Radial Part Research Articles

The relationship between the lateral cutaneous antebrachial nerve and the superficial branch of the radial nerve and its impact on regional anesthetic and pain blocks of the thumb; What is more important: Nerves or dermatomes?

BackgroundInnervation of the thumb and radial part of the dorsum of the hand is achieved primarily by the radial nerve, which is usually blocked for hand surgery. Inefficient blocks occur because the lateral antebrachial cutaneous nerve also extends into this area. The question then arises, whether skin innervation and peripheral blocking techniques should be directed at from the innervation by these nerves or more by the dermatome and its spinal segments. MethodsIn 68 human upper limbs embalmed with Thiel’s method, the topography of the lateral antebrachial cutaneous nerve (LACN), the superficial branch of the radial nerve (sbRN) and communicating branch (CB) were investigated by meticulous dissection from the cubital fossa to the most distal macroscopically dissectible branch, and the areas reached by these nerves were compared to the described dermatome. ResultsIn 52.9% of all specimens, the LACN was found proximal to the rascetta, in 35.3% it extended to the base of the thumb, and in 8 cases (11.8%) it extended distally to the base of the thumb. In 50%, the LACN was anterolateral to the brachioradialis muscle, and in 38.2%, strictly lateral. Only in 8 cases (11.8%) the LACN presented itself running more dorsally and laterally. A CB was observed in 28 specimens (41.2%). Both investigated nerves were found to innervate the dermatomes of C6 and C7. ConclusionsThe LACN should be considered for individual targeted blocks for surgical procedures and pain therapy within the wrist and thumb region as all nerves that might contribute to innervation of a targeted dermatome should be blocked.

The Dirac and Klein–Gordon equations and greybody radiation for the regular Hayward black hole

We investigate the Dirac and Klein–Gordon equations, as well as greybody radiation, for the Hayward black hole (BH) space–time. We first consider the Dirac equation using a null tetrad in the Newman–Penrose formalism. The equations are then separated into angular and radial parts. A pair of one-dimensional Schrödinger-like wave equations with effective potentials is obtained from the radial part. In order to examine the behavior of potentials, they are plotted with respect to radial distances. Additionally, the Klein–Gordon equation is considered in the Hayward BH space–time. At the end, we compute greybody factors for bosons and fermions and our results are shown graphically and discussed.

Выбор геометрии выходного устройства газотурбинной установки с минималь- ными потерями давления

Object and purpose of research. This paper discusses gas turbine exit unit consisting of axial-radial diffusor and pockettype volute. The purpose of the study was to select the exit unit geometry that would offer minimum losses of total pressure. Subject matter and methods. Experimental results obtained for the models of gas turbine exit units. Calculation of total pressure losses in SolidWorks package with Flow simulation extension. Correction coefficients were obtained through regression analysis. The exit unit geometry offering minimum losses of total pressure was obtained using the theory of experiment planning. Main results. The study yielded correction coefficients to the calculation results obtained in SolidWorks package with Flow simulation extension. Exit unit geometry offering minimum losses of total pressure has been successfully found. The effect of strut location in the radial part of diffusor in terms of pressure losses has been quantified. Conclusion. This study enables early identification of exit unit geometry with minimum total pressure losses, so it is valuable for practical gas turbine design.

Exploring physical properties of minimally deformed strange star model and constraints on maximum mass limit in f(\U0001d4ac) gravity

Our current investigation is inherently linked to the observations of gravitational waves from the GW190814 event which suggests that the source of the signals can be ascribed to a compact binary coalescence of a 22.2 to 24.3M ⊙ black hole and a compact object endowed with a mass of 2.50 to 2.67M ⊙. In the current exposition, we are concerned with modeling of the lower mass component of the coalescence pair. We utilize the f(\U0001d4ac) gravity together with the Minimal Geometric Deformation (MGD) technique to obtain compact stellar objects with masses aligned with the GW190814 event. Starting off with the Tolman IV ansatz for one of the metric functions, together with an MIT Bag model equation of state we are able to reduce the problem of fully describing the gravitational behavior of the seed solution to a quadrature. Through the MGD technique, we introduce anisotropy by deforming the radial part of the gravitational potential. This enables us to obtain two new classes of solutions which depend on the metricity parameter, \U0001d4ac and the deformation constant, β. We show that these two parameters play a crucial role in determining the thermodynamical behavior and stability of our models. In particular, we show that the interplay between the metricity parameter and the deformation constant predicts the mass of the progenitor articulating as the secondary component of GW190814.

