Role Of Geometry Research Articles

Screw-theoretic analysis models for felid jaw mechanisms

In this paper, we examine the development of quasi-static computational models for musculoskeletal analysis, leveraging screw-theoretic techniques traditionally employed for the analysis of articulated multibody systems (MBS). The case study of analysis of bite- and muscle-forces in the articulated jaws of members of the felid (cat) family is used to highlight the critical aspects. In particular, musculoskeletal systems with multiple muscles superimposed on an underlying articulated skeleton share many features with the subclass of cable actuated parallel MBS (including redundancy in actuation and unidirectional nature of actuation forces). The screw-theoretic formulation facilitates the development of a computational model for resolving such redundancy while retaining explicit geometric meaning in terms of lines-of-action, motions and forces. The low-computational-complexity of the ensuing quasi-static models makes them well-suited both for: (a) iterative/parametric studies of the roles of geometry (muscle locations) or physiology (muscle-parameters) on skeletal load-distributions, as well as (b) implementing online inverse-dynamics-based muscle-force planners for biomimetic physical prototypes. A MATLAB Graphical User Interface was also developed to aid lay users (non-computational scientists) in performing iterative parametric force optimization and muscle location studies.

Decay of Entanglement Due to Pure Dephasing: the Role of Geometry of Entangled States

The study of the effect that pure dephasing has on the entanglement of a pair of two-level systems shows that complete disentanglement may be caused by partial pure dephasing for some initial entangled states. We examine the behaviour of the entanglement of two confined charge states under the influence of partial pure dephasing introduced by a super-Ohmic reservoir (typical for semiconductors). We classify the set of completely dephasible states and provide an explanation of this effect.

Distortion of polymer matrix composite panels under transverse thermal gradients

This paper discusses the distortion of panels made by fiber reinforced polymer matrix composites under transverse thermal-loading conditions. This is the continuation of our previous paper [Gu P, Asaro RJ. Structural buckling of polymer matrix composites due to reduced stiffness from fire damage. Compos Struct 2005;69:65–75] on fire performance of polymer matrix composites, in particular, the continuation of the discussion given in the last section of the paper for thermal distortion of the composite panels. We formulate thermal distortion from the bending theory of functionally graded materials. General solution for thermal distortion is derived in terms of material variation and temperature profile along the thickness of the panels. Using the general solution, analytical expressions of thermal distortion and associated internal forces for commonly used end supports are obtained. From these solutions, we discuss the failure mechanism induced by thermal distortion and design criteria that can be placed to prevent such failure. The roles of geometry, temperature and temperature gradients, and the competition among them in the process of structural failure are addressed.

Introduction

In 1972, the Mathematics Teacher published a series of three articles in “The Forum,” a section of the journal devoted to diverging opinions with respect to the role of geometry and the best approach to it. The February issue addressed the question “What should become of the high school geometry course?” The articles in “The Forum” in February were written by Howard F. Fehr, Frank M. Eccles, and Bruce E. Meserve. I chose the article by Fehr as one that has had an effect on high school curricula and still poses some answers to the original question today. The question was the subject of a panel discussion at the August 2006 MathFest of the Mathematical Association of America sponsored by the NCTM/MAA Joint Committee on Mutual Concerns.

The role of geometry in the friction generated on the colonic surface by mucoadhesive films

One of the main challenges in designing diagnostic devices able to move along the colon is their locomotion method. Generating friction without applying high normal forces is a key requirement in order to eliminate the risk of tissue damage. One possible solution is to generate friction by means of adhesive forces. For this reason, the device can be covered with mucoadhesive films, which are able to stick on the colonic surface. This paper identifies that the friction of mucoadhesive films depends strongly on their geometry. It seems therefore feasible to adapt the level of the friction to the properties of the colonic surface by altering the geometry of the films covering the device. Moreover, an eventual influence of the film geometry on the generated friction can reveal film shapes which create high grip despite their small size, leading to a decrease in the overall size of the device. The aim of the paper is to test in vitro the relationship between film geometry and generated friction, to fit the experimental findings in a simplified but generic macroscopic theoretical model able to predict the behavior of various geometries, and to embed those findings in the principles of the design implementation.

