Relative Shift Research Articles

A fully coupled model for predicting geomechanical and multiphase flow behaviour in fractured rocks

Geomechanical and multiphase flow characteristics are essential in recovering oil from naturally fractured rocks during hydrocarbon production because of changes in pore pressure and tension within the rock. It is a well-established fact that the geomechanical and multiphase flow characteristics of fractured rocks are interdependent on each other. Evaluation of these characteristics, for hydrocarbons displaced by water in fractured rocks under external stress loading, is severely lacking in published literature. This study aims to develop a novel numerical framework for a fully coupled model of fractured rocks, taking into consideration the pore pressure and porous media discontinuity at the fracture-matrix interface, along with an expanded Darcy's equation. The fully coupled Finite Element Method (FEM) and Computational Fluid Dynamics (CFD) model developed in this study is shown to accurately predict geomechanical and multiphase flow behaviour at the fracture-matrix interface. The results show that as external stress loading on the fractured rock increases, the porosity and permeability of the rock matrix decrease, capillary pressure at the fracture-matrix interface decreases, and the relative permeability curves shift to the right, indicating a water-soaked fracture-matrix interface. The findings of this study can be used to develop innovative strategies for enhanced oil recovery from fractured rocks.

Determination of metal-biomolecule interactions by relative mobility shift partial filling affinity capillary electrophoresis

Metal ions and their interactions with biomolecules play an important role in human health. However, optical detectors commonly used for HPCE cannot directly detect metal ions without UV absorption. To...

First-principles study on electronic structure of GaS/Mg(OH)<sub>2</sub> heterostructure

Constructing Type-II heterostructure is an effective scheme to tailor the electronic structure and improve the application performance. Motivated by recently successful syntheses of Mg(OH)<sub>2</sub> and GaS monolayers, we investigate the stability, electronic, and optical properties of GaS/Mg(OH)<sub>2</sub> heterostructure by using the density functional theory method. The calculated results show that GaS/Mg(OH)<sub>2</sub> heterostructure is easily constructed due to its small lattice mismatch, negative binding energy, and thermodynamic stability. Compared with monolayer materials, the GaS/Mg(OH)<sub>2</sub> heterostructure has a band gap that effectively decreases to 2.021 eV and has Type-II band structure, facilitating the spatial separation of photo-generated carriers where electrons are localized in the GaS and holes reside in the Mg(OH)<sub>2</sub> monolayers. The built-in electric field induced by the interlayer charge transfer points from GaS to Mg(OH)<sub>2</sub> monolayer, which can further improve the separation and suppress the recombination of electron-hole pairs. Under the biaxial strain, the valance band maximum and conduction band minimum of GaS/Mg(OH)<sub>2</sub> heterostructure shift in the downward direction to different extents, resulting in obvious change of band gap, with the change reaching about 0.5 eV. Furthermore, the band structure of GaS/Mg(OH)<sub>2</sub> heterostructure can be transformed from indirect band gap semiconductor into direct band gap semiconductor under the tensile strain, while GaS/Mg(OH)<sub>2</sub> heterostructure maintains Type-II band structure. Additionally, the band edge positions of GaS/Mg(OH)<sub>2</sub> heterostructure can also be effectively adjusted to cross the redox potentials of water decomposition at pH = 0–7. The light absorption spectra show that GaS/Mg(OH)<sub>2</sub> heterostructure has stronger light absorption capability than the constituent monolayers. Especially, the light absorption has an obvious redshift phenomenon at a tensile strain of 3%. These findings indicate that the GaS/Mg(OH)<sub>2</sub> heterostructure has a wide range of applications in the field of optoelectronics due to the tunable electronic properties, and also provides some valuable insights for future research.

Antikoni in a Settler Classroom on Kumeyaay Land: Storytelling “in the Meantime” to Imagine “Beyond” It

This article documents the process that led two groups of students enrolled in a course at UC San Diego to enter into a deeper and more reciprocal embodied relationship with the play Antikoni (a Nez Perce adaptation of Sophocles’ Antigone), its author Beth Piatote, and with UC San Diego’s fraught history related to the repatriation of Kumeyaay ancestors. Building on Theresa Stewart-Ambo and K. Wayne Yang’s urgent invitation to think “beyond land acknowledgement” and to invest time and energy in creating a world beyond settler colonialism, this article examines how being entrusted with a story—Antikoni in this case—can serve to activate settler accountability and, potentially, usher in the relational shift imagined by Stewart-Ambo and Yang. This article documents how the students chose to reciprocate the gift that is Antikoni in tangible ways in the form of two staged readings and offers a reflection on how this experience can extend beyond the classroom and lead to lasting transformative work among larger campus communities.

