancient Greece's rich history. In this article, the author describes how her students created their own Greek-inspired clay vessels as artifacts of their study. (Contains 6 online resources.)
Inspirational catalogue of Master Thesis proposals 2014
DEFF Research Database (Denmark)
This catalog presents different topics for master thesis projects. It is important to emphasize that the project descriptions only serves as an inspiration and that you always can discuss with the potential supervisors the specific contents of a project. If you have an idea for a project which...
Water Treatment Technologies Inspire Healthy Beverages
2013-01-01
Mike Johnson, a former technician at Johnson Space Center, drew on his expertise as a wastewater engineer to create a line of kombucha-based probiotic drinks. Unpeeled Inc., based in Minneapolis-St. Paul, Minnesota, employs 12 people and has sold more than 6 million units of its NASA-inspired beverage.
Inspiring a Life Full of Learning
Ludlam, John
2012-01-01
The Secrets and Words films had everything one would expect from a BBC drama--great writing, acting and directing allied with high production values. But the dramas were also powerful learning tools, co-commissioned by BBC Learning and aimed at inspiring people who have difficulty with reading and writing to seek help. The BBC's learning vision is…
Trauma-Inspired Prosocial Leadership Development
Williams, Jenifer Wolf; Allen, Stuart
2015-01-01
Though trauma survivors sometimes emerge as leaders in prosocial causes related to their previous negative or traumatic experiences, little is known about this transition, and limited guidance is available for survivors who hope to make prosocial contributions. To understand what enables trauma-inspired prosocial leadership development, the…
Pop Art--Inspired Self-Portraits
Goodwin, Donna J.
2011-01-01
In this article, the author describes an art lesson that was inspired by Andy Warhol's mass-produced portraits. Warhol began his career as a graphic artist and illustrator. His artwork was a response to the redundancy of the advertising images put in front of the American public. Celebrities and famous people in magazines and newspapers were seen…
Surfacing Authentic Leadership: Inspiration from "After Life"
Billsberry, Jon; North-Samardzic, Andrea
2016-01-01
This paper advocates an innovative approach to help leadership students analyze, capture, and remember the nature of their authentic leadership. This developmental activity was inspired by the Japanese film, "Wandâfuru raifu" ("After Life") (Kore-Eda, Sato, & Shigenobu, 1998), in which the recently deceased are asked to…
Coaching som inspiration til dialogbaseret lederskab
DEFF Research Database (Denmark)
Stelter, Reinhard
2013-01-01
, hvor mening og værdiskabende processer er i centrum. De centrale grunddimensioner for denne form for coachende dialog ligger i et fokus på værdier, i muligheder for meningsskabelse og i det narrativ-samskabende perspektiv. På dette grundlag kan tredje generations coaching være inspiration i forhold til...
A Novel Geometry for Shear Test Using Axial Tensile Setup
Directory of Open Access Journals (Sweden)
Sibo Yuan
2018-05-01
Full Text Available This paper studies a novel geometry for the in-plane shear test performed with an axial electromechanical testing machine. In order to investigate the influence of the triaxiality rate on the mechanical behavior, different tests will be performed on the studied material: simple tensile tests, large tensile tests and shear tests. For the whole campaign, a common equipment should be employed to minimize the impact of the testing device. As a consequence, for the shear tests, the geometry of the specimen must be carefully designed in order to adapt the force value and make it comparable to the one obtained for the tensile tests. Like most of the existing shear-included tensile test specimens, the axial loading is converted to shear loading at a particular region through the effect of geometry. A symmetric shape is generally preferred, since it can restrict the in-plane rotation of the shear section, keep shear increasing in a more monotonic path and double the force level thanks to the two shear zones. Due to the specific experimental conditions, such as dimensions of the furnace and the clamping system, the position of the extensometer or the restriction of sheet thickness (related to the further studies of size effect at mesoscale and hot temperature, several geometries were brought up and evaluated in an iterative procedure via finite element simulations. Both the numerical and experimental results reveal that the final geometry ensures some advantages. For instance, a relatively low triaxiality in the shear zone, limited in-plane rotation and no necking are observed. Moreover, it also prevents any out-of-plane displacement of the specimen which seems to be highly sensitive to the geometry, and presents a very limited influence of the material and the thickness.
Complex analysis and CR geometry
Zampieri, Giuseppe
2008-01-01
Cauchy-Riemann (CR) geometry is the study of manifolds equipped with a system of CR-type equations. Compared to the early days when the purpose of CR geometry was to supply tools for the analysis of the existence and regularity of solutions to the \\bar\\partial-Neumann problem, it has rapidly acquired a life of its own and has became an important topic in differential geometry and the study of non-linear partial differential equations. A full understanding of modern CR geometry requires knowledge of various topics such as real/complex differential and symplectic geometry, foliation theory, the geometric theory of PDE's, and microlocal analysis. Nowadays, the subject of CR geometry is very rich in results, and the amount of material required to reach competence is daunting to graduate students who wish to learn it. However, the present book does not aim at introducing all the topics of current interest in CR geometry. Instead, an attempt is made to be friendly to the novice by moving, in a fairly relaxed way, f...
The geometry description markup language
International Nuclear Information System (INIS)
Chytracek, R.
2001-01-01
Currently, a lot of effort is being put on designing complex detectors. A number of simulation and reconstruction frameworks and applications have been developed with the aim to make this job easier. A very important role in this activity is played by the geometry description of the detector apparatus layout and its working environment. However, no real common approach to represent geometry data is available and such data can be found in various forms starting from custom semi-structured text files, source code (C/C++/FORTRAN), to XML and database solutions. The XML (Extensible Markup Language) has proven to provide an interesting approach for describing detector geometries, with several different but incompatible XML-based solutions existing. Therefore, interoperability and geometry data exchange among different frameworks is not possible at present. The author introduces a markup language for geometry descriptions. Its aim is to define a common approach for sharing and exchanging of geometry description data. Its requirements and design have been driven by experience and user feedback from existing projects which have their geometry description in XML
Rotating frames in special relativity
International Nuclear Information System (INIS)
Strauss, M.
1979-01-01
The transformation theory for rotating frames presented in a previous paper is generalized by replacing the usual condition r = R for ωR < c (invariance of radius) by r = Rg(βsub(R)) so that r is now defined for all values of R, 0 <= R <= infinity. This generalization does not affect the kinematic transformation bracetheta, T → bracethetasup(r), bracesup(r) and the result group structure required by the theoretical constraints previously established, provided the old parameter 'r' (=R) is now identified throughout with either r or R; for physical reasons it must be identified with R. The function g, which cannot be fixed by theoretical constraints, determines the degree of geometrical anisotropy in the rotating plane z = const. More specifically, since g enters the expression for the ratio C/D (circumference/diameter) its choice corresponds to the choice of a congruence definition for lengths in radial and tangential directions. While on this (purely geometrical) level g remains undetermined, it can be uniquely determined experimentally on the kinematic level, e.g. by observing in Σsup(ω) the motion of a free particle. Thus the supremacy of kinematics over geometry is explicated by a further instance. At the same time, special relativity theory (SRT) is shown to belong to the class of theories with theoretically unsolvable problems. (author)
Fallow), Stray
2009-01-01
Having trouble with geometry? Do Pi, The Pythagorean Theorem, and angle calculations just make your head spin? Relax. With Head First 2D Geometry, you'll master everything from triangles, quads and polygons to the time-saving secrets of similar and congruent angles -- and it'll be quick, painless, and fun. Through entertaining stories and practical examples from the world around you, this book takes you beyond boring problems. You'll actually use what you learn to make real-life decisions, like using angles and parallel lines to crack a mysterious CSI case. Put geometry to work for you, and
Walsh, Edward T
2014-01-01
This introductory text is designed to help undergraduate students develop a solid foundation in geometry. Early chapters progress slowly, cultivating the necessary understanding and self-confidence for the more rapid development that follows. The extensive treatment can be easily adapted to accommodate shorter courses. Starting with the language of mathematics as expressed in the algebra of logic and sets, the text covers geometric sets of points, separation and angles, triangles, parallel lines, similarity, polygons and area, circles, space geometry, and coordinate geometry. Each chapter incl
Differential geometry curves, surfaces, manifolds
Kohnel, Wolfgang
2002-01-01
This carefully written book is an introduction to the beautiful ideas and results of differential geometry. The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. Special topics that are explored include Frenet frames, ruled surfaces, minimal surfaces and the Gauss-Bonnet theorem. The second part is an introduction to the geometry of general manifolds, with particular emphasis on connections and curvature. The final two chapters are insightful examinations of the special cases of spaces of constant curvature and Einstein manifolds. The text is illustrated with many figures and examples. The prerequisites are undergraduate analysis and linear algebra.
Generation of plasma rotation by ICRH in tokamaks
International Nuclear Information System (INIS)
Chang, C.; Phillips, C.K.; White, R.B.; Zweben, S.; Bonoli, P.T.; Rice, J.; Greenwald, M.; Grassie, J.S. de
2001-01-01
A physical mechanism to generate plasma rotation by ICRH is presented in a tokamak geometry. By breaking the omnigenity of resonant ion orbits, ICRH can induce a non-ambipolar minor-radial flow of resonant ions. This induces a return current j p r in the plasma, which then drives plasma rotation through the j p r xB force. It is estimated that the fast-wave power in the present-day tokamak experiments can be strong enough to give a significant modification to plasma rotation. (author)
Rotations with Rodrigues' vector
International Nuclear Information System (INIS)
Pina, E
2011-01-01
The rotational dynamics was studied from the point of view of Rodrigues' vector. This vector is defined here by its connection with other forms of parametrization of the rotation matrix. The rotation matrix was expressed in terms of this vector. The angular velocity was computed using the components of Rodrigues' vector as coordinates. It appears to be a fundamental matrix that is used to express the components of the angular velocity, the rotation matrix and the angular momentum vector. The Hamiltonian formalism of rotational dynamics in terms of this vector uses the same matrix. The quantization of the rotational dynamics is performed with simple rules if one uses Rodrigues' vector and similar formal expressions for the quantum operators that mimic the Hamiltonian classical dynamics.
DEFF Research Database (Denmark)
Gramkow, Claus
2001-01-01
In this paper two common approaches to averaging rotations are compared to a more advanced approach based on a Riemannian metric. Very often the barycenter of the quaternions or matrices that represent the rotations are used as an estimate of the mean. These methods neglect that rotations belong ...... approximations to the Riemannian metric, and that the subsequent corrections are inherent in the least squares estimation.......In this paper two common approaches to averaging rotations are compared to a more advanced approach based on a Riemannian metric. Very often the barycenter of the quaternions or matrices that represent the rotations are used as an estimate of the mean. These methods neglect that rotations belong...
Neoclassical rotation velocities in multispecies plasmas
International Nuclear Information System (INIS)
Houlberg, W.A.; Hirshman, S.P.; Shaing, K.C.
1996-01-01
We examine the relationships between the poloidal, toroidal and parallel rotation velocities for typical plasma conditions in existing tokamak experiments. The radial force balance, neoclassical solution to the poloidal flow from the parallel force balance, and anomalous toroidal rotation axe included. A full multispecies formulation of the neoclassical transport theory is implemented in the NCLASS code (which includes arbitrary axisymmetric geometries and plasma collisionalities) to determine the poloidal rotation velocities. Comparisons are made with analytic relationships derived from a single impurity formulation of the problem. The roles of the radial electric field and species density and pressure gradients are evaluated. The determination of the radial electric field using the NCLASS solution for poloidal rotation and a local measurement of the toroidal rotation in conjunction with measured plasma profiles is discussed; it has been used in analysis of TFTR enhanced reverse shear plasmas. The ordering of banana orbit size small relative to local minor radius and gradients (as incorporated into initial versions of NCLASS) are examined for typical negative shear plasmas. We show the degree to which these constraints axe violated and demonstrate that finite orbit corrections axe required for better determination of the bootstrap current, particle fluxes and ion heat fluxes, i.e., the conditions r much-lt Δ b much-lt r n , r T , r E are significantly violated. Progress in relaxing these constraints is discussed
Rotational inhomogeneities from pre-big bang?
International Nuclear Information System (INIS)
Giovannini, Massimo
2005-01-01
The evolution of the rotational inhomogeneities is investigated in the specific framework of four-dimensional pre-big bang models. While minimal (dilaton-driven) scenarios do not lead to rotational fluctuations, in the case of non-minimal (string-driven) models, fluid sources are present in the pre-big bang phase. The rotational modes of the geometry, coupled to the divergenceless part of the velocity field, can then be amplified depending upon the value of the barotropic index of the perfect fluids. In the light of a possible production of rotational inhomogeneities, solutions describing the coupled evolution of the dilaton field and of the fluid sources are scrutinized in both the string and Einstein frames. In semi-realistic scenarios, where the curvature divergences are regularized by means of a non-local dilaton potential, the rotational inhomogeneities are amplified during the pre-big bang phase but they decay later on. Similar analyses can also be performed when a contraction occurs directly in the string frame metric
Rotational inhomogeneities from pre-big bang?
Energy Technology Data Exchange (ETDEWEB)
Giovannini, Massimo [Department of Physics, Theory Division, CERN, 1211 Geneva 23 (Switzerland)
2005-01-21
The evolution of the rotational inhomogeneities is investigated in the specific framework of four-dimensional pre-big bang models. While minimal (dilaton-driven) scenarios do not lead to rotational fluctuations, in the case of non-minimal (string-driven) models, fluid sources are present in the pre-big bang phase. The rotational modes of the geometry, coupled to the divergenceless part of the velocity field, can then be amplified depending upon the value of the barotropic index of the perfect fluids. In the light of a possible production of rotational inhomogeneities, solutions describing the coupled evolution of the dilaton field and of the fluid sources are scrutinized in both the string and Einstein frames. In semi-realistic scenarios, where the curvature divergences are regularized by means of a non-local dilaton potential, the rotational inhomogeneities are amplified during the pre-big bang phase but they decay later on. Similar analyses can also be performed when a contraction occurs directly in the string frame metric.
Advances in discrete differential geometry
2016-01-01
This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, ...
Hyperbolic Metamaterials with Complex Geometry
DEFF Research Database (Denmark)
Lavrinenko, Andrei; Andryieuski, Andrei; Zhukovsky, Sergei
2016-01-01
We investigate new geometries of hyperbolic metamaterialssuch as highly corrugated structures, nanoparticle monolayer assemblies, super-structured or vertically arranged multilayersand nanopillars. All structures retain basic propertiesof hyperbolic metamaterials, but have functionality improved...
An introduction to differential geometry
Willmore, T J
2012-01-01
This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.
Symplectic geometry and Fourier analysis
Wallach, Nolan R
2018-01-01
Suitable for graduate students in mathematics, this monograph covers differential and symplectic geometry, homogeneous symplectic manifolds, Fourier analysis, metaplectic representation, quantization, Kirillov theory. Includes Appendix on Quantum Mechanics by Robert Hermann. 1977 edition.
Bio-Inspired Multi-Functional Drug Transport Design Concept and Simulations.
Pidaparti, Ramana M; Cartin, Charles; Su, Guoguang
2017-04-25
In this study, we developed a microdevice concept for drug/fluidic transport taking an inspiration from supramolecular motor found in biological cells. Specifically, idealized multi-functional design geometry (nozzle/diffuser/nozzle) was developed for (i) fluidic/particle transport; (ii) particle separation; and (iii) droplet generation. Several design simulations were conducted to demonstrate the working principles of the multi-functional device. The design simulations illustrate that the proposed design concept is feasible for multi-functionality. However, further experimentation and optimization studies are needed to fully evaluate the multifunctional device concept for multiple applications.
Topology and geometry for physicists
Nash, Charles
1983-01-01
Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. ""Thoroughly recommended"" by The Physics Bulletin, this volume's physics applications range fr
Spectral dimension of quantum geometries
International Nuclear Information System (INIS)
Calcagni, Gianluca; Oriti, Daniele; Thürigen, Johannes
2014-01-01
The spectral dimension is an indicator of geometry and topology of spacetime and a tool to compare the description of quantum geometry in various approaches to quantum gravity. This is possible because it can be defined not only on smooth geometries but also on discrete (e.g., simplicial) ones. In this paper, we consider the spectral dimension of quantum states of spatial geometry defined on combinatorial complexes endowed with additional algebraic data: the kinematical quantum states of loop quantum gravity (LQG). Preliminarily, the effects of topology and discreteness of classical discrete geometries are studied in a systematic manner. We look for states reproducing the spectral dimension of a classical space in the appropriate regime. We also test the hypothesis that in LQG, as in other approaches, there is a scale dependence of the spectral dimension, which runs from the topological dimension at large scales to a smaller one at short distances. While our results do not give any strong support to this hypothesis, we can however pinpoint when the topological dimension is reproduced by LQG quantum states. Overall, by exploring the interplay of combinatorial, topological and geometrical effects, and by considering various kinds of quantum states such as coherent states and their superpositions, we find that the spectral dimension of discrete quantum geometries is more sensitive to the underlying combinatorial structures than to the details of the additional data associated with them. (paper)
Geometrical themes inspired by the n-body problem
Herrera, Haydeé; Herrera, Rafael
2018-01-01
Presenting a selection of recent developments in geometrical problems inspired by the N-body problem, these lecture notes offer a variety of approaches to study them, ranging from variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references. A. Guillot’s notes aim to describe differential equations in the complex domain, motivated by the evolution of N particles moving on the plane subject to the influence of a magnetic field. Guillot studies such differential equations using different geometric structures on complex curves (in the sense of W. Thurston) in order to find isochronicity conditions. R. Montgomery’s notes deal with a version of the planar Newtonian three-body equation. Namely, he investigates the problem of whether every free homotopy class is realized by a periodic geodesic. The solution involves geometry, dynamical systems, and the McGehee blow-up. A novelty of the approach is the use of energy-balance in order t...