Effects of scarf joints on bending strength and modulus of elasticity to laminated veneer lumber (LVL)

The role of geometry on the mechanical performance of scarf joints in laminated veneer lumber (LVL) bonded with phenol formaldehyde and melamine formaldehyde (MF) adhesives was investigated. Model joints consists of 3, 4 and 5 mm veneer thicknesses at 30°, 45° and 60° of varying scarf joints for LVL produced from brutia pine ( Pinus brutia Ten) and elm ( Ulmus compestris l.) woods. However, there is little information available concerning the bending strength and modulus of elasticity for LVL, and in particular, scarf joints in these field. In this study, it was aimed to determine the bending strength and modulus of elasticity for LVL. For this purpose, samples were tested according to TS EN 310 standard. It was observed that the highest bending strength (291.5 N/mm 2) and modulus of elasticity (28 101 N/mm 2) were obtained in control (solid wood) samples having three layered LVL, jointed with 30° angle and bonded with MF adhesive. As a result of the effects scarf joints on bending strength and modulus elasticity test, if the scarf angle decreases, the properties of LVL increase.

The role of geometry on dispersive forces

The role of geometry on dispersive forces is investigated by calculating the energy between different spheroidal particles and planar surfaces, both with arbitrary dielectric properties. The energy is obtained in the non-retarded limit using a spectral representation formalism and calculating the interaction between the surface plasmons of the two macroscopic bodies. The energy is a power-law function of the separation of the bodies, where the exponent value depends on the geometrical parameters of the system, like the separation distance between bodies, and the aspect ratio among minor and major axes of the spheroid.

Virtual reconstruction: a primer in computer-assisted paleontology and biomedicine