Scavenger Receptor BI Deficiency in Mice Is Associated With Plasma Ceramide and Sphingomyelin Accumulation and a Reduced Cholesteryl Ester Fatty Acid Length and Unsaturation Degree.

Scavenger receptor class B type I (SR-BI) is primarily known for its role in the selective uptake of cholesteryl esters (CEs) from high-density lipoproteins (HDLs). Here we investigated whether SR-BI deficiency is associated with other potentially relevant changes in the plasma lipidome than the established effect of HDL-cholesterol elevation. Targeted ultra-high-performance liquid chromatography-tandem mass spectrometry was utilized to measure lipid species in plasma from female wild-type and SR-BI knockout mice. SR-BI deficiency was associated with a reduction in the average CE fatty acid length (-2%; p<0.001) and degree of CE fatty acid unsaturation (-18%; p<0.001) due to a relative shift from longer, polyunsaturated CE species CE (20:4), CE (20:5), and CE (22:6) towards the mono-unsaturated CE (18:1) species. Sphingomyelin (SM) levels were 64% higher (p<0.001) in SR-BI knockout mice without a parallel change in (lyso)phosphatidylcholine (LPC) concentrations, resulting in an increase in the SM/LPC ratio from 0.102±0.005 to 0.163±0.003 (p<0.001). In addition, lower LPC lengths (-5%; p<0.05) and fatty acid unsaturation degrees (-20%; p<0.01) were detected in SR-BI knockout mice. Furthermore, SR-BI deficiency was associated with a 4.7-fold increase (p<0.001) in total plasma ceramide (Cer) levels, with a marked >9-fold rise (p<0.001) in Cer (d18:1/24:1) concentrations. We have shown that SR-BI deficiency in mice not only impacts the CE concentrations, length, and saturation index within the plasma compartment, but is also associated with plasma accumulation of several Cer and SM species that may contribute to the development of specific hematological and metabolic (disease) phenotypes previously detected in SR-BI knockout mice.

Translation Shifts in relation to Cultural Implications from English to Urdu Translation of Shafak’s Honour

Translation Shifts in relation to Cultural Implications from English to Urdu Translation of Shafak’s Honour

The Impact of Regional and Global Dynamics on Pakistan-Iran Relations

The research explores the geopolitical significance of the "Goldsmith Line," a border between Iran and Pakistan. Serving as a strategic link between the Middle East and South Asia, the Goldsmith Line connects the Balochistan provinces on both sides, inhabited by the Baloch people. The study delves into historical shifts in Iran-Pakistan relations, highlighting the impact of the Joint Comprehensive Plan of Action (JCPOA) and the potential for enhanced collaboration. Challenges, including security tensions, sectarian elements, and regional dynamics, are discussed. Furthermore, it emphasizes the shared cultural, ethnic, and economic ties between Baloch people on both sides, proposing measures for economic development and border security improvement. It also explores the evolving dynamics of Russia-Pakistan relations, addressing historical contexts and recent developments. The research concludes by examining obstacles and opportunities in current Iran-Pakistan ties, emphasizing the need for cautious navigation amid geopolitical complexities.

Is a unified model for patient empowerment possible or desirable?