A microfabricated gecko-inspired controllable and reusable dry adhesive
International Nuclear Information System (INIS)
Chary, Sathya; Tamelier, John; Turner, Kimberly
2013-01-01
Geckos utilize a robust reversible adhesive to repeatedly attach and detach from a variety of vertical and inverted surfaces, using structurally anisotropic micro- and nano-scale fibrillar structures. These fibers, when suitably articulated, are able to control the real area of contact and thereby generate high-to-low van der Waals forces. Key characteristics of the natural system include highly anisotropic adhesion and shear forces for controllable attachment, a high adhesion to initial preload force ratio (μ′) of 8–16, lack of inter-fiber self-adhesion, and operation over more than 30 000 cycles without loss of adhesion performance. A highly reusable synthetic adhesive has been developed using tilted polydimethylsiloxane (PDMS) half-cylinder micron-scale fibers, retaining up to 77% of the initial value over 10 000 repeated test cycles against a flat glass puck. In comparison with other gecko-inspired adhesives tested over 10 000 cycles or more thus far, this paper reports the highest value of μ′, along with a large shear force of ∼78 kPa, approaching the 88–226 kPa range of gecko toes. The anisotropic adhesion forces are close to theoretical estimates from the Kendall peel model, quantitatively showing how lateral shearing articulation in a manner similar to the gecko may be used to obtain adhesion anisotropy with synthetic fibers using a combination of tilt angle and anisotropic fiber geometry. (paper)
Hydrodynamics of an Under-actuated Plesiosaur-inspired robot
Weymouth, Gabriel; Devereux, Kate; Copsey, Nick; Muscutt, Luke; Downes, Jon; Ganapathisubramani, Bharath
2017-11-01
Underwater vehicles are increasingly important tools for use in science and engineering, but maneuverability and mission life seem to be mutually exclusive goals. Inspired by the unique swimming method of the plesiosaur, which used four flippers of essentially equal size and musculature, we analyzed designed and built an underwater vehicle with the potential for both gliding and active maneuvering modes. Using 2D simulations and strip theory approximation to account for the changing arc length along the flipper span, we studied the wake and forces on the foils and determined the optimum flipper geometry, spacing and kinematics. To reduce mechanical and control complexity and cost, we next studied the impact of under-actuated kinematics. Even after optimizing pivot location and range of motion, leaving the foils free to pitch was found to reduce efficiency by approximately 50%. Based on these specifications, the vehicle was built and tested over a range of free swimming and maneuvering cases using motion tracking equipment. The excellent maneuverability of the under-actuated vehicle validates the concept, and the new platform should enable further detailed experimental measurements in the future.
Contact problem for a composite material with nacre inspired microstructure
Berinskii, Igor; Ryvkin, Michael; Aboudi, Jacob
2017-12-01
Bi-material composites with nacre inspired brick and mortar microstructures, characterized by stiff elements of one phase with high aspect ratio separated by thin layers of the second one, are considered. Such microstructure is proved to provide an efficient solution for the problem of a crack arrest. However, contrary to the case of a homogeneous material, an external pressure, applied to a part of the composite boundary, can cause significant tensile stresses which increase the danger of crack nucleation. Investigation of the influence of microstructure parameters on the magnitude of tensile stresses is performed by means of the classical Flamant-like problem of an orthotropic half-plane subjected to a normal external distributed loading. Adequate analysis of this problem represents a serious computational task due to the geometry of the considered layout and the high contrast between the composite constituents. This difficulty is presently circumvented by deriving a micro-to-macro analysis in the framework of which an analytical solution of the auxiliary elasticity problem, followed by the discrete Fourier transform and the higher-order theory are employed. As a result, full scale continuum modeling of both composite constituents without employing any simplifying assumptions is presented. In the framework of the present proposed modeling, the influence of stiff elements aspect ratio on the overall stress distribution is demonstrated.
A microfabricated gecko-inspired controllable and reusable dry adhesive
Chary, Sathya; Tamelier, John; Turner, Kimberly
2013-02-01
Geckos utilize a robust reversible adhesive to repeatedly attach and detach from a variety of vertical and inverted surfaces, using structurally anisotropic micro- and nano-scale fibrillar structures. These fibers, when suitably articulated, are able to control the real area of contact and thereby generate high-to-low van der Waals forces. Key characteristics of the natural system include highly anisotropic adhesion and shear forces for controllable attachment, a high adhesion to initial preload force ratio (μ‧) of 8-16, lack of inter-fiber self-adhesion, and operation over more than 30 000 cycles without loss of adhesion performance. A highly reusable synthetic adhesive has been developed using tilted polydimethylsiloxane (PDMS) half-cylinder micron-scale fibers, retaining up to 77% of the initial value over 10 000 repeated test cycles against a flat glass puck. In comparison with other gecko-inspired adhesives tested over 10 000 cycles or more thus far, this paper reports the highest value of μ‧, along with a large shear force of ˜78 kPa, approaching the 88-226 kPa range of gecko toes. The anisotropic adhesion forces are close to theoretical estimates from the Kendall peel model, quantitatively showing how lateral shearing articulation in a manner similar to the gecko may be used to obtain adhesion anisotropy with synthetic fibers using a combination of tilt angle and anisotropic fiber geometry.
InSpiRe - Intelligent Spine Rehabilitation
DEFF Research Database (Denmark)
Bøg, Kasper Hafstrøm; Helms, Niels Henrik; Kjær, Per
Rapport on InSpiRe-projektet: InSpiRe er et nationalt netværk, der skal fremme mulighederne for intelligent genoptræning i forhold til ryglidelser. I netværket mødes forskere, virksomheder, kiropraktorer og fysioterapeuter for at udvikle nye genoptrænings og/eller behandlingsteknologier.......Rapport on InSpiRe-projektet: InSpiRe er et nationalt netværk, der skal fremme mulighederne for intelligent genoptræning i forhold til ryglidelser. I netværket mødes forskere, virksomheder, kiropraktorer og fysioterapeuter for at udvikle nye genoptrænings og/eller behandlingsteknologier....
Taxonomic etymology – in search of inspiration
Directory of Open Access Journals (Sweden)
Piotr Jozwiak
2015-07-01
Full Text Available We present a review of the etymology of zoological taxonomic names with emphasis on the most unusual examples. The names were divided into several categories, starting from the most common – given after morphological features – through inspiration from mythology, legends, and classic literature but also from fictional and nonfictional pop-culture characters (e.g., music, movies or cartoons, science, and politics. A separate category includes zoological names created using word-play and figures of speech such as tautonyms, acronyms, anagrams, and palindromes. Our intention was to give an overview of possibilities of how and where taxonomists can find the inspirations that will be consistent with the ICZN rules and generate more detail afterthought about the naming process itself, the meaningful character of naming, as well as the recognition and understanding of names.
Biologically inspired water purification through selective transport
International Nuclear Information System (INIS)
Freeman, E C; Soncini, R M; Weiland, L M
2013-01-01
Biologically inspired systems based on cellular mechanics demonstrate the ability to selectively transport ions across a bilayer membrane. These systems may be observed in nature in plant roots, which remove select nutrients from the surrounding soil against significant concentration gradients. Using biomimetic principles in the design of tailored active materials allows for the development of selective membranes for capturing and filtering targeted ions. Combining this biomimetic transport system with a method for reclaiming the captured ions will allow for increased removal potential. To illustrate this concept, a device for removing nutrients from waterways to aid in reducing eutrophication is outlined and discussed. Presented is a feasibility study of various cellular configurations designed for this purpose, focusing on maximizing nutrient uptake. The results enable a better understanding of the benefits and obstacles when developing these cellularly inspired systems. (paper)
A new perspective on relativity an odyssey in non-Euclidean geometries
Lavenda, Bernard H
2012-01-01
Starting off from noneuclidean geometries, apart from the method of Einstein's equations, this book derives and describes the phenomena of gravitation and diffraction. A historical account is presented, exposing the missing link in Einstein's construction of the theory of general relativity: the uniformly rotating disc, together with his failure to realize, that the Beltrami metric of hyperbolic geometry with constant curvature describes exactly the uniform acceleration observed.
Neurobiologically inspired mobile robot navigation and planning
Directory of Open Access Journals (Sweden)
Mathias Quoy
2007-11-01
Full Text Available After a short review of biologically inspired navigation architectures, mainly relying on modeling the hippocampal anatomy, or at least some of its functions, we present a navigation and planning model for mobile robots. This architecture is based on a model of the hippocampal and prefrontal interactions. In particular, the system relies on the definition of a new cell type “transition cells” that encompasses traditional “place cells”.
Biological Inspiration for Agile Autonomous Air Vehicles
2007-11-01
half of one wing, bees with legs packed with pollen , butterflies or moths with torn and frayed wings likewise are capable of apparently normal flight...technologies. To appreciate this, consider a not unreasonable extension of a wide area autonomous search (WAAS) munition operational scenario. Here...detect and destroy missile launchers that are operating in the back alleys of an urban areas or search Evers, J.H. (2007) Biological Inspiration for Agile
Humidification of inspired gases during mechanical ventilation.
Gross, J L; Park, G R
2012-04-01
Humidification of inspired gas is mandatory for all mechanically ventilated patients to prevent secretion retention, tracheal tube blockage and adverse changes occurring to the respiratory tract epithelium. However, the debate over "ideal" humidification continues. Several devices are available that include active and passive heat and moisture exchangers and hot water humidifiers Each have their advantages and disadvantages in mechanically ventilated patients. This review explores each device in turn and defines their role in clinical practice.
Drawing inspiration from biological optical systems
Wolpert, H. D.
2009-08-01
Bio-Mimicking/Bio-Inspiration: How can we not be inspired by Nature? Life has evolved on earth over the last 3.5 to 4 billion years. Materials formed during this time were not toxic; they were created at low temperatures and low pressures unlike many of the materials developed today. The natural materials formed are self-assembled, multifunctional, nonlinear, complex, adaptive, self-repairing and biodegradable. The designs that failed are fossils. Those that survived are the success stories. Natural materials are mostly formed from organics, inorganic crystals and amorphous phases. The materials make economic sense by optimizing the design of the structures or systems to meet multiple needs. We constantly "see" many similar strategies in approaches, between man and nature, but we seldom look at the details of natures approaches. The power of image processing, in many of natures creatures, is a detail that is often overlooked. Seldon does the engineer interact with the biologist and learn what nature has to teach us. The variety and complexity of biological materials and the optical systems formed should inspire us.
Biologically inspired coupled antenna beampattern design
Energy Technology Data Exchange (ETDEWEB)
Akcakaya, Murat; Nehorai, Arye, E-mail: makcak2@ese.wustl.ed, E-mail: nehorai@ese.wustl.ed [Department of Electrical and Systems Engineering, Washington University in St Louis, St Louis, MO 63130 (United States)
2010-12-15
We propose to design a small-size transmission-coupled antenna array, and corresponding radiation pattern, having high performance inspired by the female Ormia ochracea's coupled ears. For reproduction purposes, the female Ormia is able to locate male crickets' call accurately despite the small distance between its ears compared with the incoming wavelength. This phenomenon has been explained by the mechanical coupling between the Ormia's ears, which has been modeled by a pair of differential equations. In this paper, we first solve these differential equations governing the Ormia ochracea's ear response, and convert the response to the pre-specified radio frequencies. We then apply the converted response of the biological coupling in the array factor of a uniform linear array composed of finite-length dipole antennas, and also include the undesired electromagnetic coupling due to the proximity of the elements. Moreover, we propose an algorithm to optimally choose the biologically inspired coupling for maximum array performance. In our numerical examples, we compute the radiation intensity of the designed system for binomial and uniform ordinary end-fire arrays, and demonstrate the improvement in the half-power beamwidth, sidelobe suppression and directivity of the radiation pattern due to the biologically inspired coupling.
International Nuclear Information System (INIS)
Binzel, R.P.; Farinella, P.
1989-01-01
Within the last decade the data base of asteroid rotation parameters (rotation rates and lightcurve amplitudes) has become sufficiently large to identify some definite rends and properties which can help us to interpret asteroid collisional evolution. Many significant correlations are found between rotation parameters and diameter, with distinct changes occurring near 125 km. The size range, which is also the diameter above which self-gravity may become important, perhaps represents a division between surviving primordial asteroids and collisional fragments. A Maxwellian is able to fit the observed rotation rate distributions of asteroids with D>125 km, implying that their rotation rates may be determined by collisional evolution. Asteroids with D<125 km show an excess of slow rotators and their non-Maxwellian distributions suggests that their rotation rates are more strongly influenced by other processes, such as the distribution resulting from their formation in catastrophic disruption events. Other correlations observed in the data set include different mean rotation rates for C, S and M type asteroids implying that their surface spectra are indicative of bulk properties
DEFF Research Database (Denmark)
Rasmusson, Allan; Hahn, Ute; Larsen, Jytte Overgaard
2013-01-01
This paper presents a new local volume estimator, the spatial rotator, which is based on measurements on a virtual 3D probe, using computer assisted microscopy. The basic design of the probe builds upon the rotator principle which requires only a few manual intersection markings, thus making...
Superconducting rotating machines
International Nuclear Information System (INIS)
Smith, J.L. Jr.; Kirtley, J.L. Jr.; Thullen, P.
1975-01-01
The opportunities and limitations of the applications of superconductors in rotating electric machines are given. The relevant properties of superconductors and the fundamental requirements for rotating electric machines are discussed. The current state-of-the-art of superconducting machines is reviewed. Key problems, future developments and the long range potential of superconducting machines are assessed
Fundamental Relativistic Rotator
International Nuclear Information System (INIS)
Staruszkiewicz, A.
2008-01-01
Professor Jan Weyssenhoff was Myron Mathisson's sponsor and collaborator. He introduced a class of objects known in Cracow as '' kreciolki Weyssenhoffa '', '' Weyssenhoff's rotating little beasts ''. The Author describes a particularly simple object from this class. The relativistic rotator described in the paper is such that its both Casimir invariants are parameters rather than constants of motion. (author)
Le Vine, David
2016-01-01
Faraday rotation is a change in the polarization as signal propagates through the ionosphere. At L-band it is necessary to correct for this change and measurements are made on the spacecraft of the rotation angle. These figures show that there is good agreement between the SMAP measurements (blue) and predictions based on models (red).
Units of rotational information
Yang, Yuxiang; Chiribella, Giulio; Hu, Qinheping
2017-12-01
Entanglement in angular momentum degrees of freedom is a precious resource for quantum metrology and control. Here we study the conversions of this resource, focusing on Bell pairs of spin-J particles, where one particle is used to probe unknown rotations and the other particle is used as reference. When a large number of pairs are given, we show that every rotated spin-J Bell state can be reversibly converted into an equivalent number of rotated spin one-half Bell states, at a rate determined by the quantum Fisher information. This result provides the foundation for the definition of an elementary unit of information about rotations in space, which we call the Cartesian refbit. In the finite copy scenario, we design machines that approximately break down Bell states of higher spins into Cartesian refbits, as well as machines that approximately implement the inverse process. In addition, we establish a quantitative link between the conversion of Bell states and the simulation of unitary gates, showing that the fidelity of probabilistic state conversion provides upper and lower bounds on the fidelity of deterministic gate simulation. The result holds not only for rotation gates, but also to all sets of gates that form finite-dimensional representations of compact groups. For rotation gates, we show how rotations on a system of given spin can simulate rotations on a system of different spin.
The structure of sidewall boundary layers in conned rotating Rayleigh-Bénard convection
Kunnen, R.P.J.; Clercx, H.J.H.; van Heijst, G.J.F.
2013-01-01
Turbulent rotating convection is usually studied in a cylindrical geometry, as this is its most convenient experimental realization. In our previous work (Kunnen et al., J. Fluid Mech., vol. 688, 2011, pp. 422–442) we studied turbulent rotating convection in a cylinder with the emphasis on the
International Nuclear Information System (INIS)
Ruben, G.; Treder, H.J.
1987-01-01
For a long time the question whether the universe rotates or not is discussed. Aspects of Huygens, Newton, Mach and other important historical scientists in this field are reported. The investigations of the mathematician Kurt Groedel in order to prove the rotation of the universe are illustrated. Kurt Groedel has shown that Einstein's gravitational equations of general relativity theory and the cosmological postulate of global homogeneity of cosmic matter (that is the Copernical principle) are not contradictionary to a rotating universe. Abberation measurements, position determination by means of radiointerferometry and methods for the determination of the rotation of the universe from the isotropy of the background radiation are presented. From these experiments it can be concluded that the universe seems not to rotate as already Einstein expected
International Nuclear Information System (INIS)
Sevec, J.B.
