Symmetric Point Research Articles

On q-analogue of Janowski-type starlike functions with respect to symmetric points

Abstract The main objective of the present paper is to define a class of q q -starlike functions with respect to symmetric points in circular domain. Some interesting results of these functions have been evaluated in this article. The sufficiency criteria in the form of convolutions are evaluated. Furthermore, other geometric properties such as coefficient bounds, distortion theorem, closure theorem and extreme point theorem are also obtained for these newly defined functions.

Numerical analysis of two hollow drops simultaneously impacting a wet surface

The impingement behaviors of two hollow drops or two continuous dense drops simultaneously impacting a thin liquid film were analyzed numerically using a three-dimensional coupled level-set and volume-of-fraction method. The findings indicate the formation of a counter-jet during the simultaneous impact of two hollow drops, whereas a relatively stable residual film is formed during the impingement of two continuous dense drops. This counter-jet generates heat-transfer blind spots in the case of simultaneous impact by hollow drops, leading to the easy splitting of the residual liquid film. The heat around the blind spot region is difficult to release due to flow stagnation and the squeezing of the initial cold liquid film to the symmetric point. These findings indicate that more focus should be placed on the uniformity of heat transfer in realistic applications involving drop impingement. Finally, analyses of pressure gradient and flow separation revealed the formation process of the counter-jet and central liquid sheet. The findings are valuable for guiding industrial technical practice.

Fermion mass hierarchies, large lepton mixing and residual modular symmetries

In modular-invariant models of flavour, hierarchical fermion mass matrices may arise solely due to the proximity of the modulus τ to a point of residual symmetry. This mechanism does not require flavon fields, and modular weights are not analogous to Froggatt-Nielsen charges. Instead, we show that hierarchies depend on the decomposition of field representations under the residual symmetry group. We systematically go through the possible fermion field representation choices which may yield hierarchical structures in the vicinity of symmetric points, for the four smallest finite modular groups, isomorphic to S3, A4, S4, and A5, as well as for their double covers. We find a restricted set of pairs of representations for which the discussed mechanism may produce viable fermion (charged-lepton and quark) mass hierarchies. We present two lepton flavour models in which the charged-lepton mass hierarchies are naturally obtained, while lepton mixing is somewhat fine-tuned. After formulating the conditions for obtaining a viable lepton mixing matrix in the symmetric limit, we construct a model in which both the charged-lepton and neutrino sectors are free from fine-tuning.

Application of tight-binding method to calculate the band structure and the effect of pressure in crystal ZnSe

In this research tight-binding method has been applied to calculate the band structure in ZnSe crystal, the matrix elements of have been calculated using the method used by Vogl and Cohen. A computer program has been designed in MATLAB language to calculate the band structure in the ZnSe crystal, a sample of points has been formed in the first Brillouin zone (reduced zone) between the high symmetry points (L →Γ,Γ→X→(U,K) →Γ) . The energy eigen values is calculated along the high symmetry paths, the obtained results have been compared with previous works of Vogl and Cohen which shows a good agreements. A comparison between the ZnSe band structure based on sp3 and sp3s* models has been done and the energy gap between the conduction and valence bands at the high symmetry points is calculated for the sp3s*. The effect of pressure on the ZnSe band structure is calculated in the range (10-40) Gpa by calculating the matrix element under different pressure, the results show broadening in band gap due to applied pressure, the conduction band is shifted toward the high energy while the valence band is shifted toward the lower energy. The band gap is calculated values for high symmetric points were determined with pressure change and compared with theoretical calculations.

On $lambda$-Pseudo Bi-Starlike Functions with Respect to Symmetric Points Associated to Shell-Like Curves

In this paper we define a new subclass λ−pseudo bi-starlike functions with respect to symmetric points of Σ related to shell-like curves connected with Fibonacci numbers and determine the initial Taylor-Maclaurin coefficients |a2| and |a3| for f ∈????????ℒs,Σλ(α,˜p (z)). Further we determine the Fekete-Szegö result for the function class ????????ℒs,Σλ(α,˜p (z)) and for special cases, corollaries are stated which some of them are new and have not been studied so far.