Background: Patient empowerment has a history going back to the 1960’s ( Kayser et al. BMC Health Services Research (2019) 19:242) and originates in the movement for greater citizen participation in societal decision-making (e.g. ‘power to the people’). In the decade of the 1970’s there was a related shift in some healthcare thinking.&#x0D; While there has been a proliferation of terms, such as citizen engagement, patient participation, patient empowerment, patient activation and so forth, the fundamental underlying principle is the shift from the patient/citizen as a passive recipient of services to the patient /citizen as active, informed participant in their own health and healthcare.&#x0D; These shifts have been reflected in health care policy- person/patient centred care, personalised care and integrated care all put forward models of working that are designed to enhance patient empowerment and a shift from a bio-medical model of health care t a more holistic bio- psychosocial model of care&#x0D; Although there had been active proponents of this change, especially in parts of Northern Europe it remains a fragile part of health care&#x0D; Method: Unlike some health topics, although patient empowerment is often cited, for example in relation to current work on health technology including mHealth, there appears to be no overarching consensus on a strategy for local implementation, nor even how patient empowerment is defined for strategic purposes. This survey aimed to gather information which would, when collated, help to address these issues. To explore the current standing of patient empowerment at the beginning of 2021 a survey of experts including people expert in lived experience was carried out in a number of European countries (the final total was 25 responses from 14 countries) &#x0D; This was followed up in 2022 by a international round table event of people of lived experience, researchers, policy makers and leading experts to explore this issue and to record the discussion as a marker for future thinking about the concept.&#x0D; Results and conclusions: Despite significant activity it was clear it was very siloed and y the concept was diversely defined or interpreted in practice.&#x0D; We concluded it seems that the majority of respondents from the 14 countries only use aspects of the concept with no common understanding.&#x0D; . If there is such a disparate use of terminology, is it meaningful to refer to ‘empowerment’ as a definition of anything? Is there a better term to use for an umbrella concept?&#x0D; These findings confirm that concepts such as person centred care, personalised care and patient empowerment have considerable variations in how they are understood.&#x0D; This has significant implication for their implementation when there is such diverse understandings at all levels - Macro, Miso and Micro leading to fragmentation and a lack of a unified approach to evaluation.

Exploring Optimal Biomarker Sources: A Comparative Analysis of Exosomes and Whole Plasma in Fasting and Non-Fasting Conditions for Liquid Biopsy Applications.

The study of liquid biopsy with plasma samples is being conducted to identify biomarkers for clinical use. Exosomes, containing nucleic acids and metabolites, have emerged as possible sources for biomarkers. To evaluate the effectiveness of exosomes over plasma, we analyzed the small non-coding RNAs (sncRNAs) and metabolites extracted from exosomes in comparison to those directly extracted from whole plasma under both fasting and non-fasting conditions. We found that sncRNA profiles were not affected by fasting in either exosome or plasma samples. Our results showed that exosomal sncRNAs were found to have more consistent profiles. The plasma miRNA profiles contained high concentrations of cell-derived miRNAs that were likely due to hemolysis. We determined that certain metabolites in whole plasma exhibited noteworthy concentration shifts in relation to fasting status, while others did not. Here, we propose that (1) fasting is not required for a liquid biopsy study that involves both sncRNA and metabolomic profiling, as long as metabolites that are not influenced by fasting status are selected, and (2) the utilization of exosomal RNAs promotes robust and consistent findings in plasma samples, mitigating the impact of batch effects derived from hemolysis. These findings advance the optimization of liquid biopsy methodologies for clinical applications.

Seasonal Changes in Nycthemeral Availability of Sympatric Temperate Mixed Forest Rodents: The Predators' Perspective.

(1) Background: Bank voles (Clethrionomys glareolus) and Apodemus mice are of exceptional importance as prey for predators in temperate mixed forests. We hypothesized that overall prey availability would increase linearly with prey frequency, and that the daylight hours, which are considered particularly dangerous, would be used only during seasonal rodent population peaks and only in the twilight hours. (2) Methods: We conducted a two-year camera-trapping study in an inner alpine mixed forest and collected 19,138 1 min videos in 215 camera-trap nights. Prey availability was defined as the pseudo-replication-limited maximum number of the respective rodent taxon per 30 min period, summed per season. (3) Results: Overall prey availability increased with frequency, i.e., the maximum number of rodent individuals per camera-trap night. Seasonally, Apodemus mice were particularly available to predators in the summer and bank voles in the autumn after a tree mast year. In both cases, this was accompanied by a significant increase in diurnal availability. During the population peak of Apodemus mice, the nocturnal availability of bank voles decreased without a concurrent increase in absolute diurnal availability, even though the significant relative shift to diurnal activity superficially suggested this. Bank voles were active throughout the day, while Apodemus mice were nocturnal and (rarely) crepuscular. (4) Conclusions: Availability of rodents to predators, especially during daylight hours, was mainly dependent on their tree mast-induced increased frequencies. Bank voles likewise responded strongly to interspecific competition with the larger and aggressive Apodemus mice, which negatively affected availability to predators. At our seasonal level of evaluation, we conclude that nycthemeral availability of forest-dwelling rodents to generalist predators of temperate mixed forests is predominantly driven by bottom-up mechanisms.

Effects of Electrons on Nuclear Clock Transition Frequency in ^{229}Th Ions.

