New solution generating algorithm for isotropic static Einstein-Gauss-Bonnet metrics

The static isotropic gravitational field equation, governing the geometry and dynamics of stellar structure, is considered in Einstein–Gauss–Bonnet (EGB) gravity. This is a nonlinear Abelian differential equation which generalizes the simpler general relativistic pressure isotropy condition. A gravitational potential decomposition is postulated in order to generate new exact solutions from known solutions. The conditions for a successful integration are examined. Remarkably we generate a new exact solution to the Abelian equation from the well known Schwarzschild interior seed metric. The metric potentials are given in terms of elementary functions. A physical analysis of the model is performed in five and six spacetime dimensions. It is shown that the six-dimensional case is physically more reasonable and is consistent with the conditions restricting the physics of realistic stars.

A modified agile-eye mechanism for robotic manipulation of wristed laparoscopic instruments

<div>Replacement of the exclusively designed instruments of the robotic surgery systems with the commercial hand-held wristed instruments provides advantages such as single-usability and cost reduction. A 4-DOF robotic system, based on a modified non-symmetric 2-DOF agile-eye mechanism, was developed to manipulate the hand-held wristed instruments. The kinematics of the mechanism was analyzed, its dimensions were optimized, and a functional prototype was tested experimentally. The optimized mechanism had a great kinematic isotropy (condition number <1.31) in the target workspace. Experimental studies revealed a high tracking accuracy ($0.27 +- 0.01 deg rms for the worse case) and a reasonably acceptable compliance (0.19 deg/N.m and 0.45 deg/N.m for the first and second kinematic chains respectively). By satisfying the design requirement, the robotic manipulator provides an attractive choice for robotic surgery systems. The performance of the manipulator can be improved further by increasing the stiffness of the second kinematic chain and performing kinematic calibration.</div>

A modified agile-eye mechanism for robotic manipulation of wristed laparoscopic instruments

<div>Replacement of the exclusively designed instruments of the robotic surgery systems with the commercial hand-held wristed instruments provides advantages such as single-usability and cost reduction. A 4-DOF robotic system, based on a modified non-symmetric 2-DOF agile-eye mechanism, was developed to manipulate the hand-held wristed instruments. The kinematics of the mechanism was analyzed, its dimensions were optimized, and a functional prototype was tested experimentally. The optimized mechanism had a great kinematic isotropy (condition number <1.31) in the target workspace. Experimental studies revealed a high tracking accuracy ($0.27 +- 0.01 deg rms for the worse case) and a reasonably acceptable compliance (0.19 deg/N.m and 0.45 deg/N.m for the first and second kinematic chains respectively). By satisfying the design requirement, the robotic manipulator provides an attractive choice for robotic surgery systems. The performance of the manipulator can be improved further by increasing the stiffness of the second kinematic chain and performing kinematic calibration.</div>

Isotropy Analysis of Parallel Six-Axis Accelerometer on Circular Hyperboloids

This paper introduced the isotropic accelerometer using the circular hyperboloids method, which based on modified Gough-Stewart platform (GSP). By the static model of the accelerometer, the isotropy is defined on the acceleration matrix. On the basis of the isotropy condition, the relationship between isotropy index and geometric parameters of circular hyperboloids was investigated. Calculating the isotropy index by the optimization tool, this paper verified that it is feasible to achieve isotropy for the accelerometer. Then taking mass into account, a case is presented to optimize the parameters to construct isotropic accelerometer on circular hyperboloids. According to the 3D model of isotropic accelerometer, the static characteristic simulation was carried out by the finite element method. Based on the simulation experimental results, the calibration matrix was deduced, and the experimental isotropy index was obtained. Comparing the theoretical and experimental isotropy index, the method of circular hyperboloids was proved to be reliable and valid to construct isotropic accelerometer.