New classes of harmonic meromorphic multivalent starlike functions in Janowski domain

In this article some applications of harmonic analysis are discussed in the field of Geometric Function Theory in the form of a new class of meromorphic multivalent functions. A differential operator for these function have been used to define classes of meromorphic multivalent functions in association with Janowski functions in symmetric points. Various geometric properties like sufficiency criteria, growth theorem, convex combination, weighted mean for these functions have been evaluated for this newly defined class.

Universality Class around the SU(3) Symmetric Point of the Dimer–Trimer Spin-1 Chain

We study critical phenomena of the SU(3) symmetric spin-1 chains when adding the SU(3) asymmetric term. To investigate such system, we numerically diagonalize the Dimer-Trimer (DT) model Hamiltonian around the SU(3) symmetric point, named the pure trimer (PT) point. We analyze our numerical results with the conformal field theory (CFT). First of all, we discover soft modes at the wave number q = 0 and q = 2{\pi}/3 for the PT point, and then the system is critical. Secondly, we find that the system at the PT point belongs to the CFT with the central charge c = 2 and the scaling dimension x = 2/3. Finally, by investigating the eigenvalues of the Hamiltonian in the vicinity of the PT point, we find that there is a phase transition at the PT point from a massive phase to a massless phase. From these numerical results, the phase transition at the PT point belongs to the Berezinskii-Kosterlitz-Thouless (BKT)-like universality class that is explained by the level-1 SU(3) Wess-Zumino-Witten (SU(3) 1 WZW) model.

On Bessel Functions Related with Certain Classes of Analytic Functions with respect to Symmetrical Points

In the present investigation, subclasses of analytic functions with respect to symmetrical points which are defined by the generalized Bessel functions of the first kind of orderμare introduced. Furthermore, some alluring geometric properties of these classes, which include inclusion property, integral-preserving properties, coefficients, and distortion results are studied. Moreover, some consequences of our results are also given.

Optical design of the Origins Space Telescope

Our paper discusses the optical design of the Origins Space Telescope. Origins is one of four large missions under study in preparation for the 2020 Decadal Survey in Astronomy and Astrophysics. Sensitive to the mid- and far-infrared spectrum (between 2.8 and 588 μm), Origins sets out to answer a number of important scientific questions by addressing NASA’s three key science goals in astrophysics. The Origins telescope operates at f / 14. The design includes a 5.9-m-diameter primary mirror. The large on-axis primary consists of 18 “keystone” segments of two different prescriptions arranged in two annuli (six inner and twelve outer segments) that together form a circular aperture in the goal of achieving a symmetric point spread function. To accommodate the 46 × 15 arc min full field of view (FOV) of the telescope at the design wavelength of λ = 30 μm, a three-mirror anastigmat configuration is used. The design is diffraction-limited across its instruments’ FOV. A brief discussion of each of the three baselined instruments within the Instrument Accommodation Module is presented: (1) Origins Survey Spectrometer, (2) Mid-infrared Spectrometer, Camera transit spectrometer channel, and (3) Far-Infrared Polarimeter/Imager. In addition, the upscope options for the observatory are laid out as well including a fourth instrument: the Heterodyne Receiver for Origins.

Observation of positive\u2013negative sub-wavelength interference without intensity correlation calculation

We report an experimental demonstration of positive–negative sub-wavelength interference without correlation. Typically, people can achieve sub-wavelength effects with correlation measurement no matter by using bi-photon or thermal light sources. In this paper, we adopt a thermal light source, and we count the realizations in which the intensities of the definite symmetric points are above or below a certain threshold. The distribution of numbers of these realizations which meet the restriction will show a sub-wavelength effect. With proper constrictions, positive and negative interference patterns are demonstrated.

On Janowski Type Harmonic Meromorphic Functions with respect to Symmetric Point

In this paper, we define a new class of Sakaguchi type-meromorphic harmonic functions in the Janowski domain that are starlike with respect to symmetric point. Furthermore, we investigate some important geometric properties like sufficiency criteria, distortion bound, extreme point theorem, convex combination, and weighted means.

