Gaussian Density Distribution Research Articles

Evolution of Tidal Disruption Event Disks with Magnetically Driven Winds

We present a time-dependent, one-dimensional, magnetically driven disk wind model based on magnetohydrodynamic (MHD) equations, in the context of tidal disruption events (TDEs). We assume that the disk is geometrically thin, is gas pressure dominated, and explicitly accounts for magnetic braking and turbulent viscosity through an extended α-viscosity prescription. We find a particular wind solution for a set of basic equations that satisfies the necessary and sufficient conditions for vertically unbound MHD flows. The solution shows that the disk evolves with mass loss due to wind and accretion from the initial Gaussian density distribution. We confirm that the mass accretion rate follows the power law of time t −19/16 at late times in the absence of wind, which matches the classical solution of J. K. Cannizzo et al. We find that the mass accretion rate is steeper than the t −19/16 curve when the wind is present. Mass accretion is also induced by magnetic braking, known as the wind-driven accretion mechanism, which results in a faster decay with time of both the mass accretion and mass-loss rates. In the disk emission, the ultraviolet (UV) luminosity is the highest among the optical, UV, and X-ray luminosities. While the optical and X-ray emission is observationally insignificant without magnetic braking, the X-ray emission is brighter at late times, especially in the presence of magnetic braking. This provides a possible explanation for observed delayed X-ray flares. Our model predicts that late-time bolometric light curves steeper than t −19/16 in UV-bright TDEs are potentially compelling indicators of magnetically driven winds.

Vertebral cortical thickness and cortical bone density: an automated CT assessment - towards enhanced spine segmentation

ABSTRACT In this paper a non-invasive method using routine CT scan to assess the vertebral geometry through normalised Cortical Thickness (CTh) and Cortical Bone Density (CBD) is proposed. This paper aims to propose a new automated method to segment cortical bone and measure its thickness and local density. This method were then used as a tool to compare these parameters between different vertebra models (in-vivo, cadaver and swine) and vertebra levels. An automated technique to segment cortical bone was proposed, assuming a two Gaussian bone density distribution. 42 vertebrae (3 high-thoracic, 3 low-thoracic and 1 lumbar vertebra for each subject) from three sub-groups (human in-vivo, cadaver and swine) were investigated. In the human in-vivo sub-group, the vertebral level was shown to influence normalised CTh and CBD. The CBD was found uniform within all the functional areas of the vertebral body (p > 0.05), while the normalised CTh showed significant differences (p < 0.001). Both CBD and normalised CTh showed significantly different between the inferior articular processes area and the posterior arch area d (p < 0.02 *). In each of the three sub-groups (human in-vivo Vs cadaveric Vs swine), normalised CTh and CBD were found significantly different across most functional areas (p < 0.001 ***). The proposed method offers an automated and accurate way of measuring cortical thickness and cortical bone density. Vertebra level and vertebra function areas were found to have influences on both proposed cortical bone characteristics. The influence of the vertebral level and of the vertebral functional areas on normalised CTh and CBD were reported within in-vivo and two vertebral models. Such a methodology could be used as a tool for image-guided surgery.

Electron Densities in H ii Regions from Observation of [N ii] 205 μm Fine Structure and Radio Recombination Lines

We employ observations of the 205 μm [N ii] fine structure (FS) line and radio recombination line (RRL) emission to derive the electron density in 10 well-known H ii regions. The combination of these two spectral lines (the RRL–FS line method) provides a sensitive probe of electron density in regions with n(e) ≥ 30 cm−3 without requiring knowledge of the size of the ionized region. By using H54α data from the Green Bank Telescope and 205 μm data from the SOFIA Airborne Observatory, we have almost identical 18″ beamwidths, removing a significant source of error for observations of H ii regions due to nonuniform density across the sources observed. The electron densities vary widely among the sources observed, from 2600 to 36,000 cm−3, with two low-density outliers at 94 and 520 cm−3. On average, these densities are a factor of 4 greater than the highest-resolution single-antenna data and a factor of almost 13 greater than the 182″ angular resolution single-antenna data having more sources in common. The total 1σ fractional uncertainties in n(e) are in the range 0.15–0.29. In the RRL–FS line method, the observationally determined quantity is proportional to ∫n 2(z)dz / ∫n(z)dz. For a Gaussian density distribution much more extended than its 1/e radius, this is equal to n0/2 , where n 0 is the peak electron density. The high values of electron density found are plausibly the result of the RRL–FS line technique sampling the peak of a centrally condensed density distribution.