We perform calculations of the energy shift of the nuclear clock transition frequency ^{229}Th as a function of the number of electrons in Th ion. We demonstrate that the dependence of the nuclear frequency on electron configuration is significant, for example, removing one electron from the atom leads to relative shift of the nuclear frequency ∼10^{-7}, which is 12 orders of magnitude larger than the expected relative uncertainty of the nuclear clock transition frequency (∼10^{-19}). This leads to the difference of the nuclear clock frequencies in Th IV, Th III, Th II, and Th I. The relative change of the nuclear frequency between neutral Th and its bare nucleus is 1%. We also calculate the field shift constants for isotopic and isomeric shifts of atomic electron transitions in Th ions.

Stokes’ Second Flow Problem Revisited for Particle–Fluid Suspensions

Abstract An alternative analytical model is proposed for hydrodynamics of incompressible Newtonian fluids with suspended solid particles. Unlike existing single-phase models that do not distinguish the velocity field of suspended particles from the velocity field of host fluid, the present model accounts for the relative shift between the two velocity fields and assumes that its effect can be largely captured by substituting the inertia term of Navier–Stokes equations with the acceleration field of the mass center of the representative unit cell. The proposed model enjoys a relatively concise mathematical formulation. The oscillating flow of a particle–fluid suspension between two flat plates is studied with the present model, and detailed results are presented for Stokes’ second flow problem on the oscillating flow of a suspension half-space induced by an oscillating plate with specific examples of dusty gases and nanofluids. Remarkably, leading-order asymptotic expressions derived by the present model, for the effect of suspended particles on the decay index and wavenumber of the velocity field, are shown to be identical to known results derived based on the widely adopted Saffman model for dusty gases. It is hoped that the present work could offer a relatively simplified and yet reasonably accurate model for hydrodynamic problems of particle–fluid suspensions.

Characteristics of changes in the level of resistance of mixed martial arts athletes to a stress stimulus in the conditions of different force load regimes

The presented article is devoted to the study of the problem of developing effective strength training regimens for mixed martial arts athletes, taking into account the specifics of this sport and determining the level of resistance of their body and the manifestation of processes of long-term adaptation to a stressful stimulus of the appropriate nature. The purpose of the study was to study the characteristics of the change in the level of resistance of the body of mixed martial arts athletes under the conditions of the use of power load regimes with different parameters of volume and intensity. 75 athletes aged 19±0.7 years, who were divided into 3 groups, took part in the research. The following research methods were used: theoretical and methodological analysis of data from scientific and methodological literature, control testing of the development of maximum muscle strength of athletes, a method of quantitative assessment of the level of physical exertion in power sports, biochemical methods of controlling the concentration of cortisol in the blood serum of participants, a pedagogical experiment, mathematics - statistical methods of processing results. The results of the study indicate that mainly in the athletes of group 3, who during the 12 weeks of the study used a regime of high-intensity loads (Rа=0.72) under the conditions of anaerobic-lactate type of energy supply of muscle activity, we observe the most accelerated growth rates of the power capabilities of the pectoral m muscles on the background of the lowest load volume indicators in a separate set among the groups. At the same time, under the given conditions of training activity, the level of the body's resistance to such a stress stimulus of a force orientation is maximally increased in such a short period of time among athletes of the 3rd group. At the same time, in the athletes of the first group under the conditions of using the mode of low-intensity power loads (Rа=0.53), not only a minimal shift in relation to the investigated problem was detected, but also a fixed manifestation of compensatory reactions to the stressful stimulus.

Impact of 2015 Earthquake on the Shifts in Internal and International Relations of Nepal

The devastation generated by the 2015 Nepal Gorkha earthquake greatly affected the country’s politics and security, impacting the lives of around 8 million individuals with 9000 recorded deaths, more than 22 thousand injured. Thousands of private houses, public building, cultural heritages and critical infrastructures were damaged. More than 30 districts of Nepal felt the surmounting consequences of the terrible aftershocks. The aim of the paper is to evaluate the shifts within the domestic discourse in Nepal’s political happenings and also to look at the role of global actors in the humanitarian efforts in the country, filling the gaps left by state actors in the kerfuffle. The Constitution and the call for assistance by the central government were important in guaranteeing a certain kind of post-disaster stability and restoring as well as uplifting public morale and belief in the state systems. Adopting a qualitative method, through an analytical lens the study looked at the overall impact of the quake on Nepal’s politics and the trends of bilateral, regional and global assistance, focusing on the major donor agencies and the role of Nepal’s neighbouring states. There were several new developments and outlooks with regards to both state interests and the framework of disaster response. The paper also recognizes the importance of regional integration either by means of institutional instruments or through some other measure alongside a cohesive internal policy arrangement amongst the parties for future strategies aiming at effective disaster reduction and response.

