Symmetric Body Research Articles

Representational change of symmetric body parts in body representation

Representational change of symmetric body parts in body representation

Modeling of the Dark Phase of Flight and the Impact Area for Meteorites of Real Shapes

Aims. The complex dynamics of bodies, originating from the interplanetary matter and passing through Earth’s atmosphere, defines their further position, velocity, and final location on Earth’s surface in the form of meteorites. One of the important factors that affect the movement of a body in the atmosphere is its shape and orientation. Our goal is to model the interaction of real shape meteoroids with Earth’s atmosphere and compare the results with the standard spherical body approach. Methods. In the simulation, we use 3D models of fragments of the Košice meteorite with different sizes and shapes. Using a 3D model of fragments, we consider the real shape of the body to define its resistance properties during atmospheric transition more specifically. The simulation is performed using virtual wind tunnel in the MicroCFD (Computational Fluid Dynamics) software to obtain more realistic drag coefficients and using the µ(m)-Trajectory software to model the particle trajectory in the atmosphere including the wind profile. The final outputs from these programs are the drag coefficient as a function of the altitude and the particle orientation. Using these parameters we get the more realistic body trajectory and the impact area coordinates. Comparison of the results for real and spherical model meteorite impact location is discussed. Results. Simulation showed significant differences in trajectory and the impact area for the different real body orientations compared to the spherically symmetric body. Also, an important result is a difference in the impact area of the real body with a specific orientation without rotation and the body with considered rotation. The significant difference between the modeled impact of a real shape body and its real place of finding compared to a spherically symmetric body indicates the importance of the method used.

Theoretical study on slamming and transition stages of normal impacts of symmetrical bodies on calm and wavy water surfaces

Wave impact problems attract extensive attention and have a wide range of applications in the marine field. There is an increasing need to propose a general theoretical solution for the impacts of bodies on both calm and wavy water surfaces. In this paper, the slamming and transition stages of the high-speed normal impacts of two-dimensional (2D) symmetrical bodies on calm and wavy water surfaces are studied theoretically, where the body surfaces can be linear, concave or convex. The fluid is assumed to be incompressible, inviscid, and weightless and to have a negligible surface tension effect, and the flow is assumed to be irrotational. For the slamming stage of a wave impact, a modified Wagner model (MWM) is proposed to accurately predict the wetted length of bodies and the pressure distribution on the body surface. The MWM has a better prediction performance than the modified Logvinovich model (MLM) compared with the similarity solution for the impacts of linear wedges on the linear incident wave. For the transition stage of the normal impact of wedges on calm and wavy water surfaces, a curved fictitious body continuation (FBC) is proposed to extend the MWM from the slamming stage to the transition stage. The MWM with a curved FBC can better predict the force than the linear FBC compared with the CFD results.

On the topology of some hyperspaces of convex bodies associated to tensor norms

For every tuple d1,…,dl≥2, let Rd1⊗⋯⊗Rdl denote the tensor product of Rdi, i=1,…,l. Let us denote by B(d) the hyperspace of centrally symmetric convex bodies in Rd, d=d1⋯dl, endowed with the Hausdorff distance, and by B⊗(d1,…,dl) the subset of B(d) consisting of the convex bodies that are closed unit balls of reasonable crossnorms on Rd1⊗⋯⊗Rdl. It is known that B⊗(d1,…,dl) is a closed, contractible and locally compact subset of B(d). The hyperspace B⊗(d1,…,dl) is called the space of tensorial bodies. In this work we determine the homeomorphism type of B⊗(d1,…,dl). We show that even if B⊗(d1,…,dl) is not closed with respect to the Minkowski sum, it is an absolute retract homeomorphic to Q×Rp, where Q is the Hilbert cube and p=d1(d1+1)+⋯+dl(dl+1)2. Among other results, the relation between the Banach-Mazur compactum and the Banach-Mazur type compactum associated to B⊗(d1,…,dl) is examined.

"En fullkomlig man"

“The Complete Man”: Body and Society in Viktor Rydberg The article treats the place of the body in the cultural criticism of Viktor Rydberg, not only as a central theme but also as an image with the potential to figuratively describe societal and even cosmic relationships. Rydberg’s ideal of the symmetrical and athletic body is seen in the perspective of his dependence on German neo-humanism and the gymnastic movement. The ideal of bodily symmetry figures as an image of universal man who defies the division of labor, while the deformed body inversely figures as an image of the lack of wholeness in a stratified bourgeois society. This is further elucidated by an analysis of Rydberg’s view of Darwinism and his fear of degeneration. In the final section, special attention is given to Rydberg’s broodings on the “Future of the White Race”. In this text, the body is a figure of the collectivity (the body politic) and its diseases signify political and moral crisis, while the remedy for this state of affairs lies in recognizing the unity of the living, the dead and the unborn in the body of Christ.