Modeling the Effect of Ionospheric Electron Density Profile and Its Inhomogeneities on Sprite Halos

Sprite halos are diffuse glow discharges in the D-region ionosphere triggered by the quasi-electrostatic (QES) fields of lightning discharges. A three-dimensional (3D) QES model is adopted to investigate the effect of ionospheric electron density on sprite halos. The electron density is described by an exponential formula, parameterized by reference height (h’) and sharpness (β), and the local inhomogeneity has a Gaussian density distribution. Simulation results indicate that the reference height and steepness of the nighttime electron density affect the penetration altitudes and amplitudes of normalized electric fields, as well as the altitudes and intensities of the corresponding sprite halos optical emissions. A comparison of the daytime and nighttime conditions demonstrates that the daytime electron density profile is not favorable for generating sprite halos emissions. Furthermore, the pre-existing electron density inhomogeneities lead to enhanced local electric fields and optical emissions, potentially offering a plausible explanation for the horizontal displacement between sprites and their parent lightning, as well as their clustering.

Dust magnetoacoustic waves in an inhomogeneous cylindrical four-component dusty plasma in the presence of polarization force

Abstract Dust magnetoacoustic waves have been examined in an inhomogeneous, bounded, cylindrical dusty plasma containing oppositely polarized dust particles. Considering polarization force, dust dynamics in r − θ plane is studied in the presence of inhomogeneous external magnetic field along z axis. At equilibrium, the dusty plasma components are supposed to follow Gaussian density distribution. Using reductive perturbation method (RPM), a variable coefficient cylindrical Kadomtsev–Petviashvili (VCCKP) equation has been derived. For weak azimuthal perturbation, an analytical solution, obtained by Zhang (“Exact solutions of a kdv equation with variable coefficients via exp-function method,” Nonlinear Dynam., vol. 52, nos. 1–2, pp. 11–17, 2008) using Exp-function method, is chosen. Phase velocity of dust magnetoacoustic wave is found to be modified by the density inhomogeneities, polarization force, dust charge state ratio and ion-to-electron temperature ratio. Spatio-temporal evolution of the dust number densities has been noticed. Existence of the compressive electromagnetic solitary waves is observed numerically for the chosen dusty plasma parameter range. The impacts of the inhomogeneity, polarization force, dust charge state ratio and ion-to-electron temperature ratio on the relative amplitude of the dust magnetoacoustic wave are also discussed.

A big data analytics method for the evaluation of maritime traffic safety using automatic identification system data

The complex traffic situations are among the factors influencing maritime safety. They can be quantitatively estimated through the analysis of traffic data. This paper explores the impact of complex traffic situations on maritime safety, focusing on inland waterway traffic. It presents a big data analytics method, utilizing data from the Automatic Identification System (AIS) and historical maritime accident records. The methodology involves AIS data preprocessing and spatial autocorrelation models, including Moran's index, to extract and evaluate the dynamic characteristics of maritime traffic. The analysis of traffic characteristic includes a thorough investigation into the spatial-temporal distribution of ship average speed and trajectory density. The paper then introduces an effective traffic characteristic analysis model that evaluates the relationship between maritime traffic patterns and accidents. The study, specifically targeting the Nanjing section of the Yangtze River, reveals variations in ship trajectory density and average speed over time. It identifies several hotspots with a significant local correlation between these factors. Moreover, a substantial correlation is found between the locations of maritime accidents and areas with increased ship trajectory density and average speed. These results may provide insights for traffic safety management and highlight strategies for preventing maritime accidents.

Influence of temperature and pressure gradient on power deposition and field pattern in High Magnetic field Helicon eXperiment

AbstractBased on High Magnetic field Helicon eXperiment, considering the parabolic distribution and Gaussian distribution of radial plasma density, HELIC code was used to study the influence of temperature and pressure gradient on power deposition, electric field, and current density of Helicon Wave Plasma. Three different gradients (positive, negative, and zero gradient) were selected. The results show that positive temperature gradient is beneficial to increase the relative absorption power at the center of plasma. Compared with negative and zero pressure gradients, positive pressure gradient increases the relative absorption power and weakens the current density at the center of plasma, and increases the electric field intensity at the edge of plasma. Larger edge heating will cause the relative absorption power at edge to rise rapidly, which is not conducive to the coupling at the center of plasma. In practical experiments, it is particularly important to reduce the heating effect at edge by cooling the antenna itself. Three different gradients of temperature and pressure have little effect on electric field intensity and current density in plasma, and the variation trend is basically similar, which proves the stability of the antenna mode: m = 1.