Preface. Acknowledgments. Introduction. 1. Virtual Reconstruction. 1.1 A Virtual Reality Contest. 1.2 Virtual Reconstruction. 1.3 Computer-Assisted Paleontology. 1.3.1 Data Acquisition. 1.3.2 Data Segmentation and Three-Dimensional Reconstruction. 1.3.3 Virtual Fossil Reconstruction. 1.3.4 From Virtual Reality to Real Virtuality. 1.3.5 Databases and Morphometry. 1.3.6 Virtual Reconstruction in Space and Time. 1.4 Computer-Assisted Surgery. 1.5 Further Reading. 2. Data Representation. 2.1 World Food on a Chessboard. 2.2 Facts About Data to Get Data About Facts. 2.2.1 Analog and Digital Data. 2.2.2 Bits, Bytes, and Words. 2.2.3 Characters, Numbers, Pixels, and Voxels. 2.2.4 Representing Gray Tones and Colors. 2.2.5 Data Compression. 2.2.6 Some Common Image File Formats. 2.2.7 Implicit Versus Explicit Representation of Object Data. 2.2.8 Modeling Three-Dimensional Objects. 2.3 A Taxonomy of Biomedical Data. 2.3.1 Perspectives on Data. 2.3.2 Volume Data. 2.3.3 Surface Data. 2.3.4 Landmark Data. 2.3.5 Extent-Based Data. 2.3.6 Relational Data. 2.4 Further Reading. 3. Data Acquisition. 3.1 Data and the Physical World. 3.2 Vision and Photography as Data Acquisition: Performance Considerations. 3.3 Computed Tomography. 3.3.1 Frau RAntgena s Wedding Ring. 3.3.2 Radiographic Projections. 3.3.3 Reconstructing CT Images. 3.3.4 CT Scanning: Technical Considerations. 3.3.5 Limitations of CT Data Acquisition. 3.3.6 Slice-to-Slice, Helical, and Multislice CT. 3.3.7 Industrial and Micro Computed Tomography. 3.3.8 Three-Dimensional Data Acquisition with a Medical Scanner. 3.4 Magnetic Resonance Imaging. 3.5 Surface Scanners. 3.6 3D Digitizers. 3.7 Further Reading. 4. Image Data Processing. 4.1 Recovering Objects from Images. 4.2 Converting a CT Image into a Screen Image. 4.3 Filtering Images. 4.3.1 Coffee and Kernels. 4.3.2 Convolution and Fourier Analysis. 4.3.3 Statistical Filters. 4.3.4 Edge Detection Filters. 4.4 Extracting Isosurfaces. 4.4.1 Determining Boundaries in CT Images. 4.4.2 From Edges to Isocontours and Isosurfaces. 4.5 Interactive Segmentation. 4.6 Further Reading. 5. Visualization and Interaction. 5.1 Visualizing Data in Two and More Dimensions. 5.2 Interaction with Virtual Worlds. 5.3 The Graphics Rendering Pipeline. 5.4 Setting Up a Virtual Environment. 5.4.1 Object Materials, Lighting, and Shading. 5.4.2 Setting Up the Camera. 5.4.3 Object Manipulation and Interaction. 5.5 Volume Rendering. 5.6 Further Reading. 6. Virtual Fossil Reconstruction. 6.1 A Baroque Puzzle. 6.2 Principles of Reconstruction. 6.3 Physical and Virtual Reconstruction. 6.4 Preparing and Restoring Fossils on the Computer Screen. 6.5 Reconstructing Fossil Morphologies. 6.5.1 Recovering Implicit Anatomic Information. 6.5.2 Combining Computer Graphics and Anatomy: The Globe Paradigm. 6.5.3 Inferring Missing Information. 6.5.4 Interpolation and Extrapolation. 6.6 Correcting Fossil Deformation. 6.6.1 Taphonomic Scenarios. 6.6.2 Correcting Plastic Deformation. 6.7 Validating Virtual Reconstructions. 6.8 Paleodiagnostics and Paleoforensics. 6.9 Inferring Soft Tissue Structures. 6.9.1 Motivation. 6.9.2 Fossil Soft Tissue Reconstruction: Classic and Virtual Approaches. 6.9.3 What Shall Be Reconstructed? 6.9.4 Soft Tissue Reconstruction and Measurement. 6.10 Virtual Surgery: A Paleoanthropologista s Eye View. 6.10.1 Motivation. 6.10.2 Virtual Planning and Simulation of Surgical Interventions. 6.10.3 Custom Implant Design. 6.10.4 Soft Tissue Reconstruction. 6.11 Further Reading. 7. From Virtual Reality to Real Virtuality. 7.1 Reifying Virtual Objects. 7.2 Principles of Rapid Prototyping. 7.3 Combining Virtual Reality and Real Virtuality. 7.4 Further Reading. 8. Morphometric Analysis. 8.1 Morphometry as Reconstruction. 8.2 Morphometry and Geometry. 8.2.1 The Role of Geometry. 8.2.2 The Role of Size and Shape. 8.2.3 Multivariate Morphometry. 8.2.4 Principal Components Analysis and Dimension Reduction. 8.2.5 Classic Multivariate Morphometry: Geometry Lost. 8.2.6 Geometric Morphometrics: Geometry Recovered. 8.3 Shape Space Analysis. 8.3.1 From Da Arcy Thompson to Kendall. 8.3.2 The Workflow of Shape Space Analysis. 8.3.3 Determining a Reference Shape. 8.3.4 Analyzing Data in Shape Space. 8.3.5 Visualizing Patterns of Shape Difference and Shape Change. 8.3.5 Visualizing Patterns of Shape Difference and Shape Change. 8.4 Euclidean Distance Matrix Analysis. 8.4.1 In Search of the Golden Mean. 8.4.2 Exploring Form Variability with EDMA. 8.5 Outline Analysis. 8.6 A Comparison of Geometric Morphometric Methods. 8.6.1 Criteria for Comparison. 8.6.2 From Pattern to Process. 8.7 Exploring Morphometric Patterns. 8.8 Further Reading. Appendix A. Image Data Acquisition Systems: Performance Considerations. Appendix B. Parameters Influencing the Quality of CT Image Data. Appendix C. CT Scanning of Fossil Specimens and Recent Skeletal Specimens: How to Proceed? Appendix D. Object Manipulation in Virtual Space. Appendix E. A Parsimonious Approach to Correction of Taphonomic Deformation. Appendix F. Morphometry. References. Index.