1978-01-01
A protective device to provide a warning if a piece of rotating machinery slows or stops is comprised of a pair of hinged weights disposed to rotate on a rotating shaft of the equipment. When the equipment is rotating, the weights remain in a plane essentially perpendicular to the shaft and constitute part of an electrical circuit that is open. When the shaft slows or stops, the weights are attracted to a pair of concentric electrically conducting disks disposed in a plane perpendicular to the shaft and parallel to the plane of the weights when rotating. A disk magnet attracts the weights to the electrically conducting plates and maintains the electrical contact at the plates to complete an electrical circuit that can then provide an alarm signal
Paschalidis, Vasileios; Stergioulas, Nikolaos
2017-01-01
Rotating relativistic stars have been studied extensively in recent years, both theoretically and observationally, because of the information they might yield about the equation of state of matter at extremely high densities and because they are considered to be promising sources of gravitational waves. The latest theoretical understanding of rotating stars in relativity is reviewed in this updated article. The sections on equilibrium properties and on nonaxisymmetric oscillations and instabilities in f -modes and r -modes have been updated. Several new sections have been added on equilibria in modified theories of gravity, approximate universal relationships, the one-arm spiral instability, on analytic solutions for the exterior spacetime, rotating stars in LMXBs, rotating strange stars, and on rotating stars in numerical relativity including both hydrodynamic and magnetohydrodynamic studies of these objects.
Extension of the comet method to 2-D hexagonal geometry
International Nuclear Information System (INIS)
Connolly, Kevin John; Rahnema, Farzad; Zhang, Dingkang
2011-01-01
The capability of the heterogeneous coarse mesh radiation transport (COMET) method developed at Georgia Tech has been expanded. COMET is now able to treat hexagonal geometry in two dimensions, allowing reactor problems to be solved for those next-generation reactors which utilize prismatic block structure and hexagonal lattice geometry in their designs. The COMET method is used to solve whole core reactor analysis problems without resorting to homogenization or low-order transport approximations. The eigenvalue and fission density distribution of the reactor are determined iteratively using response functions. The method has previously proven accurate in solving PWR, BWR, and CANDU eigenvalue problems. In this paper, three simple test cases inspired by high temperature test reactor material cross sections and fuel block geometry are presented. These cases are given not in an attempt to model realistic nuclear power systems, but in order to test the ability of the improved method. Solutions determined by the new hexagonal version of COMET, COMET-Hex, are compared with solutions determined by MCNP5, and the results show the accuracy and efficiency of the improved COMET-Hex method in calculating the eigenvalue and fuel pin fission density in sample full-core problems. COMETHex determines the eigenvalues of these simple problems to an order of within 50 pcm of the reference solutions and all pin fission densities to an average error of 0.2%, and it requires fewer than three minutes to produce these results. (author)
Interplay between geometry and temperature in the Casimir effect
Energy Technology Data Exchange (ETDEWEB)
Weber, Alexej
2010-06-23
In this thesis, we investigate the interplay between geometry and temperature in the Casimir effect for the inclined-plates, sphere-plate and cylinder-plate configurations. We use the worldline approach, which combines the string-inspired quantum field theoretical formalism with Monte Carlo techniques. The approach allows the precise computation of Casimir energies in arbitrary geometries. We analyze the dependence of the Casimir energy, force and torque on the separation parameter and temperature T, and find Casimir phenomena which are dominated by long-range fluctuations. We demonstrate that for open geometries, thermal energy densities are typically distributed on scales of thermal wavelengths. As an important consequence, approximation methods for thermal corrections based on local energy-density estimates, such as the proximity-force approximation, are found to become unreliable even at small surface-separations. Whereas the hightemperature behavior is always found to be linear in T, richer power-law behaviors at small temperatures emerge. In particular, thermal forces can develop a non-monotonic behavior. Many novel numerical as well as analytical results are presented. (orig.)
Interplay between geometry and temperature in the Casimir effect
International Nuclear Information System (INIS)
Weber, Alexej
2010-01-01
In this thesis, we investigate the interplay between geometry and temperature in the Casimir effect for the inclined-plates, sphere-plate and cylinder-plate configurations. We use the worldline approach, which combines the string-inspired quantum field theoretical formalism with Monte Carlo techniques. The approach allows the precise computation of Casimir energies in arbitrary geometries. We analyze the dependence of the Casimir energy, force and torque on the separation parameter and temperature T, and find Casimir phenomena which are dominated by long-range fluctuations. We demonstrate that for open geometries, thermal energy densities are typically distributed on scales of thermal wavelengths. As an important consequence, approximation methods for thermal corrections based on local energy-density estimates, such as the proximity-force approximation, are found to become unreliable even at small surface-separations. Whereas the hightemperature behavior is always found to be linear in T, richer power-law behaviors at small temperatures emerge. In particular, thermal forces can develop a non-monotonic behavior. Many novel numerical as well as analytical results are presented. (orig.)
Directory of Open Access Journals (Sweden)
Edwin Eduardo Millán Rojas
2018-02-01
Full Text Available Context: Management to care for the environment and the Earth (geo can be source of inspiration for developing models that allow addressing complexity issues; the objective of this research was to develop an additional aspect of the inspired models. The geoinspired model has two features, the first covering aspects related to environmental management and the behavior of natural resources, and the second has a component of spatial location associated with existing objects on the Earth's surface. Method: The approach developed in the research is descriptive and its main objective is the representation or characterization of a case study within a particular context. Results: The result was the design of a model to emulate the natural behavior of the water tributaries of the Amazon foothills, in order to extend the application of the inspired models and allow the use of elements such as geo-referencing and environmental management. The proposed geoinspired model is called “natural vectors agents inspired in environmental management”. Conclusions: The agents vectors naturals inspired by the environmental are polyform elements that can assume the behavior of environmental entities, which makes it possible to achieve progress in other fields of environmental management (use of soil, climate, flora, fauna, and link environmental issues with the structure of the proposed model.
Modeling flow for modified concentric cylinder rheometer geometry
Ekeruche, Karen; Connelly, Kelly; Kavehpour, H. Pirouz
2016-11-01
Rheology experiments on biological fluids can be difficult when samples are limited in volume, sensitive to degradation, and delicate to extract from tissues. A probe-like geometry has been developed to perform shear creep experiments on biological fluids and to use the creep response to characterize fluid material properties. This probe geometry is a modified concentric cylinder setup, where the gap is large and we assume the inner cylinder rotates in an infinite fluid. To validate this assumption we perform shear creep tests with the designed probe on Newtonian and non-Newtonian fluids and vary the outer cylinder container diameter. We have also created a numerical model based on the probe geometry setup to compare with experimental results at different outer cylinder diameters. A creep test is modeled by applying rotation to the inner cylinder and solving for the deformation of the fluid throughout the gap. Steady state viscosity values are calculated from creep compliance curves and compared between experimental and numerical results.
Feeling Is Believing: Inspiration Encourages Belief in God.
Critcher, Clayton R; Lee, Chan Jean
2018-05-01
Even without direct evidence of God's existence, about half of the world's population believes in God. Although previous research has found that people arrive at such beliefs intuitively instead of analytically, relatively little research has aimed to understand what experiences encourage or legitimate theistic belief systems. Using cross-cultural correlational and experimental methods, we investigated whether the experience of inspiration encourages a belief in God. Participants who dispositionally experience more inspiration, were randomly assigned to relive or have an inspirational experience, or reported such experiences to be more inspirational all showed stronger belief in God. These effects were specific to inspiration (instead of adjacent affective experiences) and a belief in God (instead of other empirically unverifiable claims). Being inspired by someone or something (but not inspired to do something) offers a spiritually transcendent experience that elevates belief in God, in part because it makes people feel connected to something beyond themselves.
Spatial reorientation by geometry in bumblebees.
Directory of Open Access Journals (Sweden)
Valeria Anna Sovrano
Full Text Available Human and non-human animals are capable of using basic geometric information to reorient in an environment. Geometric information includes metric properties associated with spatial surfaces (e.g., short vs. long wall and left-right directionality or 'sense' (e.g. a long wall to the left of a short wall. However, it remains unclear whether geometric information is encoded by explicitly computing the layout of surface geometry or by matching images of the environment. View-based spatial encoding is generally thought to hold for insect navigation and, very recently, evidence for navigation by geometry has been reported in ants but only in a condition which does not allow the animals to use features located far from the goal. In this study we tested the spatial reorientation abilities of bumblebees (Bombus terrestris. After spatial disorientation, by passive rotation both clockwise and anticlockwise, bumblebees had to find one of the four exit holes located in the corners of a rectangular enclosure. Bumblebees systematically confused geometrically equivalent exit corners (i.e. corners with the same geometric arrangement of metric properties and sense, for example a short wall to the left of a long wall. However, when one wall of the enclosure was a different colour, bumblebees appeared to combine this featural information (either near or far from the goal with geometric information to find the correct exit corner. Our results show that bumblebees are able to use both geometric and featural information to reorient themselves, even when features are located far from the goal.
Flux compactifications and generalized geometries
International Nuclear Information System (INIS)
Grana, Mariana
2006-01-01
Following the lectures given at CERN Winter School 2006, we present a pedagogical overview of flux compactifications and generalized geometries, concentrating on closed string fluxes in type II theories. We start by reviewing the supersymmetric flux configurations with maximally symmetric four-dimensional spaces. We then discuss the no-go theorems (and their evasion) for compactifications with fluxes. We analyse the resulting four-dimensional effective theories for Calabi-Yau and Calabi-Yau orientifold compactifications, concentrating on the flux-induced superpotentials. We discuss the generic mechanism of moduli stabilization and illustrate with two examples: the conifold in IIB and a T 6 /(Z 3 x Z 3 ) torus in IIA. We finish by studying the effective action and flux vacua for generalized geometries in the context of generalized complex geometry
Flux compactifications and generalized geometries
Energy Technology Data Exchange (ETDEWEB)
Grana, Mariana [Service de Physique Theorique, CEA/Saclay, 91191 Gif-sur-Yvette Cedex (France)
2006-11-07
Following the lectures given at CERN Winter School 2006, we present a pedagogical overview of flux compactifications and generalized geometries, concentrating on closed string fluxes in type II theories. We start by reviewing the supersymmetric flux configurations with maximally symmetric four-dimensional spaces. We then discuss the no-go theorems (and their evasion) for compactifications with fluxes. We analyse the resulting four-dimensional effective theories for Calabi-Yau and Calabi-Yau orientifold compactifications, concentrating on the flux-induced superpotentials. We discuss the generic mechanism of moduli stabilization and illustrate with two examples: the conifold in IIB and a T{sup 6} /(Z{sub 3} x Z{sub 3}) torus in IIA. We finish by studying the effective action and flux vacua for generalized geometries in the context of generalized complex geometry.
Euclidean geometry and its subgeometries
Specht, Edward John; Calkins, Keith G; Rhoads, Donald H
2015-01-01
In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings. The authors present thirteen axioms in sequence, proving as many theorems as possible at each stage and, in the process, building up subgeometries, most notably the Pasch and neutral geometries. Standard topics such as the congruence theorems for triangles, embedding the real numbers in a line, and coordinatization of the plane are included, as well as theorems of Pythagoras, Desargues, Pappas, Menelaus, and Ceva. The final chapter covers consistency and independence of axioms, as well as independence of definition properties. There are over 300 exercises; solutions to many of the...
Guide to Computational Geometry Processing
DEFF Research Database (Denmark)
Bærentzen, Jakob Andreas; Gravesen, Jens; Anton, François
be processed before it is useful. This Guide to Computational Geometry Processing reviews the algorithms for processing geometric data, with a practical focus on important techniques not covered by traditional courses on computer vision and computer graphics. This is balanced with an introduction...... to the theoretical and mathematical underpinnings of each technique, enabling the reader to not only implement a given method, but also to understand the ideas behind it, its limitations and its advantages. Topics and features: Presents an overview of the underlying mathematical theory, covering vector spaces......, metric space, affine spaces, differential geometry, and finite difference methods for derivatives and differential equations Reviews geometry representations, including polygonal meshes, splines, and subdivision surfaces Examines techniques for computing curvature from polygonal meshes Describes...
Electrodynamics and Spacetime Geometry: Foundations
Cabral, Francisco; Lobo, Francisco S. N.
2017-02-01
We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry (and causal structure) of spacetime.
DOGBONE GEOMETRY FOR RECIRCULATING ACCELERATORS
International Nuclear Information System (INIS)
BERG, J.S.; JOHNSTONE, C.; SUMMERS, D.
2001-01-01
Most scenarios for accelerating muons require recirculating acceleration. A racetrack shape for the accelerator requires particles with lower energy in early passes to traverse almost the same length of arc as particles with the highest energy. This extra arc length may lead to excess decays and excess cost. Changing the geometry to a dogbone shape, where there is a single linac and the beam turns completely around at the end of the linac, returning to the same end of the linac from which it exited, addresses this problem. In this design, the arc lengths can be proportional to the particle's momentum. This paper proposes an approximate cost model for a recirculating accelerator, attempts to make cost-optimized designs for both racetrack and dogbone geometries, and demonstrates that the dogbone geometry does appear to be more cost effective
Geometric Transformations in Engineering Geometry
Directory of Open Access Journals (Sweden)
I. F. Borovikov
2015-01-01
Full Text Available Recently, for business purposes, in view of current trends and world experience in training engineers, research and faculty staff there has been a need to transform traditional courses of descriptive geometry into the course of engineering geometry in which the geometrical transformations have to become its main section. On the basis of critical analysis the paper gives suggestions to improve a presentation technique of this section both in the classroom and in academic literature, extend an application scope of geometrical transformations to solve the position and metric tasks and simulation of surfaces, as well as to design complex engineering configurations, which meet a number of pre-specified conditions.The article offers to make a number of considerable amendments to the terms and definitions used in the existing courses of descriptive geometry. It draws some conclusions and makes the appropriate proposals on feasibility of coordination in teaching the movement transformation in the courses of analytical and descriptive geometry. This will provide interdisciplinary team teaching and allow students to be convinced that a combination of analytical and graphic ways to solve geometric tasks is useful and reasonable.The traditional sections of learning courses need to be added with a theory of projective and bi-rational transformations. In terms of application simplicity and convenience it is enough to consider the central transformations when solving the applied tasks. These transformations contain a beam of sub-invariant (low-invariant straight lines on which the invariant curve induces non-involution and involution projectivities. The expediency of nonlinear transformations application is shown in the article by a specific example of geometric modeling of the interfacing surface "spar-blade".Implementation of these suggestions will contribute to a real transformation of a traditional course of descriptive geometry to the engineering geometry
Horizon quantum mechanics of rotating black holes
Energy Technology Data Exchange (ETDEWEB)
Casadio, Roberto [Universita di Bologna, Dipartimento di Fisica e Astronomia, Bologna (Italy); I.N.F.N., Sezione di Bologna, I.S. FLAG, Bologna (Italy); Giugno, Andrea [Ludwig-Maximilians-Universitaet, Arnold Sommerfeld Center, Munich (Germany); Giusti, Andrea [Universita di Bologna, Dipartimento di Fisica e Astronomia, Bologna (Italy); I.N.F.N., Sezione di Bologna, I.S. FLAG, Bologna (Italy); Ludwig-Maximilians-Universitaet, Arnold Sommerfeld Center, Munich (Germany); Micu, Octavian [Institute of Space Science, Bucharest, P.O. Box MG-23, Bucharest-Magurele (Romania)
2017-05-15
The horizon quantum mechanics is an approach that was previously introduced in order to analyze the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. In this work, we first extend the formalism to general space-times with asymptotic (ADM) mass and angular momentum. We then apply the extended horizon quantum mechanics to a harmonic model of rotating corpuscular black holes. We find that simple configurations of this model naturally suppress the appearance of the inner horizon and seem to disfavor extremal (macroscopic) geometries. (orig.)
Graphical debugging of combinational geometry
International Nuclear Information System (INIS)
Burns, T.J.; Smith, M.S.
1992-01-01
A graphical debugger for combinatorial geometry being developed at Oak Ridge National Laboratory is described. The prototype debugger consists of two parts: a FORTRAN-based ''view'' generator and a Microsoft Windows application for displaying the geometry. Options and features of both modules are discussed. Examples illustrating the various options available are presented. The potential for utilizing the images produced using the debugger as a visualization tool for the output of the radiation transport codes is discussed as is the future direction of the development
Lectures on Algebraic Geometry I
Harder, Gunter
2012-01-01
This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own. In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern metho
Combinatorial geometry in the plane
Hadwiger, Hugo; Klee, Victor
2014-01-01
Geared toward advanced undergraduates familiar with analysis and college geometry, this concise book discusses theorems on topics restricted to the plane such as convexity, coverings, and graphs. In addition to helping students cultivate rigorous thought, the text encourages the development of mathematical intuition and clarifies the nature of mathematical research.The two-part treatment begins with specific topics including integral distances, covering problems, point set geometry and convexity, simple paradoxes involving point sets, and pure combinatorics, among other subjects. The second pa
Modern differential geometry for physicists
Isham, C J
1989-01-01
These notes are the content of an introductory course on modern, coordinate-free differential geometry which is taken by the first-year theoretical physics PhD students, or by students attending the one-year MSc course "Fundamental Fields and Forces" at Imperial College. The book is concerned entirely with mathematics proper, although the emphasis and detailed topics have been chosen with an eye to the way in which differential geometry is applied these days to modern theoretical physics. This includes not only the traditional area of general relativity but also the theory of Yang-Mills fields
Comparison theorems in Riemannian geometry
Cheeger, Jeff
2008-01-01
The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem-the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most re
Geometry, topology, and string theory
Energy Technology Data Exchange (ETDEWEB)
Varadarajan, Uday [Univ. of California, Berkeley, CA (United States)
2003-01-01
A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.