Spatial-temporal analysis of hepatitis E in Hainan Province, China (2013-2022): insights from four major hospitals.

Exploring the Incidence, Epidemic Trends, and Spatial Distribution Characteristics of Sporadic Hepatitis E in Hainan Province from 2013 to 2022 through four major tertiary hospitals in the Province. We collected data on confirmed cases of hepatitis E in Hainan residents admitted to the four major tertiary hospitals in Haikou City from January 2013 to December 2022. We used SPSS software to analyze the correlation between incidence rate and economy, population density and geographical location, and origin software to draw a scatter chart and SAS 9.4 software to conduct a descriptive analysis of the time trend. The distribution was analyzed using ArcMap 10.8 software (spatial autocorrelation analysis, hotspot identification, concentration, and dispersion trend analysis). SAS software was used to build an autoregressive integrated moving average model (ARIMA) to predict the monthly number of cases in 2023 and 2024. From 2013 to 2022, 1,922 patients with sporadic hepatitis E were treated in the four hospitals of Hainan Province. The highest proportion of patients (n = 555, 28.88%) were aged 50-59 years. The annual incidence of hepatitis E increased from 2013 to 2019, with a slight decrease in 2020 and 2021 and an increase in 2022. The highest number of cases was reported in Haikou, followed by Dongfang and Danzhou. We found that there was a correlation between the economy, population density, latitude, and the number of cases, with the correlation coefficient |r| value fluctuating between 0.403 and 0.421, indicating a linear correlation. At the same time, a scatter plot shows the correlation between population density and incidence from 2013 to 2022, with r2 values fluctuating between 0.5405 and 0.7116, indicating a linear correlation. Global Moran's I, calculated through spatial autocorrelation analysis, showed that each year from 2013 to 2022 all had a Moran's I value >0, indicating positive spatial autocorrelation (p < 0.01). Local Moran's I analysis revealed that from 2013 to 2022, local hotspots were mainly concentrated in the northern part of Hainan Province, with Haikou, Wenchang, Ding'an, and Chengmai being frequent hotspot regions, whereas Baoting, Qiongzhong, and Ledong were frequent cold-spot regions. Concentration and dispersion analysis indicated a clear directional pattern in the average density distribution, moving from northeast to southwest. Time-series forecast modeling showed that the forecast number of newly reported cases per month remained relatively stable in 2023 and 2024, fluctuating between 17 and 19. The overall incidence of hepatitis E in Hainan Province remains relatively stable. The incidence of hepatitis E in Hainan Province increased from 2013 to 2019, with a higher clustering of cases in the northeast region and a gradual spread toward the southwest over time. The ARIMA model predicted a relatively stable number of new cases each month in 2023 and 2024.

Enhanced negative refraction in one- and two-dimensional chiral atomic lattices

We consider a physical scheme for the realization of optical lattices that have negative refracting under certain conditions. The lattice is formed by clusters of five-level closed-loop chiral atoms assumed to have a Gaussian density distribution in dipole traps along one or two dimensions. With a suitable combination of strong standing wave control fields, spatial symmetry of atoms is achieved. Besides, the dispersion properties of an atomic lattice can be modified conveniently by adjusting various parameters related to the atoms or the lattice. We show that negative-like refraction is not specific to the atoms themselves, but also emerges due to the periodicity of the lattice. We further reveal that the refraction is negative over specific regions on the lattice and strongly depends on the number of atoms trapped along a particular direction. Our model is effectively controllable remotely and may have applications in negative refraction devices and optical information processing.

Assessment of Tidal Current Energy Resources in the Pearl River Estuary Using a Numerical Method

In this paper, a numerical method is employed to assess tidal current energy resources in the Pearl River Estuary, China. The numerical model for tidal current simulation in the estuary is developed based on the MIKE 21 model, which enables numerical simulations in estuaries, coastal areas, and oceans. The model has a grid resolution that varies from about 2500 m at the open boundary to 500–1000 m inside the estuary. Extensive model validation is performed by comparing the model predictions with field observations of tidal level and velocity at various stations in the Pearl River Estuary. The tidal characteristics are thoroughly analyzed. Energy fluxes and power densities are calculated along selected cross sections to evaluate the feasibility of tidal energy development in the Pearl River Estuary. The results indicate that the distribution of annual average tidal current power density in the Pearl River Estuary generally aligns with the spatial distribution of tidal currents. The annual average power density of tidal energy is typically below 0.10 kW/m2. The theoretical potential of tidal current energy resources in the Pearl River Estuary is assessed to be approximately 11,000 kW.