Magnetoresistance of a HgTe/CdHgTe Double Quantum Well in an In-Plane Magnetic Field

A magnetic field parallel to the layers of a double quantum well with conventional semiconductor constituentsleads to a relative shift of the conduction band spectra of the constituent layers along the wave vector perpendicularto the field. If the states of the layers are tunnel-coupled, a tunneling gap is formed at the intersectionof the single-layer spectra and is shifted upward with increasing field. This leads to striking features in themagnetoresistance caused by intersections of the Fermi level with the edges of the tunneling gap. Similarstudies of transformations of the spectrum of the double quantum well in a HgTe/CdHgTe heterosystem,which has a p-type conductivity and HgTe layers with a gapless inverse energy spectrum, are reported in thiswork. Our experiments and corresponding calculations in the eight-band kp approach indicate that the evolutionof the magnetoresistance with the variation of the in-plane field here has a much more complex anddiverse character depending qualitatively on the thickness of the layers.

The distribution of triatomine (Hemiptera: Reduviidae) vectors of Trypanosoma cruzi (Kinetoplastida: Trypanosomatidae) in Illinois and Missouri: historical records and specimen submissions from community science programs.

Triatomine species (kissing bugs) infected with Trypanosoma cruzi are found across the southern United States. The northern limits of Trypanosoma cruzi infected kissing bugs are less understood. The objective of this work was to describe the locations of kissing bugs from Illinois and Missouri based on historical records, submissions to Texas A&M University's (TAMU) Kissing Bug Community Science Program and the Centers for Disease Control and Prevention (CDC), and records from online platforms (iNaturalist, BugGuide, and GBIF) up to and including 2022. A total of 228 records were discovered, including 186 from historical or observation platforms and 42 specimens submitted to TAMU or CDC. Species included Triatoma sanguisuga (221 total records, 9 nymphs) and Triatoma lecticularia (7 records). Notably, nearly all (24/26) records submitted to TAMU were collected indoors. Twelve of the 30 (40%) specimens tested were positive for the presence of T. cruzi, including parasite discrete taxonomic units TcI and TcIV. One triatomine sample had been found in a bed feeding on the submitter; this bug was positive for T. cruzi and had evidence of human blood in its gut. Records suggest a ubiquitous distribution in Missouri and potentially to the northernmost border in Illinois. Further investigations into triatomine distribution and infection status are needed within states assumed to be northern limits in order to create public health and veterinary health messaging and baseline distributional maps from which to measure future range shifts in relation to a changing climate.

Spin-Hall Effect of Cylindrical Vector Vortex Beams

Spin-Hall effect (SHE) of light is one of the main manifestations of the spin-orbit interaction of photons, and has been extensively studied for optical beams with homogeneous polarization. Here, we present a theoretical study of the SHE of cylindrical vector vortex beams (CVVBs) possessing inhomogeneous polarization. We derive the analytical expressions of the SHE of CVVBs reflected and refracted at a dielectric interface with radial and azimuthal polarization of incidence. The spin-dependent shifts of the SHE of light linearly depend on the topological charge of the CVVBs. In contrast to the conventional SHE of horizontally or vertically polarized beams, the SHE shifts of the CVVBs are asymmetrical when the topological charge is nonzero. This asymmetry results in the transverse Imbert–Fedorov (IF) shifts that are proportional to the topological charge. Furthermore, based on weak measurement, we propose an experimental scheme to enhance the SHE and related IF shifts with proper pre- and post-selection polarization states. Our results advance the study of the SHE of structured light and may find applications in SHE-based techniques such as precision measurement.

Potential of measured relative shifts in collision cross section values for biotransformation studies.