Spatial geometry and special relativity
DEFF Research Database (Denmark)
Kneubil, Fabiana Botelho
2016-01-01
In this work, it is shown the interplay of relative and absolute entities, which are present in both spatial geometry and special relativity. In order to strengthen the understanding of special relativity, we discuss firstly an instance of geometry and the existence of both frame......-dependent and frame-independent entities. We depart from a subject well known by students, which is the three-dimensional geometric space in order to compare, afterwards, with the treatment of four-dimensional space in the special relativity. The differences and similarities between these two subjects are also...
Stochastic geometry and its applications
Chiu, Sung Nok; Kendall, Wilfrid S; Mecke, Joseph
2013-01-01
An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis. The previous edition of this book has served as the key reference in its field for over 18 years and is regarded as the best treatment of the subject of stochastic geometry, both as a subject with vital a
Introduction to topology and geometry
Stahl, Saul
2014-01-01
An easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition ". . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained." -CHOICE This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparallele
Algebraic geometry and theta functions
Coble, Arthur B
1929-01-01
This book is the result of extending and deepening all questions from algebraic geometry that are connected to the central problem of this book: the determination of the tritangent planes of a space curve of order six and genus four, which the author treated in his Colloquium Lecture in 1928 at Amherst. The first two chapters recall fundamental ideas of algebraic geometry and theta functions in such fashion as will be most helpful in later applications. In order to clearly present the state of the central problem, the author first presents the better-known cases of genus two (Chapter III) and
Geometry, topology, and string theory
International Nuclear Information System (INIS)
Varadarajan, Uday
2003-01-01
A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated
Rotation, Stability and Transport
Energy Technology Data Exchange (ETDEWEB)
Connor, J. W.
2007-07-01
Tokamak plasmas can frequently exhibit high levels of rotation and rotation shear. This can usually be attributed to various sources: injection of momentum, e.g. through neutral beams, flows driven by plasma gradients or torques resulting from non-ambipolar particle loss; however, the source sometimes remains a mystery, such as the spontaneous rotation observed in Ohmic plasmas. The equilibrium rotation profile is given by the balance of these sources with transport and other losses; the edge boundary conditions can play an important role in determining this profile . Such plasma rotation, particularly sheared rotation, is predicted theoretically to have a significant influence on plasma behaviour. In the first place, sonic flows can significantly affect tokamak equilibria and neoclassical transport losses. However, the influence of rotation on plasma stability and turbulence is more profound. At the macroscopic level it affects the behaviour of the gross MHD modes that influence plasma operational limits. This includes sawteeth, the seeding of neoclassical tearing modes, resistive wall modes and the onset of disruptions through error fields, mode locking and reconnection. At the microscopic level it has a major effect on the stability of ballooning modes, both ideal MHD and drift wave instabilities such as ion temperature gradient (ITG) modes. In the non-linear state, as unstable drift waves evolve into turbulent structures, sheared rotation also tears apart eddies, thereby reducing the resulting transport. There is considerable experimental evidence for these effects on both MHD stability and plasma confinement. In particular, the appearance of improved confinement modes with transport barriers, such as edge H-mode barriers and internal transport barriers (ITBs) appears to correlate well with the presence of sheared plasma rotation. This talk will describe the theory underlying some of these phenomena involving plasma rotation, on both macroscopic and microscopic
Metin M. Cosgel; Thomas J. Miceli
1998-01-01
A fundamental principle of economics with which Adam Smith begins The Wealth of Nations is the division of labor. Some firms, however, have been pursuing a practice called job rotation, which assigns each worker not to a single and specific task but to a set of several tasks among which he or she rotates with some frequency. We examine the practice of job rotation as a serious alternative to specialization, with three objectives. The first is to consider current and historical examples of job...
... this page: //medlineplus.gov/ency/patientinstructions/000358.htm Rotator cuff - self-care To use the sharing features on ... and shoulder exercises may help ease your symptoms. Rotator Cuff Problems Common rotator cuff problems include: Tendinitis , which ...
The Idea of Order at Geometry Class.
Rishel, Thomas
The idea of order in geometry is explored using the experience of assignments given to undergraduates in a college geometry course "From Space to Geometry." Discussed are the definition of geometry, and earth measurement using architecture, art, and common experience. This discussion concludes with a consideration of the question of whether…
Teaching Spatial Geometry in a Virtual World
DEFF Research Database (Denmark)
Förster, Klaus-Tycho
2017-01-01
Spatial geometry is one of the fundamental mathematical building blocks of any engineering education. However, it is overshadowed by planar geometry in the curriculum between playful early primary education and later analytical geometry, leaving a multi-year gap where spatial geometry is absent...
Biomimetic microsensors inspired by marine life
Kottapalli, Ajay Giri Prakash; Miao, Jianmin; Triantafyllou, Michael S
2017-01-01
This book narrates the development of various biomimetic microelectromechanical systems (MEMS) sensors, such as pressure, flow, acceleration, chemical, and tactile sensors, that are inspired by sensing phenomenon that exist in marine life. The research described in this book is multi-faceted and combines the expertise and understanding from diverse fields, including biomimetics, microfabrication, sensor engineering, MEMS design, nanotechnology, and material science. A series of chapters examine the design and fabrication of MEMS sensors that function on piezoresistive, piezoelectric, strain gauge, and chemical sensing principles. By translating nature-based engineering solutions to artificial manmade technology, we could find innovative solutions to critical problems.
Skin-Inspired Electronics: An Emerging Paradigm.
Wang, Sihong; Oh, Jin Young; Xu, Jie; Tran, Helen; Bao, Zhenan
2018-05-15
Future electronics will take on more important roles in people's lives. They need to allow more intimate contact with human beings to enable advanced health monitoring, disease detection, medical therapies, and human-machine interfacing. However, current electronics are rigid, nondegradable and cannot self-repair, while the human body is soft, dynamic, stretchable, biodegradable, and self-healing. Therefore, it is critical to develop a new class of electronic materials that incorporate skinlike properties, including stretchability for conformable integration, minimal discomfort and suppressed invasive reactions; self-healing for long-term durability under harsh mechanical conditions; and biodegradability for reducing environmental impact and obviating the need for secondary device removal for medical implants. These demands have fueled the development of a new generation of electronic materials, primarily composed of polymers and polymer composites with both high electrical performance and skinlike properties, and consequently led to a new paradigm of electronics, termed "skin-inspired electronics". This Account covers recent important advances in skin-inspired electronics, from basic material developments to device components and proof-of-concept demonstrations for integrated bioelectronics applications. To date, stretchability has been the most prominent focus in this field. In contrast to strain-engineering approaches that extrinsically impart stretchability into inorganic electronics, intrinsically stretchable materials provide a direct route to achieve higher mechanical robustness, higher device density, and scalable fabrication. The key is the introduction of strain-dissipation mechanisms into the material design, which has been realized through molecular engineering (e.g., soft molecular segments, dynamic bonds) and physical engineering (e.g., nanoconfinement effect, geometric design). The material design concepts have led to the successful demonstrations of
InSpiRe - Intelligent Spine Rehabilitation
DEFF Research Database (Denmark)
Bøg, Kasper Hafstrøm; Helms, Niels Henrik; Kjær, Per
InSpiRe er et projekt, der har haft omdrejningspunkt i etableringen af et nyt netværk indenfor intelligent genoptræning med særligt fokus på rygsmerter. Projektet er gennemført i perioden 1/3 2011 2011-1/3 2012, med støtte fra Syddansk Vækstforum, og er blevet drevet af projektparterne Knowledge ...... Lab, Syddansk Universitet (SDU), Institut for Idræt og Biomekanik (IoB), SDU, samt University College Lillebælt....
A bio-inspired spatial patterning circuit.
Chen, Kai-Yuan; Joe, Danial J; Shealy, James B; Land, Bruce R; Shen, Xiling
2014-01-01
Lateral Inhibition (LI) is a widely conserved patterning mechanism in biological systems across species. Distinct from better-known Turing patterns, LI depend on cell-cell contact rather than diffusion. We built an in silico genetic circuit model to analyze the dynamic properties of LI. The model revealed that LI amplifies differences between neighboring cells to push them into opposite states, hence forming stable 2-D patterns. Inspired by this insight, we designed and implemented an electronic circuit that recapitulates LI patterning dynamics. This biomimetic system serve as a physical model to elucidate the design principle of generating robust patterning through spatial feedback, regardless of the underlying devices being biological or electrical.
Neuro-Inspired Computing with Stochastic Electronics
Naous, Rawan
2016-01-06
The extensive scaling and integration within electronic systems have set the standards for what is addressed to as stochastic electronics. The individual components are increasingly diverting away from their reliable behavior and producing un-deterministic outputs. This stochastic operation highly mimics the biological medium within the brain. Hence, building on the inherent variability, particularly within novel non-volatile memory technologies, paves the way for unconventional neuromorphic designs. Neuro-inspired networks with brain-like structures of neurons and synapses allow for computations and levels of learning for diverse recognition tasks and applications.
Biological inspiration used for robots motion synthesis.
Zielińska, Teresa
2009-01-01
This work presents a biologically inspired method of gait generation. Bipedal gait pattern (for hip and knee joints) was taken into account giving the reference trajectories in a learning task. The four coupled oscillators were taught to generate the outputs similar to those in a human gait. After applying the correction functions the obtained generation method was validated using ZMP criterion. The formula suitable for real-time motion generation taking into account the positioning errors was also formulated. The small real robot prototype was tested to be able walk successfully following the elaborated motion pattern.
Cavity-enhanced Faraday rotation measurement with auto-balanced photodetection.
Chang, Chia-Yu; Shy, Jow-Tsong
2015-10-01
Optical cavity enhancement for a tiny Faraday rotation is demonstrated with auto-balanced photodetection. This configuration is analyzed using the Jones matrix formalism. The resonant rotation signal is amplified, and thus, the angular sensitivity is improved. In the experiment, the air Faraday rotation is measured with an auto-balanced photoreceiver in single-pass and cavity geometries. The result shows that the measured Faraday rotation in the single-pass geometry is enhanced by a factor of 85 in the cavity geometry, and the sensitivity is improved to 7.54×10(-10) rad Hz(-1/2), which agrees well with the Jones matrix analysis. With this verification, we propose an AC magnetic sensor whose magnetic sensitivity is expected to achieve 10 pT Hz(-1/2).
Analogical Reasoning in Geometry Education
Magdas, Ioana
2015-01-01
The analogical reasoning isn't used only in mathematics but also in everyday life. In this article we approach the analogical reasoning in Geometry Education. The novelty of this article is a classification of geometrical analogies by reasoning type and their exemplification. Our classification includes: analogies for understanding and setting a…
Normal forms in Poisson geometry
Marcut, I.T.
2013-01-01
The structure of Poisson manifolds is highly nontrivial even locally. The first important result in this direction is Conn's linearization theorem around fixed points. One of the main results of this thesis (Theorem 2) is a normal form theorem in Poisson geometry, which is the Poisson-geometric
Exploring Bundling Theory with Geometry
Eckalbar, John C.
2006-01-01
The author shows how instructors might successfully introduce students in principles and intermediate microeconomic theory classes to the topic of bundling (i.e., the selling of two or more goods as a package, rather than separately). It is surprising how much students can learn using only the tools of high school geometry. To be specific, one can…
Stochastic Modelling of River Geometry
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Schaarup-Jensen, K.
1996-01-01
Numerical hydrodynamic river models are used in a large number of applications to estimate critical events for rivers. These estimates are subject to a number of uncertainties. In this paper, the problem to evaluate these estimates using probabilistic methods is considered. Stochastic models for ...... for river geometries are formulated and a coupling between hydraulic computational methods and numerical reliability methods is presented....
Matter in toy dynamical geometries
Konopka, T.J.
2009-01-01
One of the objectives of theories describing quantum dynamical geometry is to compute expectation values of geometrical observables. The results of such computations can be affected by whether or not matter is taken into account. It is thus important to understand to what extent and to what effect
Ca??adas, Mar??a C.; Molina, Marta; Gallardo, Sandra; Mart??nez-Santaolalla, Manuel J.; Pe??as, Mar??a
2010-01-01
In this work we present an activity for High School students in which various mathematical concepts of plane and spatial geometry are involved. The final objective of the proposed tasks is constructing a particular polyhedron, the cube, by using a modality of origami called modular origami.
Granular flows in constrained geometries
Murthy, Tejas; Viswanathan, Koushik
Confined geometries are widespread in granular processing applications. The deformation and flow fields in such a geometry, with non-trivial boundary conditions, determine the resultant mechanical properties of the material (local porosity, density, residual stresses etc.). We present experimental studies of deformation and plastic flow of a prototypical granular medium in different nontrivial geometries- flat-punch compression, Couette-shear flow and a rigid body sliding past a granular half-space. These geometries represent simplified scaled-down versions of common industrial configurations such as compaction and dredging. The corresponding granular flows show a rich variety of flow features, representing the entire gamut of material types, from elastic solids (beam buckling) to fluids (vortex-formation, boundary layers) and even plastically deforming metals (dead material zone, pile-up). The effect of changing particle-level properties (e.g., shape, size, density) on the observed flows is also explicitly demonstrated. Non-smooth contact dynamics particle simulations are shown to reproduce some of the observed flow features quantitatively. These results showcase some central challenges facing continuum-scale constitutive theories for dynamic granular flows.
General Relativity: Geometry Meets Physics
Thomsen, Dietrick E.
1975-01-01
Observing the relationship of general relativity and the geometry of space-time, the author questions whether the rest of physics has geometrical explanations. As a partial answer he discusses current research on subatomic particles employing geometric transformations, and cites the existence of geometrical definitions of physical quantities such…
Learners engaging with transformation geometry
African Journals Online (AJOL)
participants engaged in investigative semi-structured interviews with the resear- chers. ... Keywords: analysis; conversions; transformation geometry; transformations; treatments .... semiotic systems of representation is not only to designate mathematical objects or to com- municate but also to ... Research design. We believe ...
Multivariable calculus and differential geometry
Walschap, Gerard
2015-01-01
This text is a modern in-depth study of the subject that includes all the material needed from linear algebra. It then goes on to investigate topics in differential geometry, such as manifolds in Euclidean space, curvature, and the generalization of the fundamental theorem of calculus known as Stokes' theorem.
College geometry a unified development
Kay, David C
2011-01-01
""The book is a comprehensive textbook on basic geometry. … Key features of the book include numerous figures and many problems, more than half of which come with hints or even complete solutions. Frequent historical comments add to making the reading a pleasant one.""-Michael Joswig, Zentralblatt MATH 1273
On a classification of irreducible almost-commutative geometries IV
International Nuclear Information System (INIS)
Jureit, Jan-Hendrik; Stephan, Christoph A.
2008-01-01
In this paper, we will classify the finite spectral triples with KO-dimension 6, following the classification found in Iochum, B., Schuecker, T., and Stephan, C. A., J. Math. Phys. 45, 5003 (2004); Jureit, J.-H. and Stephan, C. A., J. Math. Phys. 46, 043512 (2005); Schuecker, T. (unpublished); Jureit, J.-H., Schuecker, T., and Stephan, C. A., J. Math. Phys. 46, 072302 (2005). with up to four summands in the matrix algebra. Again, heavy use is made of Krajewski diagrams [Krajewski, T., J. Geom. Phys. 28, 1 (1998).] This work has been inspired by the recent paper by Connes (unpublished) and Barrett (unpublished). In the classification, we find that the standard model of particle physics in its minimal version fits the axioms of noncommutative geometry in the case of KO-dimension 6. By minimal version, it is meant that at least one neutrino has to be massless and mass-terms mixing particles and antiparticles are prohibited
Pseudo-differential operators groups, geometry and applications
Zhu, Hongmei
2017-01-01
This volume consists of papers inspired by the special session on pseudo-differential operators at the 10th ISAAC Congress held at the University of Macau, August 3-8, 2015 and the mini-symposium on pseudo-differential operators in industries and technologies at the 8th ICIAM held at the National Convention Center in Beijing, August 10-14, 2015. The twelve papers included present cutting-edge trends in pseudo-differential operators and applications from the perspectives of Lie groups (Chapters 1-2), geometry (Chapters 3-5) and applications (Chapters 6-12). Many contributions cover applications in probability, differential equations and time-frequency analysis. A focus on the synergies of pseudo-differential operators with applications, especially real-life applications, enhances understanding of the analysis and the usefulness of these operators.
Modelling of convective heat and mass transfer in rotating flows
Shevchuk, Igor V
2016-01-01
This monograph presents results of the analytical and numerical modeling of convective heat and mass transfer in different rotating flows caused by (i) system rotation, (ii) swirl flows due to swirl generators, and (iii) surface curvature in turns and bends. Volume forces (i.e. centrifugal and Coriolis forces), which influence the flow pattern, emerge in all of these rotating flows. The main part of this work deals with rotating flows caused by system rotation, which includes several rotating-disk configurations and straight pipes rotating about a parallel axis. Swirl flows are studied in some of the configurations mentioned above. Curvilinear flows are investigated in different geometries of two-pass ribbed and smooth channels with 180° bends. The author demonstrates that the complex phenomena of fluid flow and convective heat transfer in rotating flows can be successfully simulated using not only the universal CFD methodology, but in certain cases by means of the integral methods, self-similar and analyt...