Dynamics around non-spherical symmetric bodies – I. The case of a spherical body with mass anomaly

ABSTRACT The space missions designed to visit small bodies of the Solar system boosted the study of the dynamics around non-spherical bodies. In this vein, we study the dynamics around a class of objects classified by us as non-spherical symmetric bodies, including contact binaries, triaxial ellipsoids, and spherical bodies with a mass anomaly, among others. In this work, we address the results for a body with a mass anomaly. We apply the pendulum model to obtain the width of the spin–orbit resonances raised by non-asymmetric gravitational terms of the central object. The Poincaré surface of section technique is adopted to confront our analytical results and to study the system’s dynamics by varying the parameters of the central object. We verify the existence of two distinct regions around an object with a mass anomaly: a chaotic inner region that extends beyond the corotation radius and a stable outer region. In the latter, we identify structures remarkably similar to those of the classical restrict and planar three-body problem in the Poincaré surface of sections, including asymmetric periodic orbits associated with 1:1+p resonances. We apply our results to a Chariklo with a mass anomaly, obtaining that Chariklo rings are probably related to first kind periodic orbits and not with 1:3 spin–orbit resonance, as proposed in the literature. We believe that our work presents the first tools for studying mass anomaly systems.

A spectral element approach to computing normal modes

SUMMARYWe introduce a new approach to the computation of gravito-elastic free oscillations or normal modes of spherically symmetric bodies based on a spectral element discretization of the radial ordinary differential equations. Our method avoids numerical instabilities often encountered in the classical method of radial integration and root finding of the characteristic function. To this end, the code is built around a sparse matrix formulation of the eigenvalue problem taking advantage of state-of-the-art parallel iterative solvers. We apply the method to toroidal, spheroidal and radial modes and we demonstrate its versatility in the presence of attenuation, fluid layers and gravity (including the purely elastic case, the Cowling approximation, and full gravity). We demonstrate higher-order convergence and verify the software by computing seismograms and comparing these to existing numerical solutions. Finally, to emphasize the general applicability of our code, we show spectra and eigenfunctions of Earth, Mars and Jupiter’s icy moon Europa and discuss the different types of modes that emerge.

The physical basis of mollusk shell chiral coiling

Significance A theoretical model suggests that a mechanically induced twist of the soft body underlies the formation of helicospiral shells in snails and ammonites and also accounts for the startling and unique meandering shells observed in certain species. This theory addresses fundamental developmental issues of chirality and symmetry breaking: in the case of ammonites, how a bilaterally symmetric body can sometimes secrete a nonsymmetric shell; for gastropods, how an intrinsic twist possibly due to the asymmetric development of musculature can provide a mechanical motor for generating a chiral shell. Our model highlights the importance of physical forces in biological development and sheds light on shell coiling in snails, which have been used for a century as model organisms in genetic research.

Cheeger Sets for Rotationally Symmetric Planar Convex Bodies

In this note we obtain some properties of the Cheeger set C_varOmega associated to a k-rotationally symmetric planar convex body varOmega . More precisely, we prove that C_varOmega is also k-rotationally symmetric and that the boundary of C_varOmega touches all the edges of varOmega .

Vestibular Influence on Vertebrate Skeletal Symmetry and Body Shape.

Vestibular endorgans in the vertebrate inner ear form the principal sensors for head orientation and motion in space. Following the evolutionary appearance of these organs in pre-vertebrate ancestors, specific sensory epithelial patches, such as the utricle, which is sensitive to linear acceleration and orientation of the head with respect to earth’s gravity, have become particularly important for constant postural stabilization. This influence operates through descending neuronal populations with evolutionarily conserved hindbrain origins that directly and indirectly control spinal motoneurons of axial and limb muscles. During embryogenesis and early post-embryonic periods, bilateral otolith signals contribute to the formation of symmetric skeletal elements through a balanced activation of axial muscles. This role has been validated by removal of otolith signals on one side during a specific developmental period in Xenopus laevis tadpoles. This intervention causes severe scoliotic deformations that remain permanent and extend into adulthood. Accordingly, the functional influence of weight-bearing otoconia, likely on utricular hair cells and resultant afferent discharge, represents a mechanism to ensure a symmetric muscle tonus essential for establishing a normal body shape. Such an impact is presumably occurring within a critical period that is curtailed by the functional completion of central vestibulo-motor circuits and by the modifiability of skeletal elements before ossification of the bones. Thus, bilateral otolith organs and their associated sensitivity to head orientation and linear accelerations are not only indispensable for real time postural stabilization during motion in space but also serve as a guidance for the ontogenetic establishment of a symmetric body.