Geometry of printed servo on perpendicular disks

Either perpendicular or longitudinal media can be magnetically printed with the final servo pattern of a disk drive. A simple analytical model provides an overview of the roles of geometry and magnetic properties in successful transfer. The more uniform geometry of compound phase patterns avoids the large line and space variations of conventional Gray codes.

Crossed conductance in ferromagnet/superconductor/ferromagnet double junctions: Role of out-of-equilibrium populations

We discuss a model of ferromagnet/superconductor/ferromagnet (FSF) double junction in which the quasiparticles are not in equilibrium with the condensate in a region of the superconductor containing the two FS contacts. The role of geometry is discussed, as well as the role of a small residual density of states within the superconducting gap, that allows a sequential tunneling crossed current. With elastic quasiparticle transport and the geometry with lateral contacts, the crossed conductances in the sequential tunneling channel are almost equal in the normal and superconducting phases, if the distance between the FS interfaces is sufficiently small. The sequential tunneling and spatially separated processes (the so-called crossed Andreev reflection and elastic cotunneling processes) lead to different signs of the crossed current in the antiparallel alignment for tunnel interfaces.

Density Functional Study of H−D Coupling Constants in Heavy Metal Dihydrogen and Dihydride Complexes: The Role of Geometry, Spin−Orbit Coupling, and Gradient Corrections in the Exchange-Correlation Kernel

The H-D nuclear spin-spin coupling constants J(H-D) of 14 heavy transition-metal dihydrogen and dihydride complexes were calculated with density functional theory using the "zeroth-order regular approximation" (ZORA) for the one-electron operators. The applied gradient-corrected density functional was able to achieve an average agreement with experimental data that is almost comparable to what has been obtained recently with hybrid functionals [J. Am. Chem. Soc. 2004, 126, 14249]. However, a systematic overestimation of J(H-D) for complexes with short H-D distances was obtained, which could be traced back to problems of the gradient functional to describe the H-D coupling in free dihydrogen well. We implemented gradient corrections for the exchange-correlation (XC) kernel and employed a basis sets with high-exponent 1s function for the coupled hydrogens. The gradient terms in the XC kernel turned out to be very important in order to achieve reasonable agreement with experimental coupling constants. On the other hand, our study reveals that spin-orbit relativistic corrections on the H-D coupling constants are comparatively small and need not to be considered at the accuracy level of currently available "standard" density functionals. The discussion of the results highlights the strong dependence of the coupling constants on the H-D distance and the possibility of large vibrational contributions to them. We also discuss the coupling constant for the hydrogen molecule in detail because of its relevance to the coupling in dihydrogen and dihydride complexes.