International Nuclear Information System (INIS)
Tozini, A.V.
1984-01-01
A review is made of some properties of the rotating Universe models. Godel's model is identified as a generalized filted model. Some properties of new solutions of the Einstein's equations, which are rotating non-stationary Universe models, are presented and analyzed. These models have the Godel's model as a particular case. Non-stationary cosmological models are found which are a generalization of the Godel's metrics in an analogous way in which Friedmann is to the Einstein's model. (L.C.) [pt
Rotation Invariance Neural Network
Li, Shiyuan
2017-01-01
Rotation invariance and translation invariance have great values in image recognition tasks. In this paper, we bring a new architecture in convolutional neural network (CNN) named cyclic convolutional layer to achieve rotation invariance in 2-D symbol recognition. We can also get the position and orientation of the 2-D symbol by the network to achieve detection purpose for multiple non-overlap target. Last but not least, this architecture can achieve one-shot learning in some cases using thos...
Smooth Horizonless Geometries Deep Inside the Black-Hole Regime.
Bena, Iosif; Giusto, Stefano; Martinec, Emil J; Russo, Rodolfo; Shigemori, Masaki; Turton, David; Warner, Nicholas P
2016-11-11
We construct the first family of horizonless supergravity solutions that have the same mass, charges, and angular momenta as general supersymmetric rotating D1-D5-P black holes in five dimensions. This family includes solutions with arbitrarily small angular momenta, deep within the regime of quantum numbers and couplings for which a large classical black hole exists. These geometries are well approximated by the black-hole solution, and in particular exhibit the same near-horizon throat. Deep in this throat, the black-hole singularity is resolved into a smooth cap. We also identify the holographically dual states in the N=(4,4) D1-D5 orbifold conformal field theory (CFT). Our solutions are among the states counted by the CFT elliptic genus, and provide examples of smooth microstate geometries within the ensemble of supersymmetric black-hole microstates.
An immersed boundary method for modeling a dirty geometry data
Onishi, Keiji; Tsubokura, Makoto
2017-11-01
We present a robust, fast, and low preparation cost immersed boundary method (IBM) for simulating an incompressible high Re flow around highly complex geometries. The method is achieved by the dispersion of the momentum by the axial linear projection and the approximate domain assumption satisfying the mass conservation around the wall including cells. This methodology has been verified against an analytical theory and wind tunnel experiment data. Next, we simulate the problem of flow around a rotating object and demonstrate the ability of this methodology to the moving geometry problem. This methodology provides the possibility as a method for obtaining a quick solution at a next large scale supercomputer. This research was supported by MEXT as ``Priority Issue on Post-K computer'' (Development of innovative design and production processes) and used computational resources of the K computer provided by the RIKEN Advanced Institute for Computational Science.
Mahaffey, Michael L.
One of a series of experimental units for children at the preschool level, this booklet deals with geometric concepts. A unit on volume and a unit on linear measurement are covered; for each unit a discussion of mathematical objectives, a list of materials needed, and a sequence of learning activities are provided. Directions are specified for the…
DEFF Research Database (Denmark)
Byg din egen boomerang, kast den, se den flyve, forstå hvorfor og hvordan den vender tilbage, og grib den. Det handler om opdriften på vingerne når du flyver, men det handler også og allermest om den mærkværdige gyroskop-effekt, du bruger til at holde balancen, når du kører på cykel. Vi vil bruge...
Discrete differential geometry. Consistency as integrability
Bobenko, Alexander I.; Suris, Yuri B.
2005-01-01
A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete geometry studies geometric shapes with finite number of elements (such as polyhedra), the discrete differential geometry aims at the development of discrete equivalents of notions and methods of smooth surface theory. Current interest in this field derives not ...
Spin geometry of entangled qubits under bilocal decoherence modes
International Nuclear Information System (INIS)
Durstberger, Katharina
2008-01-01
The Lindblad generators of the master equation define which kind of decoherence happens in an open quantum system. We are working with a two qubit system and choose the generators to be projection operators on the eigenstates of the system and unitary bilocal rotations of them. The resulting decoherence modes are studied in detail. Besides the general solutions we investigate the special case of maximally entangled states-the Bell singlet states. The results are depicted in the so-called spin geometry picture which allows to illustrate the evolution of the (nonlocal) correlations stored in a certain state. The question for which conditions the path traced out in the geometric picture depends only on the relative angle between the bilocal rotations is addressed
Neutron guide geometries for homogeneous phase space volume transformation
International Nuclear Information System (INIS)
Stüßer, N.; Bartkowiak, M.; Hofmann, T.
2014-01-01
We extend geometries for recently developed optical guide systems that perform homogeneous phase space volume transformations on neutron beams. These modules allow rotating beam directions and can simultaneously compress or expand the beam cross-section. Guide systems combining these modules offer the possibility to optimize ballistic guides with and without direct view on the source and beam splitters. All systems are designed for monochromatic beams with a given divergence. The case of multispectral beams with wavelength-dependent divergence distributions is addressed as well. - Highlights: • Form invariant volume transformation in phase space. • Geometrical approach. • Ballistic guide, beam splitter, beam bender
Neutron guide geometries for homogeneous phase space volume transformation
Energy Technology Data Exchange (ETDEWEB)
Stüßer, N., E-mail: stuesser@helmholtz-berlin.de; Bartkowiak, M.; Hofmann, T.
2014-06-01
We extend geometries for recently developed optical guide systems that perform homogeneous phase space volume transformations on neutron beams. These modules allow rotating beam directions and can simultaneously compress or expand the beam cross-section. Guide systems combining these modules offer the possibility to optimize ballistic guides with and without direct view on the source and beam splitters. All systems are designed for monochromatic beams with a given divergence. The case of multispectral beams with wavelength-dependent divergence distributions is addressed as well. - Highlights: • Form invariant volume transformation in phase space. • Geometrical approach. • Ballistic guide, beam splitter, beam bender.
Geometry and Optics of the Electrostatic ELENA Transfer Lines
Vanbavinckhove, G; Barna, D; Bartmann, W; Butin, F; Choisnet, O; Yamada, H
2013-01-01
The future ELENA ring at CERN will decelerate the AD anti-proton beam further from 5.3 MeV to 100 keV kinetic energy, to increase the efficiency of anti-proton trapping. At present there are four experiments in the AD hall which will be complemented with the installation of ELENA by additional three experiments and an additional source for commissioning. This paper describes the optimization of the transfer line geometry, ring rotation and source position. The optics of the transfer lines and error studies to define field and alignment tolerances are shown, and the optics particularities of electrostatic elements and their optimization highlighted.
Transient Changes in Molecular Geometries and How to Model Them
DEFF Research Database (Denmark)
Dohn, Asmus Ougaard
Light-induced chemical processes are accompanied by molecular motion on the femtosecond time scale. Uncovering this dynamical motion is central to understanding the chemical reaction on a fundamental level. This thesis focuses on the aspects of excess excitation energy dissipation via dynamic...... observe how the wide distribution of ground state geometries is responsible for decoherence, and that the solvent cage actually facilitates coherent motion, by blocking the newly discovered vibrational mode. We furthermore observe a non-specific, rotational solvent response to the excitation. The second...
Numerically robust geometry engine for compound solid geometries
International Nuclear Information System (INIS)
Vlachoudis, V.; Sinuela-Pastor, D.
2013-01-01
Monte Carlo programs heavily rely on a fast and numerically robust solid geometry engines. However the success of solid modeling, depends on facilities for specifying and editing parameterized models through a user-friendly graphical front-end. Such a user interface has to be fast enough in order to be interactive for 2D and/or 3D displays, but at the same time numerically robust in order to display possible modeling errors at real time that could be critical for the simulation. The graphical user interface Flair for FLUKA currently employs such an engine where special emphasis has been given on being fast and numerically robust. The numerically robustness is achieved by a novel method of estimating the floating precision of the operations, which dynamically adapts all the decision operations accordingly. Moreover a predictive caching mechanism is ensuring that logical errors in the geometry description are found online, without compromising the processing time by checking all regions. (authors)
Geometry of VY Canis Majoris derived from SiO maser lines
International Nuclear Information System (INIS)
Van Blerkom, D.; Auer, L.
1976-01-01
A radiation reveals transfer calculation reveals that the SiO maser lines observed in the spectrum of VY CMa are formed in a rotating equatorial disk seen nearly edge-on. Other geometries are considered and eliminated. It is suggested that the SiO lines of NML Cyg also show evidence that they are formed in a disk
Imole, Olukayode Isaiah; Krijgsman, Dinant; Weinhart, Thomas; Magnanimo, Vanessa; Chavez Montes, Bruno E.; Ramaioli, Marco; Luding, Stefan
2016-01-01
We perform experiments and discrete element simulations on the dosing of cohesive granular materials in a simplified geometry. The setup is a canister box where the powder is dosed out through the action of a constant-pitch coil feeder connected to a motor. A dosing step consists of a rotation
Adhesive Bioactive Coatings Inspired by Sea Life.
Rego, Sónia J; Vale, Ana C; Luz, Gisela M; Mano, João F; Alves, Natália M
2016-01-19
Inspired by nature, in particular by the marine mussels adhesive proteins (MAPs) and by the tough brick-and-mortar nacre-like structure, novel multilayered films are prepared in the present work. Organic-inorganic multilayered films, with an architecture similar to nacre based on bioactive glass nanoparticles (BG), chitosan, and hyaluronic acid modified with catechol groups, which are the main components responsible for the outstanding adhesion in MAPs, are developed for the first time. The biomimetic conjugate is prepared by carbodiimide chemistry and analyzed by ultraviolet-visible spectrophotometry. The buildup of the multilayered films is monitored with a quartz crystal microbalance with dissipation monitoring, and their topography is characterized by atomic force microscopy. The mechanical properties reveal that the films containing catechol groups and BG present an enhanced adhesion. Moreover, the bioactivity of the films upon immersion in a simulated body fluid solution is evaluated by scanning electron microscopy coupled with energy dispersive X-ray spectroscopy, Fourier transform infrared spectroscopy, and X-ray diffraction. It was found that the constructed films promote the formation of bonelike apatite in vitro. Such multifunctional mussel inspired LbL films, which combine enhanced adhesion and bioactivity, could be potentially used as coatings of a variety of implants for orthopedic applications.
Brain-inspired Stochastic Models and Implementations
Al-Shedivat, Maruan
2015-05-12
One of the approaches to building artificial intelligence (AI) is to decipher the princi- ples of the brain function and to employ similar mechanisms for solving cognitive tasks, such as visual perception or natural language understanding, using machines. The recent breakthrough, named deep learning, demonstrated that large multi-layer networks of arti- ficial neural-like computing units attain remarkable performance on some of these tasks. Nevertheless, such artificial networks remain to be very loosely inspired by the brain, which rich structures and mechanisms may further suggest new algorithms or even new paradigms of computation. In this thesis, we explore brain-inspired probabilistic mechanisms, such as neural and synaptic stochasticity, in the context of generative models. The two questions we ask here are: (i) what kind of models can describe a neural learning system built of stochastic components? and (ii) how can we implement such systems e ̆ciently? To give specific answers, we consider two well known models and the corresponding neural architectures: the Naive Bayes model implemented with a winner-take-all spiking neural network and the Boltzmann machine implemented in a spiking or non-spiking fashion. We propose and analyze an e ̆cient neuromorphic implementation of the stochastic neu- ral firing mechanism and study the e ̄ects of synaptic unreliability on learning generative energy-based models implemented with neural networks.
Floating and sinking: the imprint of massive scalars around rotating black holes.
Cardoso, Vitor; Chakrabarti, Sayan; Pani, Paolo; Berti, Emanuele; Gualtieri, Leonardo
2011-12-09
We study the coupling of massive scalar fields to matter in orbit around rotating black holes. It is generally expected that orbiting bodies will lose energy in gravitational waves, slowly inspiraling into the black hole. Instead, we show that the coupling of the field to matter leads to a surprising effect: because of superradiance, matter can hover into "floating orbits" for which the net gravitational energy loss at infinity is entirely provided by the black hole's rotational energy. Orbiting bodies remain floating until they extract sufficient angular momentum from the black hole, or until perturbations or nonlinear effects disrupt the orbit. For slowly rotating and nonrotating black holes floating orbits are unlikely to exist, but resonances at orbital frequencies corresponding to quasibound states of the scalar field can speed up the inspiral, so that the orbiting body sinks. These effects could be a smoking gun of deviations from general relativity.
Women in numbers Europe II contributions to number theory and arithmetic geometry
Ozman, Ekin; Johnson-Leung, Jennifer; Newton, Rachel
2018-01-01
Inspired by the September 2016 conference of the same name, this second volume highlights recent research in a wide range of topics in contemporary number theory and arithmetic geometry. Research reports from projects started at the conference, expository papers describing ongoing research, and contributed papers from women number theorists outside the conference make up this diverse volume. Topics cover a broad range of topics such as arithmetic dynamics, failure of local-global principles, geometry in positive characteristics, and heights of algebraic integers. The use of tools from algebra, analysis and geometry, as well as computational methods exemplifies the wealth of techniques available to modern researchers in number theory. Exploring connections between different branches of mathematics and combining different points of view, these papers continue the tradition of supporting and highlighting the contributions of women number theorists at a variety of career stages. Perfect for students and researche...
Nostalgia-Evoked Inspiration: Mediating Mechanisms and Motivational Implications.
Stephan, Elena; Sedikides, Constantine; Wildschut, Tim; Cheung, Wing-Yee; Routledge, Clay; Arndt, Jamie
2015-10-01
Six studies examined the nostalgia-inspiration link and its motivational implications. In Study 1, nostalgia proneness was positively associated with inspiration frequency and intensity. In Studies 2 and 3, the recollection of nostalgic (vs. ordinary) experiences increased both general inspiration and specific inspiration to engage in exploratory activities. In Study 4, serial mediational analyses supported a model in which nostalgia increases social connectedness, which subsequently fosters self-esteem, which then boosts inspiration. In Study 5, a rigorous evaluation of this serial mediational model (with a novel nostalgia induction controlling for positive affect) reinforced the idea that nostalgia-elicited social connectedness increases self-esteem, which then heightens inspiration. Study 6 extended the serial mediational model by demonstrating that nostalgia-evoked inspiration predicts goal pursuit (intentions to pursue an important goal). Nostalgia spawns inspiration via social connectedness and attendant self-esteem. In turn, nostalgia-evoked inspiration bolsters motivation. © 2015 by the Society for Personality and Social Psychology, Inc.
Creative design inspired by biological knowledge: Technologies and methods
Tan, Runhua; Liu, Wei; Cao, Guozhong; Shi, Yuan
2018-05-01
Biological knowledge is becoming an important source of inspiration for developing creative solutions to engineering design problems and even has a huge potential in formulating ideas that can help firms compete successfully in a dynamic market. To identify the technologies and methods that can facilitate the development of biologically inspired creative designs, this research briefly reviews the existing biological-knowledge-based theories and methods and examines the application of biological-knowledge-inspired designs in various fields. Afterward, this research thoroughly examines the four dimensions of key technologies that underlie the biologically inspired design (BID) process. This research then discusses the future development trends of the BID process before presenting the conclusions.
International Nuclear Information System (INIS)
Griffiths, Jerry
2003-01-01
's principle. Stuchlik has thoroughly reviewed the effect of a small cosmological constant on geodesic motion and the equipotential surfaces associated with the formation of accretion discs, and Karas, Subr and Slechta report some interesting results from their model for analysing the dynamics of a stellar cluster near a galactic centre with an accretion disc. Semerak has contributed a thorough and most useful review of exact models for realistic axially symmetric discs of matter around rotating spheroidal black holes. There is a paper by Hledik illustrating the use of optical reference geometry and embedding diagrams for analysing the properties of orbits about black holes, and Ledvinka has illustrated graphically what a rotating neutron star would actually look like to an observer. Podolsky has comprehensively reviewed exact expanding and non-expanding impulsive gravitational waves, describing the various ways they may be constructed and their global properties in Minkowski, de Sitter and anti-de Sitter backgrounds. The spinning C-metric is investigated by Pravda and Pravdova with a view to clarifying its physical interpretation as a pair of accelerating Kerr black holes, and Balek has described the properties of spacetimes that can be constructed by cutting and pasting parts of Minkowski space. The volume concludes with some remarks by Kopf on a functional approach to the renormalization of the stress-energy tensor in the semiclassical Einstein equations, and a review by Krtous of boundary quantum mechanics in which measurements at the initial and final moments in time are treated independently and which can be formulated without reference to causal structure. These are all valuable articles which deserve to be widely known. Overall, this is a most impressive tribute to a leader in the academic study of gravitation, who has clearly inspired the generation after him and helped establish a thriving research community in his beautiful native city. (book review)
Code subspaces for LLM geometries
Berenstein, David; Miller, Alexandra
2018-03-01
We consider effective field theory around classical background geometries with a gauge theory dual, specifically those in the class of LLM geometries. These are dual to half-BPS states of N= 4 SYM. We find that the language of code subspaces is natural for discussing the set of nearby states, which are built by acting with effective fields on these backgrounds. This work extends our previous work by going beyond the strict infinite N limit. We further discuss how one can extract the topology of the state beyond N→∞ and find that, as before, uncertainty and entanglement entropy calculations provide a useful tool to do so. Finally, we discuss obstructions to writing down a globally defined metric operator. We find that the answer depends on the choice of reference state that one starts with. Therefore, within this setup, there is ambiguity in trying to write an operator that describes the metric globally.