Sections of Convex Bodies in John’s and Minimal Surface Area Position

Abstract We prove several estimates for the volume, the mean width, and the value of the Wills functional of sections of convex bodies in John’s position, as well as for their polar bodies. These estimates extend some well-known results for convex bodies in John’s position to the case of lower-dimensional sections, which had mainly been studied for the cube and the regular simplex. Some estimates for centrally symmetric convex bodies in minimal surface area position are also obtained.

Isotropic inertia tensor without symmetry of mass distribution

Conventional calculations of the inertia tensor in undergraduate physics course are usually done for highly symmetrical bodies. Students might therefore get the impression that the moment of inertia about any axis through the center of mass is the same only for bodies with the highest degree of symmetry relative to this point, e.g., for spheres. A simple, seemingly counterintuitive example is presented, showing that the moment of inertia of a non-regular body, here an assembly of material points, can be the same about any axis passing through its center of mass.

Modelling of thermal stratification at the top of a planetary core: Application to the cores of Earth and Mercury and the thermal coupling with their mantles

We present a new numerical scheme for solving one-dimensional conduction problems and in the radial direction of a spherically symmetric body or shell with variable spatial domain. This numerical scheme adopts a solution of the conduction equation in each interval of the chosen discretization which is valid if the fluxes at the interval boundaries are constant in time. This ‘piece-wise steady flux’ (PWSF) numerical scheme is continuous and differentiable in the space domain. These smoothness properties are convenient for implementing the numerical scheme in an energy-conserved thermal evolution approach for a terrestrial core in which a conductive thermally stratified layer is considered that develops below the core-mantle boundary when the heat flux drops below the adiabatic heat flux. The influence of a time-variable thermally stratified region on the general evolution of the planetary body is examined, in comparison to imposing an adiabatic temperature profile for the entire core. Also, the dependence of the model's accuracy to the applied grid size of the numerical scheme is studied. We showed that a very low numerical resolution of this approach suffices for obtaining a thermal evolution of a partially conductive planetary core with high accuracy.By considering thermal stratification in a planetary core where the heat flux is lower than the adiabatic heat flux, radial variations in the cooling rate are accounted for whereas otherwise the distribution of energy in the core is fixed by the imposed adiabat. During the growth of the thermally stratified region, the deep part of the core cools more rapidly than the outer part of the core. Therefore, the inner core grows to a larger size and the temperature and heat flux at the core-mantle boundary are higher and larger, respectively, if a thermally stratified region is considered. For the Earth, the implications are likely very minor and can be neglected in thermal evolution studies that are not specifically interested in the thermally stratified region itself. For Mercury, however, these implications are larger. For example, the age of Mercury's inner core can be underestimated by about a billion of years if thermal stratification is neglected. The consideration of thermal stratification in Mercury's core is also important for the evolution of Mercury's mantle. It increases the mantle temperature, leads to a higher Rayleigh number and therefore a larger heat flux into the lithosphere and prolongation of mantle convection.

On the isometric conjecture of Banach

Let $V$ be a Banach space where for fixed $n$, $1<n<\dim(V)$, all of its $n$-dimensional subspaces are isometric. In 1932, Banach asked if under this hypothesis $V$ is necessarily a Hilbert space. Gromov, in 1967, answered it positively for even $n$ and all $V$. In this paper we give a positive answer for real $V$ and odd $n$ of the form $n=4k+1$, with the possible exception of $n=133.$ Our proof relies on a new characterization of ellipsoids in ${\mathbb{R}}^n$, $n\geq 5$, as the only symmetric convex bodies all of whose linear hyperplane sections are linearly equivalent affine bodies of revolution.

Equivalence principle in Reissner–Nordström geometry

The Equivalence Principle is a key element in the development of General Relativity. In one of its formulations, the Equivalence Principle states that a reference frame at rest in a uniform gravitational field is equivalent to a reference frame in uniformly accelerated motion in the absence of any gravitation field. We analyze the spacetime surrounding a non-rotating spherically symmetric charged body, known as Reissner–Nordström geometry, and exhibit a coordinate transformation, which makes explicit its compatibility with the Equivalence Principle. We revisit the Schwarzschild case, previously analyzed in the literature. We also consider second order terms of the relevant expansion parameters in the approximate metric, which is needed for the computed curvature quantities to be correct at zeroth order.