Study of Radial Part of Pseudo wave Function using Pseudo-spherical Methodology in Condenser Matter

Abstract: The radial part of Fl(r) of the pseudo Schrödinger equation has been developed in pseudo potential approach. Also the pseudo spherical function Fl(r), the radial part of pseudo wave function k(r, , ) is expressed in terms of ion-core electron density, Pl(r) of Hartree or Hartree-Fock one electron wave function k(r, , ) To develop the present equation, a new pseudo spherical function Yl(r) has been investigated which is helpful in determining many types of electron densities.

More on Superintegrable Models on Spaces of Constant Curvature

A known general class of superintegrable systems on 2D spaces of constant curvature can be defined by potentials separating in (geodesic) polar coordinates. The radial parts of these potentials correspond either to an isotropic harmonic oscillator or a generalised Kepler potential. The angular components, on the contrary, are given implicitly by a transcendental, in general, equation. In the present note, devoted to the previously less studied models with the radial potential of the generalised Kepler type, a new two-parameter family of relevant angular potentials is constructed in terms of elementary functions. For an appropriate choice of parameters, the family reduces to an asymmetric spherical Higgs oscillator.

Relativity of Pseudo-Spherical Concept and Hartree-Fock Concept for Condensed Matter

Abstract: The function Fn,l (r) ;the radial part of of the pseudo-wave function k (r,  ,  ) is expressed in terms of ion-core electron density, n,l (r) and its relation with the radial part Pn,l (r ) of Hartree- Fock wave function. A new mathematical function psl (x) called as pseudo-spherical function has been developed which is similar to other mathematical functions, and helpful in determining many types of electron densities. The physical and mathematical developments on various aspects such as functional densities have been described. It is further emphasized that Fn,l (r) and Pn,l (r) functions and core electron density at different electronic states of the atom that both the functions posses strong correlationship. Study concludes that the present development resulted into an innovative simpler path in the orientation of condensed matter as well as Mathematical Physics.

Calculation of atomic integrals between relativistic functions by means of algebraic methods

We propose the use of Sturmian basis set for relativistic atomic structure calculations. We describe a numerically stable algebraic calculation of one- and two-particle radial integrals. The method is illustrated on the basis set independent calculation of energies, electric dipole moments, hyperfine integrals and parity non-conserving (PNC) amplitude for Cs in Dirac-Hartree-Fock approximation with frozen core orbitals. The previously reported results for electric dipole moments and PNC amplitude are found to be strongly basis dependent. Program summaryProgram title: PASCCPC Library link to program files:https://doi.org/10.17632/xycmhhcr5h.1Licensing provisions: MITProgramming language: Fortran 2008Nature of problem: Precise atomic measurements require reliable and highly accurate atomic structure calculations. Here we deal with the problem of numerical stability of the atomic integrals and basis set independence of the calculations.Solution method: The radial parts of the electronic orbitals are expanded in a discrete Sturmian functions that are eigenfunctions of one of the generators of the so(2,1) Lie algebra. This algebraic structure is used to deduce algebraic relations between the radial parts of the atomic integrals. This leads to numerically stable calculation, which in turn allows to achieve basis set independence.Additional comments including restrictions and unusual features: The method is currently restricted to the Dirac-Hartree-Fock method. However, this limitation will be lifted in future versions, which will be extended with the coupled clusters method.

Double hyperbolic cosine basis sets for LCAO calculations

Recently, we reported a new set of hyperbolic cosine type basis sets, which include the radial part of exponential type functions. In this study, it is show that the double hyperbolic cosine basis sets with non-integer Slater type orbitals give extremely accurate results, with the accuracy superior to that of the previous similar calculations. Total energy differences and comparison between double hyperbolic cosine and other similar basis sets suggested in literature are presented. Using double hyperbolic cosine orbitals, combined Hartree–Fock-Roothaan calculations have been carried out on the ground states of atoms and their ions within the minimal basis sets framework to compare the performance of the basis sets. The basis sets achieved the accuracy far beyond the double-zeta quality. Proposed basis sets can also play an effective role in ion-atom collisions problems and semi-empirical methods.

Altered axion abundance from a dynamical Peccei-Quinn scale

We build a model in which the relic abundance of axions is altered from the standard misalignment mechanism, either increased or decreased, due to the presence of a new light scalar that couples to the radial part of the Peccei-Quinn (PQ) field. The light scalar makes the effective PQ symmetry-breaking scale dynamical, altering the early-time dynamics for the axion and affecting its late-time dark matter abundance. We analyze this new mechanism semianalytically and numerically, showing that we can accommodate both lighter or heavier axion dark matter, compared to the standard treatments. We discuss implications of the model for axion searches and fundamental physics.