Euclidean distance geometry an introduction
Liberti, Leo
2017-01-01
This textbook, the first of its kind, presents the fundamentals of distance geometry: theory, useful methodologies for obtaining solutions, and real world applications. Concise proofs are given and step-by-step algorithms for solving fundamental problems efficiently and precisely are presented in Mathematica®, enabling the reader to experiment with concepts and methods as they are introduced. Descriptive graphics, examples, and problems, accompany the real gems of the text, namely the applications in visualization of graphs, localization of sensor networks, protein conformation from distance data, clock synchronization protocols, robotics, and control of unmanned underwater vehicles, to name several. Aimed at intermediate undergraduates, beginning graduate students, researchers, and practitioners, the reader with a basic knowledge of linear algebra will gain an understanding of the basic theories of distance geometry and why they work in real life.
Fractal geometry and computer graphics
Sakas, Georgios; Peitgen, Heinz-Otto; Englert, Gabriele
1992-01-01
Fractal geometry has become popular in the last 15 years, its applications can be found in technology, science, or even arts. Fractal methods and formalism are seen today as a general, abstract, but nevertheless practical instrument for the description of nature in a wide sense. But it was Computer Graphics which made possible the increasing popularity of fractals several years ago, and long after their mathematical formulation. The two disciplines are tightly linked. The book contains the scientificcontributions presented in an international workshop in the "Computer Graphics Center" in Darmstadt, Germany. The target of the workshop was to present the wide spectrum of interrelationships and interactions between Fractal Geometry and Computer Graphics. The topics vary from fundamentals and new theoretical results to various applications and systems development. All contributions are original, unpublished papers.The presentations have been discussed in two working groups; the discussion results, together with a...
The geometry of celestial mechanics
Geiges, Hansjörg
2016-01-01
Celestial mechanics is the branch of mathematical astronomy devoted to studying the motions of celestial bodies subject to the Newtonian law of gravitation. This mathematical introductory textbook reveals that even the most basic question in celestial mechanics, the Kepler problem, leads to a cornucopia of geometric concepts: conformal and projective transformations, spherical and hyperbolic geometry, notions of curvature, and the topology of geodesic flows. For advanced undergraduate and beginning graduate students, this book explores the geometric concepts underlying celestial mechanics and is an ideal companion for introductory courses. The focus on the history of geometric ideas makes it perfect supplementary reading for students in elementary geometry and topology. Numerous exercises, historical notes and an extensive bibliography provide all the contextual information required to gain a solid grounding in celestial mechanics.
Differential geometry and mathematical physics
Rudolph, Gerd
Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous d...
Grassmannian geometry of scattering amplitudes
Arkani-Hamed, Nima; Cachazo, Freddy; Goncharov, Alexander; Postnikov, Alexander; Trnka, Jaroslav
2016-01-01
Outlining a revolutionary reformulation of the foundations of perturbative quantum field theory, this book is a self-contained and authoritative analysis of the application of this new formulation to the case of planar, maximally supersymmetric Yang–Mills theory. The book begins by deriving connections between scattering amplitudes and Grassmannian geometry from first principles before introducing novel physical and mathematical ideas in a systematic manner accessible to both physicists and mathematicians. The principle players in this process are on-shell functions which are closely related to certain sub-strata of Grassmannian manifolds called positroids - in terms of which the classification of on-shell functions and their relations becomes combinatorially manifest. This is an essential introduction to the geometry and combinatorics of the positroid stratification of the Grassmannian and an ideal text for advanced students and researchers working in the areas of field theory, high energy physics, and the...
Foliation theory in algebraic geometry
McKernan, James; Pereira, Jorge
2016-01-01
Featuring a blend of original research papers and comprehensive surveys from an international team of leading researchers in the thriving fields of foliation theory, holomorphic foliations, and birational geometry, this book presents the proceedings of the conference "Foliation Theory in Algebraic Geometry," hosted by the Simons Foundation in New York City in September 2013. Topics covered include: Fano and del Pezzo foliations; the cone theorem and rank one foliations; the structure of symmetric differentials on a smooth complex surface and a local structure theorem for closed symmetric differentials of rank two; an overview of lifting symmetric differentials from varieties with canonical singularities and the applications to the classification of AT bundles on singular varieties; an overview of the powerful theory of the variety of minimal rational tangents introduced by Hwang and Mok; recent examples of varieties which are hyperbolic and yet the Green-Griffiths locus is the whole of X; and a classificati...
Groups and Geometries : Siena Conference
Kantor, William; Lunardon, Guglielmo; Pasini, Antonio; Tamburini, Maria
1998-01-01
On September 1-7, 1996 a conference on Groups and Geometries took place in lovely Siena, Italy. It brought together experts and interested mathematicians from numerous countries. The scientific program centered around invited exposi tory lectures; there also were shorter research announcements, including talks by younger researchers. The conference concerned a broad range of topics in group theory and geometry, with emphasis on recent results and open problems. Special attention was drawn to the interplay between group-theoretic methods and geometric and combinatorial ones. Expanded versions of many of the talks appear in these Proceedings. This volume is intended to provide a stimulating collection of themes for a broad range of algebraists and geometers. Among those themes, represented within the conference or these Proceedings, are aspects of the following: 1. the classification of finite simple groups, 2. the structure and properties of groups of Lie type over finite and algebraically closed fields of f...
Rotating positron tomographs revisited
International Nuclear Information System (INIS)
Townsend, D.; Defrise, M.; Geissbuhler, A.
1994-01-01
We have compared the performance of a PET scanner comprising two rotating arrays of detectors with that of the more conventional stationary-ring design. The same total number of detectors was used in each, and neither scanner had septa. For brain imaging, we find that the noise-equivalent count rate is greater for the rotating arrays by a factor of two. Rotating arrays have a sensitivity profile that peaks in the centre of the field of view, both axially and transaxially. In the transaxial plane, this effect offsets to a certain extent the decrease in the number of photons detected towards the centre of the brain due to self-absorption. We have also compared the performance of a rotating scanner to that of a full-ring scanner with the same number of rings. We find that a full-ring scanner with an axial extent of 16.2 cm (24 rings) is a factor of 3.5 more sensitive than a rotating scanner with 40% of the detectors and the same axial extent. (Author)
Needle decompositions in Riemannian geometry
Klartag, Bo'az
2017-01-01
The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, the author's method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in the author's analysis.
Systematics of IIB spinorial geometry
Gran, U.; Gutowski, J.; Papadopoulos, G.; Roest, D.
2005-01-01
We reduce the classification of all supersymmetric backgrounds of IIB supergravity to the evaluation of the Killing spinor equations and their integrability conditions, which contain the field equations, on five types of spinors. This extends the work of [hep-th/0503046] to IIB supergravity. We give the expressions of the Killing spinor equations on all five types of spinors. In this way, the Killing spinor equations become a linear system for the fluxes, geometry and spacetime derivatives of...
Geometry Dependence of Stellarator Turbulence
International Nuclear Information System (INIS)
Mynick, H.E.; Xanthopoulos, P.; Boozer, A.H.
2009-01-01
Using the nonlinear gyrokinetic code package GENE/GIST, we study the turbulent transport in a broad family of stellarator designs, to understand the geometry-dependence of the microturbulence. By using a set of flux tubes on a given flux surface, we construct a picture of the 2D structure of the microturbulence over that surface, and relate this to relevant geometric quantities, such as the curvature, local shear, and effective potential in the Schrodinger-like equation governing linear drift modes
Superbanana orbits in stellarator geometries
International Nuclear Information System (INIS)
Derr, J.A.; Shohet, J.L.
1979-04-01
The presence of superbanana orbit types localized to either the interior or the exterior of stellarators and torsatrons is numerically investigated for 3.5 MeV alpha particles. The absence of the interior superbanana in both geometries is found to be due to non-conservation of the action. Exterior superbananas are found in the stellarator only, as a consequence of the existence of closed helical magnetic wells. No superbananas of either type are found in the torsatron
Turtle geometry the Python way
Battle, S.
2014-01-01
An introduction to coding using Python’s on-screen ‘turtle’ that can be commanded with a few simple instructions including forward, backward, left and right. The turtle leaves a trace that can be used to draw geometric figures. This workshop is aimed at beginners of all ages. The aim is to learn a smattering of programming and a little bit of geometry in a fun way.
Topics in modern differential geometry
Verstraelen, Leopold
2017-01-01
A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature. Experts in the fields of Riemannian, Lorentzian and contact geometry present state-of-the-art reviews of their topics. The contributions are written on a graduate level and contain extended bibliographies. The ten chapters are the result of various doctoral courses which were held in 2009 and 2010 at universities in Leuven, Serbia, Romania and Spain.
Transitions in rapidly rotating convection dynamos
Tilgner, A.
2013-12-01
It is commonly assumed that buoyancy in the fluid core powers the geodynamo. We study here the minimal model of a convection driven dynamo, which is a horizontal plane layer in a gravity field, filled with electrically conducting fluid, heated from below and cooled from above, and rotating about a vertical axis. Such a plane layer may be viewed as a local approximation to the geophysically more relevant spherical geometry. The numerical simulations have been run on graphics processing units with at least 960 cores. If the convection is driven stronger and stronger at fixed rotation rate, the flow behaves at some point as if it was not rotating. This transition shows in the scaling of the heat transport which can be used to distinguish slow from rapid rotation. One expects dynamos to behave differently in these two flow regimes. But even within the convection flows which are rapidly rotating according to this criterion, it will be shown that different types of dynamos exist. In one state, the magnetic field strength obeys a scaling indicative of a magnetostrophic balance, in which the Lorentz force is in equilibrium with the Coriolis force. The flow in this case is helical. A different state exists at higher magnetic Reynolds numbers, in which the magnetic energy obeys a different scaling law and the helicity of the flow is much reduced. As one increases the Rayleigh number, all other parameters kept constant, one may find both types of dynamos separated by an interval of Rayleigh numbers in which there are no dynamos at all. The effect of these transitions on energy dissipation and mean field generation have also been studied.
Manipulators inspired by the tongue of the chameleon
International Nuclear Information System (INIS)
Debray, Alexis
2011-01-01
Chameleons have developed a specialized ballistic tongue which elongates more than six times its rest length at speeds higher than 3.5 m s -1 and accelerations 350 m s -2 , with a highly flexible mobile part, and which applies no continuous force during forward motion. These characteristics are possible because this tongue consists of two highly specialized systems, an ejection system for the forward motion and an accordion-like system for the retraction. Four manipulators inspired by the tongue of the chameleon and based on this design have been developed, resulting in three characteristics similar to the tongue of the chameleon: extensibility of the manipulator, flexibility of the mobile part, and absence of continuous force during the forward motion. The first manipulator mimics the basic mechanism of the tongue of the chameleon and reproduced its basic performances. A second manipulator performs a catching function at a speed of 3.5 m s -1 with an acceleration of 573 m s -2 while elongating seven times its rest length. The design of this manipulator is such that the dc motor used for retraction applies a torque 25 times its rated torque. Moreover, during the retraction, the mobile part of the manipulator moves due to its own inertia, allowing the dc motor to rotate at full velocity. In another manipulator, the addition of an elastomer in the mobile part allows for control of the retraction velocity. A model for these two manipulators compares well with the experimental data. Finally, the addition of wings on the mobile part allows us to take the advantage of aerodynamic effects, which is unusual for manipulators.
Manipulators inspired by the tongue of the chameleon.
Debray, Alexis
2011-06-01
Chameleons have developed a specialized ballistic tongue which elongates more than six times its rest length at speeds higher than 3.5 m s(-1) and accelerations 350 m s(-2), with a highly flexible mobile part, and which applies no continuous force during forward motion. These characteristics are possible because this tongue consists of two highly specialized systems, an ejection system for the forward motion and an accordion-like system for the retraction. Four manipulators inspired by the tongue of the chameleon and based on this design have been developed, resulting in three characteristics similar to the tongue of the chameleon: extensibility of the manipulator, flexibility of the mobile part, and absence of continuous force during the forward motion. The first manipulator mimics the basic mechanism of the tongue of the chameleon and reproduced its basic performances. A second manipulator performs a catching function at a speed of 3.5 m s(-1) with an acceleration of 573 m s(-2) while elongating seven times its rest length. The design of this manipulator is such that the dc motor used for retraction applies a torque 25 times its rated torque. Moreover, during the retraction, the mobile part of the manipulator moves due to its own inertia, allowing the dc motor to rotate at full velocity. In another manipulator, the addition of an elastomer in the mobile part allows for control of the retraction velocity. A model for these two manipulators compares well with the experimental data. Finally, the addition of wings on the mobile part allows us to take the advantage of aerodynamic effects, which is unusual for manipulators.
Manipulators inspired by the tongue of the chameleon
Energy Technology Data Exchange (ETDEWEB)
Debray, Alexis, E-mail: debray.alexis@canon.co.jp [Canon Incorporation, 3-30-2, Shimomaruko, Ohta-ku, Tokyo 146-8501 (Japan)
2011-06-15
Chameleons have developed a specialized ballistic tongue which elongates more than six times its rest length at speeds higher than 3.5 m s{sup -1} and accelerations 350 m s{sup -2}, with a highly flexible mobile part, and which applies no continuous force during forward motion. These characteristics are possible because this tongue consists of two highly specialized systems, an ejection system for the forward motion and an accordion-like system for the retraction. Four manipulators inspired by the tongue of the chameleon and based on this design have been developed, resulting in three characteristics similar to the tongue of the chameleon: extensibility of the manipulator, flexibility of the mobile part, and absence of continuous force during the forward motion. The first manipulator mimics the basic mechanism of the tongue of the chameleon and reproduced its basic performances. A second manipulator performs a catching function at a speed of 3.5 m s{sup -1} with an acceleration of 573 m s{sup -2} while elongating seven times its rest length. The design of this manipulator is such that the dc motor used for retraction applies a torque 25 times its rated torque. Moreover, during the retraction, the mobile part of the manipulator moves due to its own inertia, allowing the dc motor to rotate at full velocity. In another manipulator, the addition of an elastomer in the mobile part allows for control of the retraction velocity. A model for these two manipulators compares well with the experimental data. Finally, the addition of wings on the mobile part allows us to take the advantage of aerodynamic effects, which is unusual for manipulators.
Computational geometry for reactor applications
International Nuclear Information System (INIS)
Brown, F.B.; Bischoff, F.G.
1988-01-01
Monte Carlo codes for simulating particle transport involve three basic computational sections: a geometry package for locating particles and computing distances to regional boundaries, a physics package for analyzing interactions between particles and problem materials, and an editing package for determining event statistics and overall results. This paper describes the computational geometry methods in RACER, a vectorized Monte Carlo code used for reactor physics analysis, so that comparisons may be made with techniques used in other codes. The principal applications for RACER are eigenvalue calculations and power distributions associated with reactor core physics analysis. Successive batches of neutrons are run until convergence and acceptable confidence intervals are obtained, with typical problems involving >10 6 histories. As such, the development of computational geometry methods has emphasized two basic needs: a flexible but compact geometric representation that permits accurate modeling of reactor core details and efficient geometric computation to permit very large numbers of histories to be run. The current geometric capabilities meet these needs effectively, supporting a variety of very large and demanding applications
Number theory III Diophantine geometry
1991-01-01
From the reviews of the first printing of this book, published as Volume 60 of the Encyclopaedia of Mathematical Sciences: "Between number theory and geometry there have been several stimulating influences, and this book records of these enterprises. This author, who has been at the centre of such research for many years, is one of the best guides a reader can hope for. The book is full of beautiful results, open questions, stimulating conjectures and suggestions where to look for future developments. This volume bears witness of the broad scope of knowledge of the author, and the influence of several people who have commented on the manuscript before publication ... Although in the series of number theory, this volume is on diophantine geometry, and the reader will notice that algebraic geometry is present in every chapter. ... The style of the book is clear. Ideas are well explained, and the author helps the reader to pass by several technicalities. Reading and rereading this book I noticed that the topics ...
Riemannian geometry and geometric analysis
Jost, Jürgen
2017-01-01
This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research. The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the B...
Donaldson invariants in algebraic geometry
International Nuclear Information System (INIS)
Goettsche, L.
2000-01-01
In these lectures I want to give an introduction to the relation of Donaldson invariants with algebraic geometry: Donaldson invariants are differentiable invariants of smooth compact 4-manifolds X, defined via moduli spaces of anti-self-dual connections. If X is an algebraic surface, then these moduli spaces can for a suitable choice of the metric be identified with moduli spaces of stable vector bundles on X. This can be used to compute Donaldson invariants via methods of algebraic geometry and has led to a lot of activity on moduli spaces of vector bundles and coherent sheaves on algebraic surfaces. We will first recall the definition of the Donaldson invariants via gauge theory. Then we will show the relation between moduli spaces of anti-self-dual connections and moduli spaces of vector bundles on algebraic surfaces, and how this makes it possible to compute Donaldson invariants via algebraic geometry methods. Finally we concentrate on the case that the number b + of positive eigenvalues of the intersection form on the second homology of the 4-manifold is 1. In this case the Donaldson invariants depend on the metric (or in the algebraic geometric case on the polarization) via a system of walls and chambers. We will study the change of the invariants under wall-crossing, and use this in particular to compute the Donaldson invariants of rational algebraic surfaces. (author)
Aspects of differential geometry II
Gilkey, Peter
2015-01-01
Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. Book II deals with more advanced material than Book I and is aimed at the graduate level. Chapter 4 deals with additional topics in Riemannian geometry. Properties of real analytic curves given by a single ODE and of surfaces given by a pair of ODEs are studied, and the volume of geodesic balls is treated. An introduction to both holomorphic and Kähler geometry is given. In Chapter 5, the basic properties of de Rham cohomology are discussed, the Hodge Decomposition Theorem, Poincaré duality, and the Künneth formula are proved, and a brief introduction to the theory of characteristic classes is given. In Chapter 6, Lie groups and Lie algebras are dealt with. The exponential map, the classical groups, and geodesics in the context of a bi-invariant metric are discussed. The de Rham cohomology of compact Lie groups an...