Two-nucleon S -wave interactions at the SU(3) flavor-symmetric point with mud≈msphys : A first lattice QCD calculation with the stochastic Laplacian Heaviside method

We report on the first application of the stochastic Laplacian Heaviside method for computing multi-particle interactions with lattice QCD to the two-nucleon system. Like the Laplacian Heaviside method, this method allows for the construction of interpolating operators which can be used to construct a positive definite set of two-nucleon correlation functions, unlike nearly all other applications of lattice QCD to two nucleons in the literature. It also allows for a variational analysis in which optimal linear combinations of the interpolating operators are formed that couple predominantly to the eigenstates of the system. Utilizing such methods has become of paramount importance in order to help resolve the discrepancy in the literature on whether two nucleons in either isospin channel form a bound state at pion masses heavier than physical, with the discrepancy persisting even in the $SU(3)$-flavor symmetric point with all quark masses near the physical strange quark mass. This is the first in a series of papers aimed at resolving this discrepancy. In the present work, we employ the stochastic Laplacian Heaviside method without a hexaquark operator in the basis at a lattice spacing of $a\sim0.086$~fm, lattice volume of $L=48a\simeq4.1$~fm and pion mass $m_\pi\simeq714$ MeV. With this setup, the observed spectrum of two-nucleon energy levels strongly disfavors the presence of a bound state in either the deuteron or dineutron channel.

The ULT-HSS hybrid iteration method for symmetric saddle point problems

This paper proposes a hybrid iteration method for solving symmetric saddle point problem arising in CFD. It is an implicit alternative direction iteration method and named as the ULT-HSS (upper and lower triangular, Hermitian and skew- Hermitian splitting) method. The convergence analysis is provided, and the necessary and sufficient conditions are given for the convergence of the method. Some practical approaches are formulated for setting the optimal parameter of the method. Numerical experiments are given to show its efficiency.

Subordination problems for a new class of Bazilevič functions associated with $ k $-symmetric points and fractional $ q $-calculus operators

<abstract> In this article, we introduce and investigate a new class of Bazilevič functions with respect to $ k $-symmetric points defined by using fractional $ q $-calculus operators that are analytic in the open unit disk $ \mathbb{D} $. Several interesting subordination problems are also derived for the functions belonging to this new class. </abstract>

Certain subclass of analytic functions with respect to symmetric points associated with conic region

&lt;abstract&gt;&lt;p&gt;The purpose of this paper is to introduce and study a new subclass of analytic functions with respect to symmetric points associated to a conic region impacted by Janowski functions. Also, the study has been extended to quantum calculus by replacing the ordinary derivative with a $ q $-derivative in the defined function class. Interesting results such as initial coefficients of inverse functions and Fekete-Szegö inequalities are obtained for the defined function classes. Several applications, known or new of the main results are also presented.&lt;/p&gt;&lt;/abstract&gt;

Transient non-linear optics of diamond under ultrashort excitation pulses

Electronic response of crystalline diamond as well as high harmonic generation following irradiation by a single-cycle high-intensity laser pulse was calculated through modeling the dynamics in the framework of the time-dependent density functional theory. The frequencies of the applied laser pulses vary over visible regime with a timescale shorter than typical quantum dephasing. High harmonic yields, show substantial deviation from what is obtained from the power scaling law of perfect solids under longer cycle pulses due to the key role of strong nonlinear features of dynamics at high intensities. Further, the dynamical photon dressing of electronic states are monitored by Floquet quasi-static picture for ultrashort few cycle pulses. Our results show that dynamical bandgap is diminished as a function of increasing driven field frequency and the system changes into the dynamic metallization regimes that consequently leads to new hybridization of quasi static dressed bands particularly near high symmetrical points in the Brillouin zone. These Floquet hybridization can be used to produce coherent transport of charge on the scale of the huge number of lattice sites. Moreover, the pulse-induced phonon frequency variations that relate to bond softening and hardening, are connected to different order of Floquet dressed states. Importantly, it is found that dielectric response oscillation is directly proportional to the transient bandgap value so that entering into metallization mode preserves the polarization coherency. Based on the magnitude of calculated Keldysh parameter varies for dynamical bandgap, tunneling ionization is the dominant mechanism of excitation.

