Octagon with finite bridge: free fermions and determinant identities

We continue the study of the octagon form factor which helps to evaluate a class of four-point correlation functions in $$ \mathcal{N} $$ N = 4 SYM theory. The octagon is characterised, besides the kinematical parameters, by a “bridge” of ℓ propagators connecting two nonadjacent operators. In this paper we construct an operator representation of the octagon with finite bridge as an expectation value in the Fock space of free complex fermions. The bridge ℓ appears as the level of filling of the Dirac sea. We obtain determinant identities relating octagons with different bridges, which we derive from the expression of the octagon in terms of discrete fermionic oscillators. The derivation is based on the existence of a previously conjectured similarity transformation, which we find here explicitly.

Weyssenhoff Fluid Sphere Models in Einstein-Cartan Theory

We obtain three models for Geodesic flows and three models for Non-Geodesic flows of Weyssenhoff fluid considering it as the source of gravitation and spin in the Einstein-Cartan field equations. Influence of spin on the pressure, density, equation of state and the kinematical parameters is observed in both geodesic and non-geodesic models.

Enhancing Swimming Performance by Optimizing Structure of Helical Swimmers

Untethered microrobots provide the prospect for performing minimally invasive surgery and targeted delivery of drugs in hard-to-reach areas of the human body. Recently, inspired by the way the prokaryotic flagella rotates to drive the body forward, numerous studies have been carried out to study the swimming properties of helical swimmers. In this study, the resistive force theory (RFT) was applied to analyze the influence of dimensional and kinematical parameters on the propulsion performance of conventional helical swimmers. The propulsion efficiency index was applied to quantitatively evaluate the swimming performance of helical swimmers. Quantitative analysis of the effect of different parameters on the propulsion performance was performed to optimize the design of structures. Then, RFT was modified to explore the tapered helical swimmers with the helix radius changing uniformly along the axis. Theoretical results show that the helical swimmer with a constant helix angle exhibits excellent propulsion performance. The evaluation index was found to increase with increased tapering, indicating that the tapered structures can produce more efficient motion. Additionally, the analysis method extended from RFT can be used to analyze the motion of special-shaped flagella in microorganisms.

HALOGAS: the properties of extraplanar HI in disc galaxies

We present a systematic study of the extraplanar gas (EPG) in a sample of 15 nearby late-type galaxies at intermediate inclinations using publicly available, deep interferometric H I data from the Hydrogen Accretion in LOcal GAlaxieS (HALOGAS) survey. For each system we masked the H I emission coming from the regularly rotating disc and used synthetic datacubes to model the leftover “anomalous” H I flux. Our model consists of a smooth, axisymmetric thick component described by three structural and four kinematical parameters, which are fit to the data via a Markov chain Monte Carlo (MCMC) based Bayesian method. We find that extraplanar H I is nearly ubiquitous in disc galaxies as we fail to detect it in only two of the systems with the poorest spatial resolution. The EPG component encloses ∼5−25% of the total H I mass with a mean value of 14%, and has a typical thickness of a few kpc which is incompatible with expectations based on hydrostatic equilibrium models. The EPG kinematics is remarkably similar throughout the sample, and consists of a lagging rotation with typical vertical gradients of ∼ − 10 km s−1 kpc−1, a velocity dispersion of 15−30 km s−1, and, for most galaxies, a global inflow in both the vertical and radial directions with speeds of 20−30 km s−1. The EPG H I masses are in excellent agreement with predictions from simple models of the galactic fountain that are powered by stellar feedback. The combined effect of photo-ionisation and interaction of the fountain material with the circumgalactic medium can qualitatively explain the kinematics of the EPG, but dynamical models of the galactic fountain are required to fully test this framework.

Numerical Kinematical Analysis of the Shaping Mechanism

The paper deals with the complete kinematical analysis of the mechanism that enters the machine tool structure designed to generate, in particular, plane surfaces. A machine tool of this kind is called shaping machine. For this purpose, Euler’s relations concerning the velocities distribution, written in projections on the fix reference system axes will be used. Starting from these relations we will get to a system of the first order linear differential equations whose unknowns are the kinematical parameters of the mechanism elements. The variation in time of these parameters will be obtained by solving the differential equations system the differential equations system using numerical integration methods.

Numerical Kinematical Analysis of the Articulated Quadrilateral Mechanism

The paper presents a numerical method of kinematical analysis of the articulated quadrilateral mechanism. Starting from Euler’s relation concerning the distribution of speeds written in projections on the fixed reference system axes, a system of differential equations describing the movement of the mechanism was obtained. This system of differential equations was then solved using numerical integration methods and the variation with respect to time of the position kinematical parameters, of the velocities (the first order kinematical parameters), and of the accelerations (the second order kinematical parameters), was obtained. Matrix writing of the differential equations was used in order to make the differential equations set out in the paper easier to solve using the electronic computer.

Kinematical Analysis of the Articulated Quadrilateral Mechanism Using the Principle of Virtulal Mechanical Work

The paper presents a numerical method of kinematical analysis of the articulated quadrilateral mechanism, using the principle of virtual mechanical work for establishing the relations of connection between the kinematical parameters describing the movement of its elements.

Kantowski–Sachs modified holographic Ricci dark energy model in Saez–Ballester theory of gravitation

We have considered Kantowski–Sachs space–time in the presence of matter and anisotropic modified holographic Ricci dark energy components in the scalar–tensor theory of gravitation formulated by Saez and Ballester (Phys. Lett. A, 113, 467, 1986) and derived the field equations of the theory. We have used (i) hybrid expansion law proposed by Akarsu et al. (JCAP, 022, 2014), (ii) a relation between metric potentials, and (iii) modified holographic Ricci dark energy density given by Chen and Jing (Phys. Lett. B, 679, 144, 2009) to obtain an exact solution of the field equations that describes a Kantowski–Sachs holographic modified Ricci dark energy universe in this theory. Physical and kinematical parameters are also computed and their physical behavior is discussed.