Rotation of hard particles in a soft matrix
Yang, Weizhu; Liu, Qingchang; Yue, Zhufeng; Li, Xiaodong; Xu, Baoxing
Soft-hard materials integration is ubiquitous in biological materials and structures in nature and has also attracted growing attention in the bio-inspired design of advanced functional materials, structures and devices. Due to the distinct difference in their mechanical properties, the rotation of hard phases in soft matrixes upon deformation has been acknowledged, yet is lack of theory in mechanics. In this work, we propose a theoretical mechanics framework that can describe the rotation of hard particles in a soft matrix. The rotation of multiple arbitrarily shaped, located and oriented particles with perfectly bonded interfaces in an elastic soft matrix subjected to a far-field tensile loading is established and analytical solutions are derived by using complex potentials and conformal mapping methods. Strong couplings and competitions of the rotation of hard particles among each other are discussed by investigating numbers, relative locations and orientations of particles in the matrix at different loading directions. Extensive finite element analyses are performed to validate theoretical solutions and good agreement of both rotation and stress field between them are achieved. Possible extensions of the present theory to non-rigid particles, viscoelastic matrix and imperfect bonding are also discussed. Finally, by taking advantage of the rotation of hard particles, we exemplify an application in a conceptual design of soft-hard material integrated phononic crystal and demonstrate that phononic band gaps can be successfully tuned with a high accuracy through the mechanical tension-induced rotation of hard particles. The present theory established herein is expected to be of immediate interests to the design of soft-hard materials integration based functional materials, structures and devices with tunable performance via mechanical rotation of hard phases.
Foucault and the rotation of the Earth
Sommeria, Joël
2017-11-01
In February 1851, Léon Foucault published in the Comptes rendus his famous pendulum experiment performed at the "Observatoire de Paris". This ended two centuries of quest for an experimental demonstration of Earth rotation. One month later, the experiment was reproduced at larger scale in the Panthéon and, as early as the summer of 1851, it was being repeated in many places across the world. The next year, Foucault invented the gyroscope to get a still more direct proof of Earth rotation. The theory relied on the masterpiece treatise of Laplace on celestial mechanics, published in 1805, which already contained the mathematical expression of the force that would be discovered by Gustave Coriolis 30 years later. The idea of a fictitious inertial force proposed by Coriolis prevailed by the end of 19th century, as it was conceptually simpler than Laplace's approach. The full theory of the Foucault pendulum, taking into account its unavoidable imperfections, was not obtained until three decades later by Kamerlingh Onnes, the future discoverer of liquid helium and superconductivity. Today, Foucault's exceptional creativity is still a source of inspiration for research and the promotion of science through experimental proofs widely available to the public.
Algebraic Geometry and Number Theory Summer School
Sarıoğlu, Celal; Soulé, Christophe; Zeytin, Ayberk
2017-01-01
This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.
Geometry success in 20 minutes a day
LLC, LearningExpress
2014-01-01
Whether you're new to geometry or just looking for a refresher, Geometry Success in 20 Minutes a Day offers a 20-step lesson plan that provides quick and thorough instruction in practical, critical skills. Stripped of unnecessary math jargon but bursting with geometry essentials, Geometry Success in 20 Minutes a Day: Covers all vital geometry skills, from the basic building blocks of geometry to ratio, proportion, and similarity to trigonometry and beyond Provides hundreds of practice exercises in test format Applies geometr
DEFF Research Database (Denmark)
Tandrup, T; Gundersen, Hans Jørgen Gottlieb; Jensen, Eva B. Vedel
1997-01-01
further discuss the methods derived from this principle and present two new local volume estimators. The optical rotator benefits from information obtained in all three dimensions in thick sections but avoids over-/ underprojection problems at the extremes of the cell. Using computer-assisted microscopes......The optical rotator is an unbiased, local stereological principle for estimation of cell volume and cell surface area in thick, transparent slabs, The underlying principle was first described in 1993 by Kieu Jensen (T. Microsc. 170, 45-51) who also derived an estimator of length, In this study we...... the extra measurements demand minimal extra effort and make this estimator even more efficient when it comes to estimation of individual cell size than many of the previous local estimators, We demonstrate the principle of the optical rotator in an example (the cells in the dorsal root ganglion of the rat...
Vibrations of rotating machinery
Matsushita, Osami; Kanki, Hiroshi; Kobayashi, Masao; Keogh, Patrick
2017-01-01
This book opens with an explanation of the vibrations of a single degree-of-freedom (dof) system for all beginners. Subsequently, vibration analysis of multi-dof systems is explained by modal analysis. Mode synthesis modeling is then introduced for system reduction, which aids understanding in a simplified manner of how complicated rotors behave. Rotor balancing techniques are offered for rigid and flexible rotors through several examples. Consideration of gyroscopic influences on the rotordynamics is then provided and vibration evaluation of a rotor-bearing system is emphasized in terms of forward and backward whirl rotor motions through eigenvalue (natural frequency and damping ratio) analysis. In addition to these rotordynamics concerning rotating shaft vibration measured in a stationary reference frame, blade vibrations are analyzed with Coriolis forces expressed in a rotating reference frame. Other phenomena that may be assessed in stationary and rotating reference frames include stability characteristic...
Collision of an object in the transition from adiabatic inspiral to plunge around a Kerr black hole
International Nuclear Information System (INIS)
Harada, Tomohiro; Kimura, Masashi
2011-01-01
An inspiraling object of mass μ around a Kerr black hole of mass M(>>μ) experiences a continuous transition near the innermost stable circular orbit from adiabatic inspiral to plunge into the horizon as gravitational radiation extracts its energy and angular momentum. We investigate the collision of such an object with a generic counterpart around a Kerr black hole. We find that the angular momentum of the object is fine-tuned through gravitational radiation and that the high-velocity collision of the object with a generic counterpart naturally occurs around a nearly maximally rotating black hole. We also find that the center-of-mass energy can be far beyond the Planck energy for dark matter particles colliding around a stellar mass black hole and as high as 10 58 erg for stellar mass compact objects colliding around a supermassive black hole, where the present transition formalism is well justified. Therefore, rapidly rotating black holes can accelerate objects inspiraling around them to energy high enough to be of great physical interest.
Mapping the 2017 Eclipse: Education, Navigation, Inspiration
Zeiler, M.
2015-12-01
Eclipse maps are a unique vessel of knowledge. At a glance, they communicate the essential knowledge of where and when to successfully view a total eclipse of the sun. An eclipse map also provides detailed knowledge of eclipse circumstances superimposed on the highway system for optimal navigation, especially in the event that weather forces relocation. Eclipse maps are also a vital planning tool for solar physicists and astrophotographers capturing high-resolution imagery of the solar corona. Michael Zeiler will speak to the role of eclipse maps in educating the American public and inspiring people to make the effort to reach the path of totality for the sight of a lifetime. Michael will review the role of eclipse maps in astronomical research and discuss a project under development, the 2017 Eclipse Atlas for smartphones, tablets, and desktop computers.
Biologically inspired emotion recognition from speech
Directory of Open Access Journals (Sweden)
Buscicchio Cosimo
2011-01-01
Full Text Available Abstract Emotion recognition has become a fundamental task in human-computer interaction systems. In this article, we propose an emotion recognition approach based on biologically inspired methods. Specifically, emotion classification is performed using a long short-term memory (LSTM recurrent neural network which is able to recognize long-range dependencies between successive temporal patterns. We propose to represent data using features derived from two different models: mel-frequency cepstral coefficients (MFCC and the Lyon cochlear model. In the experimental phase, results obtained from the LSTM network and the two different feature sets are compared, showing that features derived from the Lyon cochlear model give better recognition results in comparison with those obtained with the traditional MFCC representation.
Molecular machines with bio-inspired mechanisms.
Zhang, Liang; Marcos, Vanesa; Leigh, David A
2018-02-26
The widespread use of molecular-level motion in key natural processes suggests that great rewards could come from bridging the gap between the present generation of synthetic molecular machines-which by and large function as switches-and the machines of the macroscopic world, which utilize the synchronized behavior of integrated components to perform more sophisticated tasks than is possible with any individual switch. Should we try to make molecular machines of greater complexity by trying to mimic machines from the macroscopic world or instead apply unfamiliar (and no doubt have to discover or invent currently unknown) mechanisms utilized by biological machines? Here we try to answer that question by exploring some of the advances made to date using bio-inspired machine mechanisms.
Inspiration Today: Music, Astronomy, and Popular Culture
Fraknoi, A.
2016-01-01
We explore a variety of examples of music inspired by serious astronomy (as opposed to simply an astronomical title or quick allusion to spooning in June to the light of the Moon). The examples are drawn from my recently published catalog of 133 such pieces, including both classical and popular genres of music. We discuss operas based on the life and work of astronomers, six songs based on a reasonable understanding of the properties of black holes, constellation pieces written by composers from around the world who are or were active amateur astronomers, the song that compares walking on the Moon to being in love, the little-known rock song that became a reference in the Astrophysical Journal, pieces that base the patterns of the music on the rhythms of astronomical phenomena, and a number of others.
Sensing Structures Inspired by Blind Cave Fish
McConney, Michael E.; Chen, Nannan; Lu, David; Anderson, Kyle D.; Hu, Huan; Liu, Chang; Tsukruk, Vladimir V.
2009-03-01
Blind cave fish, with degenerated non-functioning eyes, have evolved to ``see'' their hydrodynamic environment by using the flow receptors of the lateral line system. The hair-cell receptors are encapsulated in a hydrogel-like material, called a cupula, which increases the sensitivity of the hair-cell receptors by coupling their motion to the surrounding flowing media. We characterized the viscoelastic properties and of blind cave fish cupulae by using colloidal-probe spectroscopy in fluid. A photo-patternable hydrogel with similar properties was developed to mimic the fish receptor coupling structure. Flow-based measurements indicated that the hydrogels enhance drag through increased surface area, but also inherent material properties. These bio-inspired structures endowed micro-fabricated flow sensors with sensitivities rivaling that of fish.
Bio-inspired nano tools for neuroscience.
Das, Suradip; Carnicer-Lombarte, Alejandro; Fawcett, James W; Bora, Utpal
2016-07-01
Research and treatment in the nervous system is challenged by many physiological barriers posing a major hurdle for neurologists. The CNS is protected by a formidable blood brain barrier (BBB) which limits surgical, therapeutic and diagnostic interventions. The hostile environment created by reactive astrocytes in the CNS along with the limited regeneration capacity of the PNS makes functional recovery after tissue damage difficult and inefficient. Nanomaterials have the unique ability to interface with neural tissue in the nano-scale and are capable of influencing the function of a single neuron. The ability of nanoparticles to transcend the BBB through surface modifications has been exploited in various neuro-imaging techniques and for targeted drug delivery. The tunable topography of nanofibers provides accurate spatio-temporal guidance to regenerating axons. This review is an attempt to comprehend the progress in understanding the obstacles posed by the complex physiology of the nervous system and the innovations in design and fabrication of advanced nanomaterials drawing inspiration from natural phenomenon. We also discuss the development of nanomaterials for use in Neuro-diagnostics, Neuro-therapy and the fabrication of advanced nano-devices for use in opto-electronic and ultrasensitive electrophysiological applications. The energy efficient and parallel computing ability of the human brain has inspired the design of advanced nanotechnology based computational systems. However, extensive use of nanomaterials in neuroscience also raises serious toxicity issues as well as ethical concerns regarding nano implants in the brain. In conclusion we summarize these challenges and provide an insight into the huge potential of nanotechnology platforms in neuroscience. Copyright © 2016 Elsevier Ltd. All rights reserved.
NASA Missions Inspire Online Video Games
2012-01-01
Fast forward to 2035. Imagine being part of a community of astronauts living and working on the Moon. Suddenly, in the middle of just another day in space, a meteorite crashes into the surface of the Moon, threatening life as you know it. The support equipment that provides oxygen for the entire community has been compromised. What would you do? While this situation is one that most people will never encounter, NASA hopes to place students in such situations - virtually - to inspire, engage, and educate about NASA technologies, job opportunities, and the future of space exploration. Specifically, NASA s Learning Technologies program, part of the Agency s Office of Education, aims to inspire and motivate students to pursue careers in the science, technology, engineering, and math (STEM) disciplines through interactive technologies. The ultimate goal of these educational programs is to support the growth of a pool of qualified scientific and technical candidates for future careers at places like NASA. STEM education has been an area of concern in the United States; according to the results of the 2009 Program for International Student Assessment, 23 countries had higher average scores in mathematics literacy than the United States. On the science literacy scale, 18 countries had higher average scores. "This is part of a much bigger picture of trying to grow skilled graduates for places like NASA that will want that technical expertise," says Daniel Laughlin, the Learning Technologies project manager at Goddard Space Flight Center. "NASA is trying to increase the number of students going into those fields, and so are other government agencies."
Rotating bubble membrane radiator
Webb, Brent J.; Coomes, Edmund P.
1988-12-06
A heat radiator useful for expelling waste heat from a power generating system aboard a space vehicle is disclosed. Liquid to be cooled is passed to the interior of a rotating bubble membrane radiator, where it is sprayed into the interior of the bubble. Liquid impacting upon the interior surface of the bubble is cooled and the heat radiated from the outer surface of the membrane. Cooled liquid is collected by the action of centrifical force about the equator of the rotating membrane and returned to the power system. Details regarding a complete space power system employing the radiator are given.
Network geometry with flavor: From complexity to quantum geometry
Bianconi, Ginestra; Rahmede, Christoph
2016-03-01
Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d -dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s =-1 ,0 ,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d . In d =1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d >1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t . Interestingly the NGF remains fully classical but
Neutrino-heated winds from rotating protomagnetars
Vlasov, Andrey D.; Metzger, Brian D.; Thompson, Todd A.
2014-11-01
We calculate the steady-state properties of neutrino-driven winds from strongly magnetized, rotating protoneutron stars (PNSs; `protomagnetars') under the assumption that the outflow geometry is set by the force-free magnetic field of an aligned dipole. Our goal is to assess protomagnetars as sites of r-process nucleosynthesis and gamma-ray burst engines using a more realistic outflow geometry than assumed in previous works. One-dimensional solutions calculated along flux tubes corresponding to different polar field lines are stitched together to determine the global properties of the flow at a given neutrino luminosity and rotation period. Protomagnetars with rotation periods of P ˜ 2-5 ms are shown to produce outflows more favourable for the production of third-peak r-process nuclei due to their much shorter expansion times through the seed nucleus formation region, yet only moderately lower entropies, as compared to normal spherical PNS winds. Protomagnetars with moderately rapid birth periods P ˜ 3-5 ms may thus represent a promising galactic r-process site which is compatible with a variety of other observations, including the recent discovery of possible magnetar-powered supernovae in metal-poor galaxies. We also confirm previous results that the outflows from protomagnetars with P ˜ 1-2 ms can achieve maximum Lorentz factors Γmax ˜ 100-1000 in the range necessary to power gamma-ray bursts (GRBs). The implications of GRB jets with a heavy nuclei-dominated composition as sources of ultrahigh energy cosmic rays are also addressed.
GALAXY ROTATION AND RAPID SUPERMASSIVE BINARY COALESCENCE
Energy Technology Data Exchange (ETDEWEB)
Holley-Bockelmann, Kelly [Vanderbilt University, Nashville, TN (United States); Khan, Fazeel Mahmood, E-mail: k.holley@vanderbilt.edu [Institute of Space Technology (IST), Islamabad (Pakistan)
2015-09-10
Galaxy mergers usher the supermassive black hole (SMBH) in each galaxy to the center of the potential, where they form an SMBH binary. The binary orbit shrinks by ejecting stars via three-body scattering, but ample work has shown that in spherical galaxy models, the binary separation stalls after ejecting all the stars in its loss cone—this is the well-known final parsec problem. However, it has been shown that SMBH binaries in non-spherical galactic nuclei harden at a nearly constant rate until reaching the gravitational wave regime. Here we use a suite of direct N-body simulations to follow SMBH binary evolution in both corotating and counterrotating flattened galaxy models. For N > 500 K, we find that the evolution of the SMBH binary is convergent and is independent of the particle number. Rotation in general increases the hardening rate of SMBH binaries even more effectively than galaxy geometry alone. SMBH binary hardening rates are similar for co- and counterrotating galaxies. In the corotating case, the center of mass of the SMBH binary settles into an orbit that is in corotation resonance with the background rotating model, and the coalescence time is roughly a few 100 Myr faster than a non-rotating flattened model. We find that counterrotation drives SMBHs to coalesce on a nearly radial orbit promptly after forming a hard binary. We discuss the implications for gravitational wave astronomy, hypervelocity star production, and the effect on the structure of the host galaxy.