Structural, vibrational and electronic properties of D03 FeNi3

The Fe-Ni invar alloys attract the great interest of researchers due to their anomalously low coefficient of thermal expansion for Fe-rich compositions and numerous technological and practical applications. The structural, vibrational and electronic properties of D03 FeNi3 studied using the first-principles plane wave self-consistent method with the Ultrasoft pseudopotential scheme under the framework of DFT. Calculated equilibrium lattice constant and isothermal bulk modulus for D03 FeNi3 presented with the other available results. Existence of imaginary phonon frequencies in the phonon dispersion curves of D03 FeNi3 suggest the dynamical instability of it. Significant contribution of d-electrons to the total electronic density of states is in agreement with the previously reported work. Electronic charge density plots for D03 FeNi3 predict weak metallic bonding between Fe and Ni compared to between Fe-Fe metal atoms. Fermi surface topology exhibit electron and/or hole character at different high symmetrical points of the Brillouin zone based on the crossing of bands at EF in the electronic band structure. Conclusions based on the phonon dispersion curves, phonon density of states, electronic band structure along with the total and projected density of states, electronic charge density and Fermi surface are summarized.

Stability of stationary points for one-dimensional Willmore energy with spatially heterogeneous term

We consider a variational problem that consists of the Willmore energy of planar curves and a linear term in the curvature with a spatially heterogeneous coefficient. This coefficient is assumed to be a piecewise constant function. The variational problem arises from the modeling of the epidermal membrane in human skin. It has been predicted that the spatial heterogeneity of cell adhesion is one of the important factors in the protuberance formation of the membrane. We investigate the existence and stability of stationary points represented by symmetric graphs and find a condition for the existence of such stationary points by using the methods developed in the study of the Navier problem for Willmore energy. Especially, we give a necessary and sufficient condition for the existence of symmetric stationary points in terms of the gap size of the spatial heterogeneity. Moreover, we show some results on the stability of these stationary points.

Geometry effects on mode I brittle fracture in U‐notched specimens

AbstractThe effects of geometrical constraints on the fracture initiation location and the fracture strength are evaluated in U‐notched specimens using theoretical and experimental analyses. It is proven that high geometrical constraints in pure mode I loading of geometrically symmetric U‐notched specimens can result in occurrence of the maximum tangential stress (MTS) at two symmetric points on both sides of the notch bisector line. The experiments also indicated that the fracture takes place from a direction that is not along the notch bisector line. The experimental results are then examined theoretically through a stress‐based brittle fracture criterion. Because the conventional MTS criterion was poor to predict the onset of fracture properly, an attempt is made to use the generalized MTS (GMTS) criterion by considering the higher order terms in the fracture model. It is shown that the GMTS criterion gives very good predictions for experimentally obtained values of crack initiation angle and notch fracture resistance.

Intrinsic magnetism and thermoelectric applicability of novel halide perovskites Cs2GeMnX6 (X = Cl, Br): Route towards spintronics and energy harvesting technologies

Novel halides becomes a point of prestige due to their intriguing multi-dimensional applications. In this work, strict and highly accurate spin-polarized Density Functional Theory (DFT) combined with Boltzmann transport scheme has been applied to extract the properties of new class of Pb-free prototypical halide semiconductors Cs2GeMnX6 (X = Cl, Br). The structural composition of these alloys suitably prefers their cubic crystalline geometry not only at room temperature but at higher temperatures also. The electronic properties were executed by Pedrew-Burke and Ernzerhof (PBE-GGA) in addition with the strong on-site Hubbard-parameter (U) implemented on Mn-partially filled d states to designate the complete understanding regarding their electronic structures. The inclusion of two calculation schemes claims p-type indirect semiconducting band profiles with the enhancement of band gap follows the trend GGA < GGA + U. The semiconducting nature at different symmetric points with ultra-spin splitting results ferromagnetic magnetic character of 5μB leads to the promising route towards spintronics. Elastically and mechanically these alloys are characterized to show brittle/ductile capability. Conservative estimates of Seebeck coefficient gears its extending application stand in thermoelectric energy harvesting technologies. The compact overview on these FM halide perovskites can develop into other highly dynamic research fields with vast implications for high-performance spin optoelectronics, spintronics, thermoelectrics and topological devices.