The nonstationary Casimir effect and quantum systems with moving boundaries

This topical issue of Journal of Optics B: Quantum and Semiclassical Optics contains 16 contributions devoted to quantum systems with moving boundaries. In a broad sense, the papers continue the studies opened exactly 100 years ago by Einstein in his seminal work on the electrodynamics of moving bodies and the quantum nature of light. Another jubilee which we wish to celebrate by launching this issue is the 80th anniversary of the publication of two papers, where the first solutions of the classical Maxwell equations in a one-dimensional cavity with moving boundaries were obtained, by T H Havelock (1924 Some dynamical illustrations of the pressure of radiation and of adiabatic invariance Phil. Mag. 47 754–71) and by E L Nicolai (1925 On a dynamical illustration of the pressure of radiation Phil. Mag. 49 171–7). As was shown by Einstein, studying the fluctuations of the electromagnetic field inevitably leads one to its quantum (corpuscular) nature. Many papers in this issue deal with problems where moving boundaries produce parametric excitation of vacuum fluctuations of the field, which could result in several different observable effects, like the modification of the famous Casimir force, or the creation of real quanta from the vacuum. It is worth emphasizing that these phenomena, frequently referred to as nonstationary (or dynamical) Casimir effects, are no longer the province only of pure theorists: some experimental groups have already started long-term work aimed at observing such effects in the laboratory. Of course, many difficult problems remain to be resolved before this dream becomes reality. Several papers here show both important progress in this direction, and possible difficulties still to be tackled. Problems that have been considered include, in particular, decoherence, entanglement, and the roles of geometry and polarization. Other papers deal with fundamental problems like the Unruh effect, the interaction of accelerated relativistic atoms with radiation, vacuum friction, and so on. Solutions of some interesting problems of nonrelativistic quantum mechanics with time-dependent boundary conditions, including applications to Bose–Einstein condensates, can also be found here. Since nonstationary Casimir effects can exist not only for photons but for any other quanta (e.g., phonons in solids or in liquid helium), we believe the approaches and results presented in this collection will find interesting applications in other branches of physics too. One possible example might be the generation of squeezed and other 'nonclassical' states of different fields by time-dependent boundary conditions. Approximately half the contributed papers stem from talks at two recent conferences: the First International Workshop on Problems with Moving Boundaries, organized by Professor J Dittrich in Prague in October 2003, and the International Workshop on the Dynamical Casimir Effect, organized by Professor G Carugno in Padua in June 2004. We wish to thank all the authors and reviewers for their efforts in preparing high quality papers, which we hope will attract the attention of other researchers, and especially of young people, to the fascinating areas covered by this special issue.

The role of geometry on regioselectivity and rate of fluorination of fluorene and diphenylmethane with Selectfluor F-TEDA-BF4.

Diphenylmethane and fluorene were used as target molecules in an investigation of the effect of the geometry of aromatic molecules on the regioselectivity and rate of fluorination with 1-chloromethyl-4-fluoro-1,4-diazoniabicyclo[2.2.2]octane bis(tetrafluoroborate) (Selectfluor F-TEDA-BF4). In acetonitrile at 80 degrees C ring fluorination of diphenylmethane was accompanied by oxidation of the saturated carbon atom, while in trifluoroacetic acid only ring fluorination with an ortho-para regioselectivity of 1.8:1 was observed. Fluorene was converted in acetonitrile as well as in trifluoroacetic acid into 2- and 4-fluoro substituted products in the relative ratio of 2:1 and 1.2:1, respectively. The reactions in acetonitrile obey a simple rate equation: v = d[F-TEDA]/dt = k2 x [F-TEDA] x [Substrate] and the second order rate constants for the reactions in acetonitrile at 65 degrees C were determined; values of 0.6 x 10(-4) M-1 s-1 for diphenylmethane and 35.5 x 10(-4) M-1 s-1 for fluorene were obtained. The reaction rates for the various functionalisations of fluorene relative to those for diphenylmethane were found to be considerably influenced by the type of functionalisation. Relative rate factors (k(rel) = k2(fluorene)/k2(diphenylmethane)) with values between 59 for fluorination and 712 for chlorination were determined, while the corresponding data for the biphenyl/diphenylmethane pair were only slightly dependent on the type of functionalisation. A reaction pathway involving electron transfer, thus forming cation radical intermediates, was proposed as the main process in the case of fluorination of fluorene with F-TEDA-BF4.

Geometry in Architectural Engineering Education Revisited

Geometric conceptualization has always been among the essential mental tools required for the invention, modeling, and visualization of spatial building structures. Furthermore, without an understanding of the geometric and mathematical base of computer graphical procedures, the ability to cope with significant developments in advanced architectural graphical representation and to adapt to the ever-changing technology in this area is limited. Despite the unquestionable significance of geometric thinking for the conception, design, and realization of buildings, the role of geometry in the education of architectural engineers, a role that traditionally constituted a significant part of their education, has been downplayed. This paper presents a systematic effort to strengthen architectural engineers’ skills in the understanding of geometric concepts and approaches that are directly related to their profession. Toward this effort a body of knowledge, mainly from Euclidean and Parabolic geometries, has been i...