GALAXY ROTATION AND RAPID SUPERMASSIVE BINARY COALESCENCE
International Nuclear Information System (INIS)
Holley-Bockelmann, Kelly; Khan, Fazeel Mahmood
2015-01-01
Galaxy mergers usher the supermassive black hole (SMBH) in each galaxy to the center of the potential, where they form an SMBH binary. The binary orbit shrinks by ejecting stars via three-body scattering, but ample work has shown that in spherical galaxy models, the binary separation stalls after ejecting all the stars in its loss cone—this is the well-known final parsec problem. However, it has been shown that SMBH binaries in non-spherical galactic nuclei harden at a nearly constant rate until reaching the gravitational wave regime. Here we use a suite of direct N-body simulations to follow SMBH binary evolution in both corotating and counterrotating flattened galaxy models. For N > 500 K, we find that the evolution of the SMBH binary is convergent and is independent of the particle number. Rotation in general increases the hardening rate of SMBH binaries even more effectively than galaxy geometry alone. SMBH binary hardening rates are similar for co- and counterrotating galaxies. In the corotating case, the center of mass of the SMBH binary settles into an orbit that is in corotation resonance with the background rotating model, and the coalescence time is roughly a few 100 Myr faster than a non-rotating flattened model. We find that counterrotation drives SMBHs to coalesce on a nearly radial orbit promptly after forming a hard binary. We discuss the implications for gravitational wave astronomy, hypervelocity star production, and the effect on the structure of the host galaxy
A Whirlwind Tour of Computational Geometry.
Graham, Ron; Yao, Frances
1990-01-01
Described is computational geometry which used concepts and results from classical geometry, topology, combinatorics, as well as standard algorithmic techniques such as sorting and searching, graph manipulations, and linear programing. Also included are special techniques and paradigms. (KR)
Optimizing solar-cell grid geometry
Crossley, A. P.
1969-01-01
Trade-off analysis and mathematical expressions calculate optimum grid geometry in terms of various cell parameters. Determination of the grid geometry provides proper balance between grid resistance and cell output to optimize the energy conversion process.
Nature-Inspired Design : Strategies for Sustainable Product Development
De Pauw, I.C.
2015-01-01
Product designers can apply different strategies, methods, and tools for sustainable product development. Nature-Inspired Design Strategies (NIDS) offer designers a distinct class of strategies that use ‘nature’ as a guiding source of knowledge and inspiration for addressing sustainability.
Exploring Creativity in the Bio-Inspired Design Process
DEFF Research Database (Denmark)
Anggakara, K.; Aksdal, T.; Onarheim, Balder
2015-01-01
The growing interest in the of field bio-inspired design has been driven by the acknowledgement that inspiration from nature can serve as a valuable source of innovation. As an emerging approach, there has been a focus on building a principled methodology to address the challenges that arise...
Traceability investigation in Computed Tomography using industry-inspired workpieces
DEFF Research Database (Denmark)
Kraemer, Alexandra; Stolfi, Alessandro; Schneider, Timm
2017-01-01
This paper concerns an investigation of the accuracy of Computed Tomography (CT) measurements using four industry-inspired workpieces. A total of 16 measurands were selected and calibrated using CMMs. CT measurements on industry-inspired workpieces were carried out using two CTs having different...
Practices of Waldorf-Inspired Schools. Research Brief
Friedlaender, Diane; Beckham, Kyle; Zheng, Xinhua; Darling-Hammond, Linda
2015-01-01
"Growing a Waldorf-Inspired Approach in a Public School District" documents the practices and outcomes of Alice Birney, a Waldorf-Inspired School in Sacramento City Unified School District (SCUSD). This study highlights how such a school addresses students' academic, social, emotional, physical, and creative development. The study also…
Supporting STEM Teachers to Inspire through Everyday Innovation
Bienkowski, Marie; Shechtman, Nicole; Remold, Julie; Knudsen, Jennifer
2014-01-01
Science teachers inspire in part by their constant adaptation to the learning needs of their students and to evolving content, curriculum, technology, and student populations. Innovation--bringing novel things to a situation to confer a benefit--is an integral part of teaching overall, and in especially inspired science teaching. While innovation…
Reggio Emilia Inspired Learning Groups: Relationships, Communication, Cognition, and Play
Hong, Seong Bock; Shaffer, LaShorage; Han, Jisu
2017-01-01
A key aspect of the Reggio Emilia inspired curriculum is a learning group approach that fosters social and cognitive development. The purpose of this paper is to investigate how a Reggio Emilia inspired learning group approach works for children with and without disabilities. This study gives insight into how to form an appropriate learning group…
Kids as Airborne Mission Scientists: Designing PBL To Inspire Kids.
Koszalka, Tiffany A.; Grabowski, Barbara L.; Kim, Younghoon
Problem-based learning (PBL) has great potential for inspiring K-12 learning. KaAMS, a NASA funded project and an example of PBL, was designed to help teachers inspire middle school students to learn science. The students participate as scientists investigating environmental problems using NASA airborne remote sensing data. Two PBL modules were…
Rotations and angular momentum
International Nuclear Information System (INIS)
Nyborg, P.; Froyland, J.
1979-01-01
This paper is devoted to the analysis of rotational invariance and the properties of angular momentum in quantum mechanics. In particular, the problem of addition of angular momenta is treated in detail, and tables of Clebsch-Gordan coefficients are included
Negative Rotation Cinch Strap.
This project discloses an improved unitary parachute torso harness, having a single fastening means, wherein an auxillary tightening strap is...attached to the groin straps of said harness. Said auxillary straps are used to prevent torso rotation or harness slippage and to prevent harness elongation
International Nuclear Information System (INIS)
Jensen, B.
1993-06-01
The author presents a global solution of Einstein's equations which represents a rotating cosmic string with a finite coreradius. The importance of pressure for the generation of closed timelike curves outside the coreregion of such strings is clearly displayed in this model due to the simplicity of the source. 10 refs
Connors, G. Patrick
Many baseball players suffer from shoulder injuries related to the rotator cuff muscles. These injuries may be classified as muscular strain, tendonitis or tenosynovitis, and impingement syndrome. Treatment varies from simple rest to surgery, so it is important to be seen by a physician as soon as possible. In order to prevent these injuries, the…
Rotational dynamics with Tracker
International Nuclear Information System (INIS)
Eadkhong, T; Danworaphong, S; Rajsadorn, R; Jannual, P
2012-01-01
We propose the use of Tracker, freeware for video analysis, to analyse the moment of inertia (I) of a cylindrical plate. Three experiments are performed to validate the proposed method. The first experiment is dedicated to find the linear coefficient of rotational friction (b) for our system. By omitting the effect of such friction, we derive I for a cylindrical plate rotated around its central axis from the other two experiments based on the relation between torque and angular acceleration of rotational motion and conservation of energy. Movies of the rotating plate and hung masses are recorded. As a result, we have the deviation of I from its theoretical value of 0.4% and 3.3%, respectively. Our setup is completely constructed from locally available inexpensive materials and the experimental results indicate that the system is highly reliable. This work should pave the way for those who prefer to build a similar setup from scratch at relatively low cost compared to commercial units. (paper)
Hunter, Walter M.
This document contains detailed directions for constructing a device that mechanically produces the three-dimensional shape resulting from the rotation of any algebraic line or curve around either axis on the coordinate plant. The device was developed in response to student difficulty in visualizing, and thus grasping the mathematical principles…
International Nuclear Information System (INIS)
Grinin, V.P.
1982-01-01
It is shown that the inclination of spectral lines observed in a number of planetary nebulae when the spectrograph slit is placed along the major axis, which is presently ascribed to nonuniform expansion of the shells, actually may be due to rotation of the nebulae about their minor axes, as Campbell and Moore have suggested in their reports. It is assumed that the rotation of the central star (or, if the core is a binary system, circular motions of gas along quasi-Keplerian orbits) serves as the source of the original rotation of a protoplanetary nebula. The mechanism providing for strengthening of the original rotation in the process of expansion of the shell is the tangential pressure of L/sub α/ radiation due to the anisotropic properties of the medium and radiation field. The dynamic effect produced by them is evidently greatest in the epoch when the optical depth of the nebula in the L/sub c/ continuum becomes on the order of unity in the course of its expansion
International Nuclear Information System (INIS)
Gervais, J.L.
1993-01-01
By analyzing the extrinsic geometry of two dimensional surfaces chirally embedded in C P n (the C P n W-surface), we give exact treatments in various aspects of the classical W-geometry in the conformal gauge: First, the basis of tangent and normal vectors are defined at regular points of the surface, such that their infinitesimal displacements are given by connections which coincide with the vector potentials of the (conformal) A n -Toda Lax pair. Since the latter is known to be intrinsically related with the W symmetries, this gives the geometrical meaning of the A n W-Algebra. Second, W-surfaces are put in one-to-one correspondence with solutions of the conformally-reduced WZNW model, which is such that the Toda fields give the Cartan part in the Gauss decomposition of its solutions. Third, the additional variables of the Toda hierarchy are used as coordinates of C P n . This allows us to show that W-transformations may be extended as particular diffeomorphisms of this target-space. Higher-dimensional generalizations of the WZNW equations are derived and related with the Zakharov-Shabat equations of the Toda hierarchy. Fourth, singular points are studied from a global viewpoint, using our earlier observation that W-surfaces may be regarded as instantons. The global indices of the W-geometry, which are written in terms of the Toda fields, are shown to be the instanton numbers for associated mappings of W-surfaces into the Grassmannians. The relation with the singularities of W-surface is derived by combining the Toda equations with the Gauss-Bonnet theorem. (orig.)
Stochastic geometry for image analysis
Descombes, Xavier
2013-01-01
This book develops the stochastic geometry framework for image analysis purpose. Two main frameworks are described: marked point process and random closed sets models. We derive the main issues for defining an appropriate model. The algorithms for sampling and optimizing the models as well as for estimating parameters are reviewed. Numerous applications, covering remote sensing images, biological and medical imaging, are detailed. This book provides all the necessary tools for developing an image analysis application based on modern stochastic modeling.
Magnetoelectrostatic thruster physical geometry tests
Ramsey, W. D.
1981-01-01
Inert gas tests are conducted with several magnetoelectrostatic containment discharge chamber geometries. The configurations tested include three discharge chamber lengths; three boundary magnet patterns; two different flux density magnet materials; hemispherical and conical shaped thrusters having different surface-to-volume ratios; and two and three grid ion optics. Argon mass utilizations of 60 to 79% are attained at 210 to 280 eV/ion in different test configurations. Short hemi thruster configurations are found to produce 70 to 92% xenon mass utilization at 185 to 220 eV/ion.
Programming system for analytic geometry
International Nuclear Information System (INIS)
Raymond, Jacques
1970-01-01
After having outlined the characteristics of computing centres which do not comply with engineering tasks, notably the time required by all different tasks to be performed when developing a software (assembly, compilation, link edition, loading, run), and identified constraints specific to engineering, the author identifies the characteristics a programming system should have to suit engineering tasks. He discussed existing conversational systems and their programming language, and their main drawbacks. Then, he presents a system which aims at facilitating programming and addressing problems of analytic geometry and trigonometry
The geometry of special relativity
International Nuclear Information System (INIS)
Parizet, Jean
2008-01-01
This book for students in mathematics or physics shows the interest of geometry to understand special relativity as a consequence of invariance of Maxwell equations and of constancy of the speed of light. Space-time is actually provided with a geometrical structure and a physical interpretation: at each observer are associated his own time and his own physical space in which occur events he is concerned with. This leads to a natural approach to special relativity. The Lorentz group and its algebra are then studied by using matrices and the Pauli algebra. Quaternions are also addressed
Moduli spaces in algebraic geometry
International Nuclear Information System (INIS)
Goettsche, L.
2000-01-01
This volume of the new series of lecture notes of the Abdus Salam International Centre for Theoretical Physics contains the lecture notes of the School on Algebraic Geometry which took place at the Abdus Salam International Centre for Theoretical Physics from 26 July to 13 August 1999. The school consisted of 2 weeks of lecture courses and one week of conference. The topic of the school was moduli spaces. More specifically the lectures were divided into three subtopics: principal bundles on Riemann surfaces, moduli spaces of vector bundles and sheaves on projective varieties, and moduli spaces of curves
Worldsheet geometries of ambitwistor string
Energy Technology Data Exchange (ETDEWEB)
Ohmori, Kantaro [Department of Physics, the University of Tokyo,Hongo, Bunkyo-ku, Tokyo 133-0022 (Japan)
2015-06-12
Mason and Skinner proposed the ambitwistor string theory which directly reproduces the formulas for the amplitudes of massless particles proposed by Cachazo, He and Yuan. In this paper we discuss geometries of the moduli space of worldsheets associated to the bosonic or the RNS ambitwistor string. Further, we investigate the factorization properties of the amplitudes when an internal momentum is near on-shell in the abstract CFT language. Along the way, we propose the existence of the ambitwistor strings with three or four fermionic worldsheet currents.
Porous media geometry and transports
Adler, Pierre
1992-01-01
The goal of ""Porous Media: Geometry and Transports"" is to provide the basis of a rational and modern approach to porous media. This book emphasizes several geometrical structures (spatially periodic, fractal, and random to reconstructed) and the three major single-phase transports (diffusion, convection, and Taylor dispersion).""Porous Media"" serves various purposes. For students it introduces basic information on structure and transports. Engineers will find this book useful as a readily accessible assemblage of al the major experimental results pertaining to single-phase tr
Geometry of physical dispersion relations
International Nuclear Information System (INIS)
Raetzel, Dennis; Rivera, Sergio; Schuller, Frederic P.
2011-01-01
To serve as a dispersion relation, a cotangent bundle function must satisfy three simple algebraic properties. These conditions are derived from the inescapable physical requirements that local matter field dynamics must be predictive and allow for an observer-independent notion of positive energy. Possible modifications of the standard relativistic dispersion relation are thereby severely restricted. For instance, the dispersion relations associated with popular deformations of Maxwell theory by Gambini-Pullin or Myers-Pospelov are not admissible. Dispersion relations passing the simple algebraic checks derived here correspond to physically admissible Finslerian refinements of Lorentzian geometry.
Projective geometry and projective metrics
Busemann, Herbert
2005-01-01
The basic results and methods of projective and non-Euclidean geometry are indispensable for the geometer, and this book--different in content, methods, and point of view from traditional texts--attempts to emphasize that fact. Results of special theorems are discussed in detail only when they are needed to develop a feeling for the subject or when they illustrate a general method. On the other hand, an unusual amount of space is devoted to the discussion of the fundamental concepts of distance, motion, area, and perpendicularity.Topics include the projective plane, polarities and conic sectio
Tropical geometry of statistical models.
Pachter, Lior; Sturmfels, Bernd
2004-11-16
This article presents a unified mathematical framework for inference in graphical models, building on the observation that graphical models are algebraic varieties. From this geometric viewpoint, observations generated from a model are coordinates of a point in the variety, and the sum-product algorithm is an efficient tool for evaluating specific coordinates. Here, we address the question of how the solutions to various inference problems depend on the model parameters. The proposed answer is expressed in terms of tropical algebraic geometry. The Newton polytope of a statistical model plays a key role. Our results are applied to the hidden Markov model and the general Markov model on a binary tree.
Geometry of supersymmetric gauge theories
International Nuclear Information System (INIS)
Gieres, F.
1988-01-01
This monograph gives a detailed and pedagogical account of the geometry of rigid superspace and supersymmetric Yang-Mills theories. While the core of the text is concerned with the classical theory, the quantization and anomaly problem are briefly discussed following a comprehensive introduction to BRS differential algebras and their field theoretical applications. Among the treated topics are invariant forms and vector fields on superspace, the matrix-representation of the super-Poincare group, invariant connections on reductive homogeneous spaces and the supermetric approach. Various aspects of the subject are discussed for the first time in textbook and are consistently presented in a unified geometric formalism
Clustering in Hilbert simplex geometry
Nielsen, Frank
2017-04-03
Clustering categorical distributions in the probability simplex is a fundamental primitive often met in applications dealing with histograms or mixtures of multinomials. Traditionally, the differential-geometric structure of the probability simplex has been used either by (i) setting the Riemannian metric tensor to the Fisher information matrix of the categorical distributions, or (ii) defining the information-geometric structure induced by a smooth dissimilarity measure, called a divergence. In this paper, we introduce a novel computationally-friendly non-Riemannian framework for modeling the probability simplex: Hilbert simplex geometry. We discuss the pros and cons of those three statistical modelings, and compare them experimentally for clustering tasks.
An invitation to noncommutative geometry
Marcolli, Matilde
2008-01-01
This is the first existing volume that collects lectures on this important and fast developing subject in mathematics. The lectures are given by leading experts in the field and the range of topics is kept as broad as possible by including both the algebraic and the differential aspects of noncommutative geometry as well as recent applications to theoretical physics and number theory. Sample Chapter(s). A Walk in the Noncommutative Garden (1,639 KB). Contents: A Walk in the Noncommutative Garden (A Connes & M Marcolli); Renormalization of Noncommutative Quantum Field Theory (H Grosse & R Wulke