Ion mobility spectrometry-mass spectrometry (IMS-MS) separates gas phase ions due to differences in drift time from which reproducible and analyte-specific collision cross section (CCS) values can be derived. Internally conducted in vitro and in vivo metabolism (biotransformation) studies indicated repetitive shifts in measured CCS values (CCSmeas) between parent drugs and their metabolites. Hence, the purpose of the present article was (i)to investigate if such relative shifts in CCSmeas were biotransformation-specific and (ii) tohighlight their potential benefits for biotransformation studies. First, mean CCSmeas values of 165 compounds were determined (up to n = 3) using a travelling wave IMS-MS device with nitrogen as drift gas (TWCCSN2, meas). Further comparison with their predicted values (TWCCSN2, pred, Waters CCSonDemand) resulted in a mean absolute error of 5.1%. Second, a reduced data set (n = 139) was utilized to create compound pairs (n = 86) covering eight common types of phase I and II biotransformations. Constant, discriminative, and almost non-overlapping relative shifts in mean TWCCSN2,meas were obtained for demethylation (- 6.5 ± 2.1 Å2), oxygenation (hydroxylation + 3.8 ± 1.4 Å2, N-oxidation + 3.4 ± 3.3 Å2), acetylation (+ 13.5 ± 1.9 Å2), sulfation (+ 17.9 ± 4.4 Å2), glucuronidation (N-linked: + 41.7 ± 7.5 Å2, O-linked: + 38.1 ± 8.9 Å2), and glutathione conjugation (+ 49.2 ± 13.2 Å2). Consequently, we propose to consider such relative shifts in TWCCSN2, meas (rather than absolute values) as well for metabolite assignment/confirmation complementing the conventional approach to associate changes in mass-to-charge (m/z) values between a parent drug and its metabolite(s). Moreover, the comparison of relative shifts in TWCCSN2, meas significantly simplifies the mapping of metabolites into metabolic pathways as demonstrated.

Temperate rocky reef fish community patterns in a coastal marine protected area (MPA) from northern Chile, utilizing remote underwater video cameras (RUVs)

Shallow water seascapes are complex systems, important for the life history and connectivity of many marine fish species. Remote Underwater Video cameras (RUVs) are an increasingly used, non-lethal technique able to record the occurrence of reef fish species with little disturbance. In this study, RUVs were installed in a Marine Protected Area (Chañaral Island, northern Chile, 29°2'S, 71°34'W) at three different depth strata (5, 10, 15 m) in three different habitats (sand and boulder, bedrock, and kelp forest) during October 2018, July 2021 and October 2021. The RUV system recorded a total of 20 species belonging to 16 families over 73.5 h of videotaping. The most recurrent fishes were damselfish Chromis crusma, Chilean sandperch Pinguipes chilensis, and marblefish Aplodactylus punctatus. There was a significant difference in fish assemblage composition among depth strata and seasons, but not among habitats. In July 2021 (austral winter) higher densities of small cryptobenthic fish (Helcogrammoides spp.) and medium-sized carnivorous Chirodactylus variegatus were detected, whereas P. chilensis was associated to the deeper stratum, and the herbivorous blenny Scartichthys viridis was related to the shallower depths, which is likely due to differences in the habitat structure and composition. Winter 2021 showed a higher species richness than in spring 2018, while the evenness (Pielou’s J’) was significantly higher in spring 2018 than winter/spring 2021. There was no other strong or consistent pattern, which suggests that most fish species use the entire depth gradient throughout the year. Finally, the results suggest that the use of RUVs for the estimation of biodiversity of rocky reef fishes is a cost-effective way to improve our understanding of nearshore community shifts in relation to environmental forcing.

Parity time symmetry in two dimensional chiral optical lattice, via positive and negative refraction

The parity time symmetry and positive/negative refraction is investigated in chiral optical lattice. Significant parity time symmetry is reported in five level chiral optical lattice which satisfied the conditions Re(nr(±)(x,y))=Re(nr∗(±)(−x,−y) and Im(nr(±)(x,y))=−Im(nr∗(±)(−x,−y) for left and right circularly polarized beams. The related group indices, phase shifts and divergent angle are also satisfied the parity time symmetry conditions ng(±)(x,y))=ng∗(±)(−x,−y), ϕ(±)(x,y))=ϕ∗(±)(−x,−y) and θd,g(x,y)=θd,g∗(−x,−y) for left and right circularly polarized beams. Maximum negative group index is calculated to −25000. The maximum phase and group divergent angles are reported to 0.001 radian and −0.9 radian. The phase shifts in LCP and RCP beams are investigated to ±0.004 radian at a length L=10λ. The modified results have potential application in nanotechnology.