Effect of different counterions on the self-assembly structures and properties of imidazole based ionic liquids surfactant: A molecular dynamics study

Self-assembly of ionic liquids (ILs) in solution has attracted wide attention due to their potential applications in various fields. The nature of counterions, especially aromatic counterions, will significantly affect the aggregation and morphological properties of ILs surfactants. In this paper, molecular dynamics (MD) simulations are applied to study the influence of three organic and inorganic counterions (phenolate (PO−), benzoate (BZ−), and Cl−) on the micellar structure of imidazolium (C14mim+) based ILs surfactant in aqueous solutions. Three micelles all possess prolate shape. The PO−, BZ−, and Cl− ions hardly affect the orientation and length of hydrophobic chains in micellar interior. Hydration numbers and average radial density distributions analyses show that interactions between micelles and water molecules are different in studied micelles. Surrounding water molecules penetrate into the deepest region in [C14mim][Cl] micelle. However, adsorbed Cl− ions are mainly located on micellar surface, not penetrating into micellar interior. Due to the intrinsic hydrophobicity of organic ions, both PO− and BZ− ions enter into deeper positions in micelles. Unlike Cl− ions, there exist π-interactions between adsorbed PO− and BZ− ions themselves. One interesting finding is that adsorbed PO− and BZ− ions can make micelle radius (Rg) increase but make solvent accessible surface area (SASA) decrease. Conversely, adsorbed Cl− ions make both Rg and SASA increase. Three MD models for different C14mim+ based micelles are proposed.

Non-commutative wormhole in non-minimal curvature–matter coupling of f(R) gravity with Gaussian and Lorentzian distributions

In this work, we construct two new wormhole solutions in the theory dealing with non-minimal coupling between curvature and matter. We take into account an explicitly non-minimal coupling between an arbitrary function of scalar curvature [Formula: see text] and the Lagrangian density of matter. For this purpose, we discuss the Wormhole geometries inspired by non-minimal curvature coupling in [Formula: see text] gravity for linear model in [Formula: see text] as well as nonlinear model in [Formula: see text]. To derive these solutions, we choose the Gaussian and Lorentzian density distributions. To check the viability of these solutions, we plot the graphs for energy conditions and wormhole parameters. It is found that obtained wormhole solutions in both distributions satisfy the energy condition. The resulting wormhole solutions for both non-commutative distributions are determined to be physically stable when we evaluate the stability of these wormhole solutions graphically. It is concluded that wormhole solutions exist with viable physical properties in the non-minimal curvature–matter coupling of [Formula: see text] gravity with Gaussian and Lorentzian distributions.

A novel approach to detect the spring corn phenology using layered strategy

Accurate and continuous crop phenology information at a regional scale is important for agronomic management and yield estimation. However, detecting continuous crop phenology remains challenging due to the low sensitivity of remote sensing signals to certain phenological stages and the limited of availability remote sensing images. Therefore, this study developed a layered strategy to detect continuous crop phenology. First, a novel Phenology Separability Index (PSI) is established to select features from the Gaussian probability density distribution. PSI quantifies the capability of optical vegetation indexes (VIs), Synthetic Aperture Radar (SAR) signals, and meteorological factors to distinguish between various phenological stages. Then, the multi-temporal sample is established to enhance training sample representation and quantity. Finally, a random forest model is trained using features extracted from multi-temporal samples to improve detection accuracy. This model effectively reduces phenological stage confusion due to redundant features and limited samples. In addition, this study validated its extensibility by mapping crop phenology in the cities of Acheng, Zhaozhou, Lishu, and Buxin and assessed its uncertainty using the Sobol approach. Results indicated that growing degree day has the highest separability among meteorological factors, surpassing both SAR singles and optical VIs. Moreover, the proposed layered strategy was robust, explaining 96% of spatial variation in crop phenology at the regional scale. The accuracy of the layered strategy method (total RMSE = 8.74 days) surpassed that of the multi-temporal sample method (total RMSE = 15.76 days) and the traditional method with a single-temporal sample (total RMSE = 17.21 days). In addition, this study indicated that optical VIs are prone to confuse with the early or late phenological stage of corn, whereas SAR singles are highly sensitive to jointing date.