Comparative performance of different hyperbolic cosine functions and generalized B functions basis sets for atomic systems

Recently, we reported a new set of Bessel type functions, which include the radial part of generalized Bessel functions for LCAO calculations of atomic systems. In this study, to achieve further improvement of the performance of generalized Bessel type basis sets in the Hartree–Fock-Roothaan calculations, different hyperbolic cosine functions inserted into the radial part of those generalized Bessel functions. For this purpose, three different generalized hyperbolic cosine functions have been used to construct the generalized Bessel type hyperbolic cosine basis sets. The accuracies of generalized Bessel type hyperbolic cosine functions within the minimal basis sets approach are compared to show their superiority to conventional approaches those in the literature. The performance of the presented basis functions is also compared to the numerical Hartree–Fock results. Our virial ratios are in good agreement to within 8-digits of the −2. It is shown that the results obtained by the new basis sets surpass the quality and accuracy of existing Bessel type basis sets.

Screening potentials derived from the central force problem in a deformed space

The action of long-range potentials can be hindered by the collective effect of free charges in a medium, a process dubbed screening. This effect is usually modeled by adding an exponential crossover to a power-law potential. We show here how these exponential cutoffs can be obtained from first principles in the central force problem through the addition of a radial deformation of space, . When considering a potential in the form , we find that the radial part of the Schrödinger equation displays an effective potential that takes the form of two well-known screening potentials, namely, the Eckart and the Manning-Rosen potentials.

Quantum particle in a spherical well confined by a cone

We consider the quantum problem of a particle in either a spherical box or a finite spherical well confined by a circular cone with an apex angle 2θ 0 emanating from the center of the sphere, with 0 < θ 0 < π. This non-central potential can be solved by an extension of techniques used in spherically-symmetric problems. The angular parts of the eigenstates depend on azimuthal angle φ and polar angle θ as where is the associated Legendre function of integer order m and (usually noninteger) degree λ. There is an infinite discrete set of values (i = 0, 1, 3, ...) that depend on m and θ 0. Each has an infinite sequence of eigenenergies , with corresponding radial parts of eigenfunctions. In a spherical box the discrete energy spectrum is determined by the zeros of the spherical Bessel functions. For several θ 0 we demonstrate the validity of Weyl’s continuous estimate for the exact number of states up to energy E, and evaluate the fluctuations of around . We examine the behavior of bound states in a well of finite depth U 0, and find the critical value U c (θ 0) when all bound states disappear. The radial part of the zero energy eigenstate outside the well is 1/r λ+1, which is not square-integrable for λ ≤ 1/2. (0 < λ ≤ 1/2) can appear for θ 0 > θ c ≈ 0.726π and has no parallel in spherically-symmetric potentials. Bound states have spatial extent ξ which diverges as a (possibly λ-dependent) power law as U 0 approaches the value where the eigenenergy of that state vanishes.

Effect of poloidal equilibrium flow and pressure gradient on the m/n = 2/1 tearing mode

The effect of equilibrium poloidal flow and pressure gradient on the m/n = 2/1 (m is the poloidal mode number and n is the toroidal mode number) tearing mode instability for tokamak plasmas is investigated. Based on the condition of p ≠ 0 (p is plasma pressure), the radial part of the motion equation is derived and approximately solved for large poloidal mode numbers (m). By solving partial differential equations (Whittaker equation) containing second order singularity, the tearing mode stability index Δ′ is obtained. It is shown that the effect of equilibrium poloidal flow and pressure gradient has an adverse effect on the tearing mode instability when the pressure gradient is nonzero. The poloidal equilibrium flow with pressure perturbation partially reduces the stability of the classical tearing mode. But the larger pressure gradient in a certain poloidal flow velocity range can abate the adverse influence of equilibrium poloidal flow and pressure gradient. The numerical results do also indicate that the derivative of pressure gradient has a significant influence on the determination of the instability region of the poloidal flow with pressure perturbation.

Quantum-information theory of a Dirichlet ring with Aharonov–Bohm field

Shannon quantum information entropies $S_{\rho,\gamma}$, Fisher informations $I_{\rho,\gamma}$, Onicescu energies $O_{\rho,\gamma}$ and R\'{e}nyi entropies $R_{\rho,\gamma}(\alpha)$ are calculated both in the position (subscript $\rho$) and momentum ($\gamma$) spaces as functions of the inner radius $r_0$ for the two-dimensional Dirichlet unit-width annulus threaded by the Aharonov-Bohm (AB) flux $\phi_{AB}$. Discussion is based on the analysis of the corresponding position and momentum waveforms. Position Shannon entropy (Onicescu energy) grows logarithmically (decreases as $1/r_0$) with large $r_0$ tending to the same asymptote $S_\rho^{asym}=\ln(4\pi r_0)-1$ [$O_\rho^{asym}=3/(4\pi r_0)$] for all orbitals whereas their Fisher counterpart $I_{\rho_{nm}}(\phi_{AB},r_0$) approaches in the same regime the $m$-independent limit mimicking in this way the energy spectrum variation with $r_0$, which for the thin structures exhibits quadratic dependence on the principal index. Frequency of the fading oscillations of the radial parts of the wave vector functions increases with the inner radius what results in the identical $r_0\gg1$ asymptote for all momentum Shannon entropies $S_{\gamma_{nm}}(\phi_{AB};r_0)$ with the alike $n$ and different $m$. The same limit causes the Fisher momentum components $I_\gamma(\phi_{AB},r_0)$ to grow exponentially with $r_0$. It is proved that the lower limit $\alpha_{TH}$ of the semi-infinite range of the dimensionless coefficient $\alpha$, where the momentum component of this one-parameter entropy exists, is \textit{not} influenced by the radius; in particular, the change of the topology from the simply, $r_0=0$, to the doubly, $r_0>0$, connected domain is \textit{un}able to change $\alpha_{TH}=2/5$. AB field influence on the measures is calculated too.