Calculations of [formula omitted] NMR shieldings in polyfluoro-1-lithioethenes : Role of geometry, solvation and comparison with experimental shifts

19 F NMR chemical shielding constants in ( E)-1,2-difluoroethenyllithium ( 1) and trifluoroethenyllithium ( 2) have been calculated by the SOS-DFPT-IGLO 1 For explanation of acronym SOS-DFPT-IGLO see Section 4. 1 method and employed for an assignment of individual signals in experimental 19 F NMR spectra of polyfluoro-1-lithioethenes. The role of solvation on equilibrium geometries and consequently on the shielding constants is discussed. In comparison to HF 2 Acronym HF stands here for computations at the Hartree–Fock level, acronym MP2 for computations including correlation using second-order Møller–Plesset correction, acronym DFT for computations using Density Functional Theory. 2 or MP2 methods, DFT calculated absolute shielding values for fluoroalkenes differ from the experimental values by an opposite offset error. All methods gave acceptable relative shielding values.

Transient response of transport at transport barrier formation

Transient transport in high-temperature and turbulent plasmas is investigated. Microscopic fluctuations in toroidal plasmas are localized in the outside of the torus, so that the radial correlation length of fluctuations is meso-scale (hybrid between micro-scale and system size). The long radial correlation induces the interference of gradient and flux in different radii, and causes a fast propagation of transient response. The upper bound of thermal diffusivity, deduced from transients, is derived. The role of geometry in transport far from thermodynamical equilibrium is highlighted.

Effect of Geometry on the Performance of Model Metal Matrix Composite Joints and Transitions

The role of geometry in the mechanical performance of various configurations of joints and transitions in metal matrix composites (MMCs) was investigated. Three types of model joints were manufactured by pressure infiltration of molten Al-4.5% Mg into preforms of continuous polycrystalline alumina fibers. This method of fabrication allows metal continuity to be achieved throughout the joint region, creating composite/monolith interfaces free of the gross defects that commonly limit joint strength. Test results indicate that changes in joint configuration affect the level of plastic flow at the composite/monolith interfaces, and suggest that increasing the level of plastic constraint in these regions enhances performance. The factors controlling interface behavior in the various joint configurations were investigated with finite element techniques, based on constitutive behavior measured experimentally. Using these methods, the evolution of the stress state which develops at the composite/monolith interfaces was probed, providing insight into the interplay between the state of stress and the failure mechanisms that limit interface performance. With this in mind, the relationship between key components of stress and the mechanical performance of the experimental specimens is discussed with respect to debonding and void growth at the composite/monolith interface.

Aircraft icing

Aircraft icing

On the Size Distribution of Asteroid Families: The Role of Geometry

The steep slopes of the size distributions of the presently known asteroid families have long represented a debated problem. The reason is that it is not easy to reproduce them by the usual modeling techniques based on the application of standard power-laws as suggested by laboratory experiments. In this paper, we suggest that the failures of the previous models were due to the fact that geometric effects were not taken into account. In other words, the finite sizes of the parent bodies and the fact that fragments tend to have convex shapes cannot be disregarded. Following this approach, we find that steep size distributions are necessarily produced by fragmentations of the parent bodies. Moreover, we have been able to reproduce fairly well the observed size distributions of the major families, and we have also obtained some reasonable constraints on the original sizes of the parent bodies. Some anomalous mass depletions, probably due to injection of fragments in nearby resonances have also been found, not unexpectedly, in a few cases (Maria, Themis).

Towards a theory of molecular recognition

Why do we have a continuous conception of the opening of doors? Actually because the rotations around the hinges act as conceptual tools that allow us to “think” of door arrangements as continuously interchangeable states. If our geometrical tooling were reduced to the identity, then our conception of door opening would reduce to the dichotomous alternative closed/non-closed. This example highlights the role of geometry in the conception of physical phenomena. Accordingly, the recently introduced “gauge” geometries result in an original approach to molecular recognition when applied to quantum molecular states. In particular, this theory features a graphical description of molecular recognition between biomolecules. The 2D theory is discussed. The application of 2D gauge geometry to the description of chirality is also briefly presented.