Rolling without falling on an inclined treadmill

The motion of a cylindrically or spherically symmetric body on an accelerated treadmill, inclined of an angle with respect to the horizontal, is described by means of Newtonian mechanics. By assuming that the conveyor belt has an acceleration , not necessarily constant, and that the body rolls on it, we analyze the dynamics of the center of mass of the rolling body in the laboratory reference system. We find that, for given values of the acceleration (proportional to ), the center of mass does not move with respect to the laboratory reference system. This feature can be used at the ‘engage’ phase of the inquiry based science education approach in a lecture addressed to advanced high school students.

Conical picks of mining machines with increased utility properties – selected construction and technological aspects

Shearers and roadheaders are commonly used to extract useful mineral deposits, especially hard coal, and for drilling roadways in underground mines, tunnels and other underground buildings in civil engineering. As the primary working process of this type of machines, mechanical mining of rocks is carried out by cutting. These machines' working units are equipped for this purpose with picks, usually conical (point-attack). They have the form of an axially symmetrical body consisting of a steel shaft and a tip usually made of tungsten carbide, connected by a hard brass solder. Due to the possibility of spontaneous rotation in the pick holders and even wear and tear of their tip around the entire perimeter, conical picks have a much longer service life compared to radial picks. Their life, especially when cutting hard and sharp abrasive rocks, is, however, still unsatisfactory. Rapid wear of the picks leads to a decrease in mining efficiency, an increase in this process's energy consumption, and an increase in dynamic surplus to which the cutting machine is subject. Among many forms of wear and tear of the conical picks, attention was paid to the problem of asymmetrical abrasive wear of the tips, pulling out the connection of the soldered pick tip and fatigue breaking of the pick shafts in the transition zone of the shank into the shoulder. The article presents original propositions of modification of the construction of the roadheaders/shearers conical pick shafts and the method of fixing the tip in the pick shaft in order to increase their operational durability significantly. The technologies and devices necessary to manufacture conical picks of the proposed structure were described. The developed modifications significantly contribute to the improvement of functional properties, including the reliability of conical picks, used in particular for hard rock mining.

A bio-inspired B-Spline Offset Feature for structural topology optimization

In this paper, we propose a B-Spline Offset Feature (BSOF) for feature-driven topology optimization. The feature is inspired from the geometric morphology of worms characterized by an elongated cylindrical, bilaterally symmetric, and well-segmented body along a highly deformable directrix. B-spline is used to define the directrix with its outward and inward offsets outlining the BSOF. This definition endows the BSOF with high deformability such as self-folding and self-intersection. To construct the implicit level-set function (LSF), the BSOF is decomposed into a sequence of segments whose LSFs can easily be constructed by Kreisselmeier–Steinhauser (KS) function. Regular or irregular shaped segments are identified by the deformation gradient. Irregular segments involving geometrical singularities, e.g. distorted and concave segments, are replaced with convex hulls. The stiffest structure design and compliant mechanism synthesis are studied to illustrate the effectiveness and advantages of the proposed BSOF for topology optimization.

A Thermo-elasto-plastic Evaluation of Stress State of Mars

There is recently an increasing interest to explore the ways to find out the characteristics of other planets and possibility of exploiting their mineral resources. The images sent to Earth from Mars exploration rovers showed that rocks and geological and tectonic structures are strikingly similar to those in Earth. In this study, the stress state of Mars is investigated using a spherical symmetric body concept together with the consideration of a thermo-elasto-plastic behaviour of the Earth’s constituting materials on the basis of the previous investigation of the stress state of Earth by Aydan [1,2,3]. Fundamentally four different situations, namely, fluid, elastic, elasto-plastic and thermo-elasto-plastic have been considered and the computational results are presented and their implications are discussed.

التحليل النظري لهوائي عكسي قصير باستخدام طريقة العزوم

The short backfire antenna is one of the important types of antennas due to its high directional and other characteristics. Therefore, this research deals with, a theoretical study to calculate the radiative structures of a short backfire antenna as an axially symmetric body using the moment method. The main goal is to theoretically calculate the radiation fields and compare them with previous practical researches. Where the mathematical analysis with the used software was verified by comparing the results and noting the extent of the match. The other goal is to study the effect of the antenna dimensions on its performance by studying the effect of adding a rim to the edge of the large back reflector, as well as studying the change of the radius of the two reflectors (large and small), where it was confirmed that the best value for the radius of the large reflectors and small (Rm=1λ) (Rs= 0.25 λ) respectively.