Partial-wave approach to the Stark resonance problem of the water molecule

A partial-wave method is developed to deal with small molecules dominated by a central atom as an extension of earlier single-center methods. In particular, a model potential for the water molecule is expanded over a basis of spherical harmonics. A finite-element method is employed to generate local polynomial functions in subintervals to represent the radial part of the wave function. The angular parts of the wave function are represented by spherical harmonics. The problem of Stark resonances is treated with the exterior complex scaling method which incorporates a wave-function discontinuity at the scaling radius. The resultant non-Hermitian matrix eigenvalue problem yields resonance positions and widths (decay rates). We present these dc Stark shifts and exponential decay rates for the valence orbitals $1{b}_{1}, 3{a}_{1}$, and the bonding orbital $1{b}_{2}$. Furthermore, comparison is made with total molecular decay rates and dc shifts obtained recently within the Hartree-Fock and coupled-cluster approaches.

Exact solution of Kerr black hole perturbations viaCFT2and instanton counting: Greybody factor, quasinormal modes, and Love numbers

We give explicit expressions for the finite frequency greybody factor, quasinormal modes, and Love numbers of Kerr black holes by computing the exact connection coefficients of the radial and angular parts of the Teukolsky equation. This is obtained by solving the connection problem of the confluent Heun equation in terms of the explicit expression of irregular Virasoro conformal blocks as sums over partitions via the Alday, Gaiotto, and Tachikawa correspondence. In the relevant approximation limits our results are in agreement with existing literature. The method we use can be extended to solve the linearized Einstein equation in other interesting gravitational backgrounds.

Exact solutions of the Schrödinger equation with Dunkl derivative for the free-particle spherical waves, the pseudo-harmonic oscillator and the Mie-type potential

In this paper, we solve exactly the Schrödinger equation for the free-particle, the pseudo-harmonic oscillator and the Mie-type potential in three dimensions with the Dunkl derivative. The equations for the radial and angular parts are obtained by using spherical coordinates and separation of variables. The wave functions and the energy spectrum for these potentials are derived in an analytical way and it is shown that our results are adequately reduced to those previously reported when we remove the Dunkl derivative parameters.

A new slit‐radial die for simultaneously measuring steady state shear viscosity and first normal stress difference of viscoelastic liquids via capillary rheometry

AbstractA new slit‐radial die capable of simultaneously obtaining steady state shear viscosity and the average first normal stress difference coefficient via capillary rheometry has been developed. The steady state shear viscosity and average first normal stress difference coefficient are calculated in the slit part and radial part of the die, respectively. The steady state shear viscosity from the slit part of the slit‐radial die is compared to shear viscosities obtained from a capillary die and also the magnitude of the complex viscosity obtained from oscillatory shear experiment. The average value of first normal stress difference coefficient which is calculated in the radial part of the slit‐radial die is compared to first normal stress difference coefficient obtained from transient shear experiment in a cone‐plate geometry and the molecular stress function model predictions. The effect of variation of power law fitting parameters (consistency index, k and power law index, n) on average value of the first normal stress difference coefficient obtained from the radial part of the slit‐radial die is discussed. As this die has the shape of the city map of Karlsruhe it is named as Karlsruhe die.

Separability of Klein-Gordon equation on near horizon extremal Myers-Perry black hole

We investigate the separability of the Klein-Gordon equation on near horizon of $d$-dimensional rotating Myers-Perry black hole in two limits: (i) generic extremal case and (ii) extremal vanishing horizon case. In the first case, there is a relation between the mass and rotation parameters so that black hole temperature vanishes. In the latter case, one of the rotation parameters is restricted to zero on top of the extremality condition. We show that the Klein-Gordon equation is separable in both cases. Also, we solved the radial part of that equation and discuss its behavior in small- and large-$r$ regions.