Body-centered-cubic structure and weak anharmonic phonon scattering in tungsten

It was recently found that the anharmonic phonon–phonon scattering in tungsten is extremely weak at high frequencies, leading to a predominance of electron–phonon scattering and consequently anomalous phonon transport behaviors. In this work, we calculate the phonon linewidths of W along high-symmetry directions from first principles. We find that the weak phonon–phonon scattering can be traced back to two factors. The first is the triple degeneracy of the phonon branches at the P and H points, a universal property of elemental body-centered-cubic (bcc) structures. The second is a relatively isotropic character of the phonon dispersions. When both are met, phonon–phonon scattering rates must vanish at the P and H points. The weak phonon–phonon scattering feature is also applicable to Mo and Cr. However, in other elemental bcc substances like Na, the isotropy condition is violated due to the unusually soft character of the lower transverse acoustic phonon branch along the Γ-N direction, opening emission channels and leading to much stronger phonon–phonon scattering. We also look into the distributions of electron mean-free paths (MFPs) at room temperature in tungsten, which can help engineer the resistivity of nanostructured W for applications such as interconnects.

FINSLER METRIZABLE ISOTROPIC SPRAYS AND HILBERT’S FOURTH PROBLEM

It is well known that a system of homogeneous second-order ordinary differential equations (spray) is necessarily isotropic in order to be metrizable by a Finsler function of scalar flag curvature. In our main result we show that the isotropy condition, together with three other conditions on the Jacobi endomorphism, characterize sprays that are metrizable by Finsler functions of scalar flag curvature. We call these conditions the scalar flag curvature (SFC) test. The proof of the main result provides an algorithm to construct the Finsler function of scalar flag curvature, in the case when a given spray is metrizable. Hilbert’s fourth problem asks to determine the Finsler functions with rectilinear geodesics. A Finsler function that is a solution to Hilbert’s fourth problem is necessarily of constant or scalar flag curvature. Therefore, we can use the constant flag curvature (CFC) test, which we developed in our previous paper, Bucataru and Muzsnay [‘Sprays metrizable by Finsler functions of constant flag curvature’, Differential Geom. Appl.31 (3)(2013), 405–415] as well as the SFC test to decide whether or not the projective deformations of a flat spray, which are isotropic, are metrizable by Finsler functions of constant or scalar flag curvature. We show how to use the algorithms provided by the CFC and SFC tests to construct solutions to Hilbert’s fourth problem.

A STEREOLOGICAL ESTIMATION OF GONAD VOLUME AND OOCYTE NUMBER IN A SPECIMEN OF A NATIVE CLAM (VENERUPIS PULLASTRA)

We obtained the gonad volume and oocyte number in a single Venerupis pullastra (Montagu, 1803) using unbiased stereological estimators. Since the gonad is not a fixed anatomical structure and is merged with other organs in the clam, we used new variance expressions to study the efficiency of these estimators, where the isotropy condition is not required for the covariogram.

STUDIES IN THE DECAY OF THE ACTIVE DEPOSIT OF ACTINIUM: I. ALPHA–GAMMA ANGULAR CORRELATION IN THE DECAY OF Bi211 (AcC)

The α–γ angular correlation of the cascade Bi211(α, 6.27 MeV)Tl207*(γ, 350 keV)Tl207 has been found to be isotropic to within [Formula: see text].Accepting the spin and parity of the ground state of Tl207as 1/2+, a search was made for all reasonable spins and angular momenta, pure and mixed, which could yield an isotropic correlation. Shell-model predictions and other situations have been examined. No case of unmixed α-, unmixed γ-angular momenta satisfies the isotropy condition. Many other cases are found which do so, but only with the spin and parity of the excited state of Tl207 taken as 3/2+. It has been shown that 5/2+ does not yield an isotropic correlation. With one radiation mixed and the other pure, there are eight possible combinations which fit the observations. With both radiations mixed, there is an infinity of combinations of the two mixing parameters which lead to an isotropic distribution. The αk value of the 350-keV transition (0.175 ± 0.017) shows the γ ray in question to be 76% M1 and 24% E2. The present work is consistent with only one of the two possibilities given by Gorodetzky et al. (1962) from polarization–correlation work. Accepting this additional evidence it would appear that the most plausible interpretation is that of shell-model spins and parities with both radiations mixed, α—(λ = 3, 5), γ—(76% M1, 24% E2).