Bubble dynamics properties of B-particles in a quasi-2D gas-solid fluidized bed: Computational particle fluid dynamics numerical simulation and post-processed by digital image analysis technique

Bubble dynamics properties play a crucial and significant role in the design and optimization of gas-solid fluidized beds. In this study, the bubble dynamics properties of four B-particles were investigated in a quasi-two-dimensional (quasi-2D) fluidized bed, including bubble equivalent diameter, bubble size distribution, average bubble density, bubble aspect ratio, bubble hold-up, bed expansion ratio, bubble radial position, and bubble velocity. The studies were performed by computational particle fluid dynamics (CPFD) numerical simulation and post-processed with digital image analysis (DIA) technique, at superficial gas velocities ranging from 2umf to 7umf. The simulated results shown that the CPFD simulation combining with DIA technique post-processing could be used as a reliable method for simulating bubble dynamics properties in quasi-2D gas-solid fluidized beds. However, it seemed not desirable for the simulation of bubble motion near the air distributor at higher superficial gas velocity from the simulated average bubble density distribution. The superficial gas velocity significantly affected the bubble equivalent diameter and evolution, while it had little influence on bubble size distribution and bubble aspect ratio distribution for the same particles. Both time-averaged bubble hold-up and bed expansion ratio increased with the increase of superficial gas velocity. Two core-annular flow structures could be found in the fluidized bed for all cases. The average bubble rising velocity increased with the increasing bubble equivalent diameter. For bubble lateral movement, the smaller bubbles might be more susceptible, and superficial gas velocity had a little influence on the absolute lateral velocity of bubbles. The simulated results presented a valuable and novel approach for studying bubble dynamics properties. The comprehensive understanding of bubble dynamics behaviors in quasi-2D gas-solid fluidized beds would provide support in the design, operation, and optimization of gas-solid fluidized bed reactors.

Melt pool size of optical glass irradiated by semiconductor laser

ABSTRACT Using a continuous laser to soften glass locally is a novel way of selective glass forming. Due to gaussian distribution of laser power density, a temperature gradient will be generated on glass treated with localized irradiation by laser, which brings about the coexistence of a glass state and a viscoelastic state. This situation creates a bulge on the surface of the softened area. Based on this phenomenon, we propose a measurement approach and a calculation model for the softening zone width of glass irradiated locally by laser and verify the calculation model through simulations and experiments. The maximum temperature deviation of the proposed temperature field prediction model is 4.7°C, while the minimum deviation is 0.53°C; making the deviation between the calculation model of the softening zone width and the experimental measurement result less than 0.319%.

Experimental investigation on the effect of superficial gas velocity on bubble dynamics properties of B particles in gas–solid fluidized bed reactor using digital image analysis technique

The bubble dynamics properties in gas–solid particle system play a crucial role in the design and optimization of gas–solid fluidized beds, and are significantly influenced by superficial gas velocity. In present study, the effect of superficial gas velocity on bubble dynamics properties in a classical B particle system were investigated at gas velocity ranging from (0.41 to 0.59) m·s−1 with umf = 0.067 m·s−1 in a quasi-two dimensional (quasi-2D) fluidized bed domain, including bubble equivalent diameter, bubble size distribution, bubble density, aspect ratio, bubble hold-up, bed expansion ratio, bubble rising and lateral velocity. Those were derived from the taken image by digital image analysis (DIA) technique. The results show that superficial gas velocity has a significant effect on the bubble equivalent diameter, while it has little effect on bubble size distribution (BSD), average bubble density distribution and bubble aspect ratio distribution for the same particle system. Both time-averaged bed expansion ratio and bubble hold-up increase with the increase of superficial gas velocity under the range of gas velocity in this work. Two uniform core-annular flows form in the bed for all cases. The bubble rising velocity coefficients of developed correlation range from 0.69 to 1.00. For bubble lateral movement, smaller bubbles may be more susceptible, and superficial gas velocity has a little influence on the absolute lateral velocity of bubbles. Overall understanding the effect of gas velocity on bubbles dynamics properties is good for the design and optimization of fluidized bed reactors, leading to the better process outcomes and performance.

Spatiotemporal distribution of schistosomiasis transmission risk in Jiangling County, Hubei Province, P.R. China.

This study aims to explore the spatiotemporal distribution of schistosomiasis in Jiangling County, and provide insights into the precise schistosomiasis control. The descriptive epidemiological method and Joinpoint regression model were used to analyze the changes in infection rates of humans, livestock, snails, average density of living snails and occurrence rate of frames with snails in Jiangling County from 2005 to 2021. Spatial epidemiology methods were used to detect the spatiotemporal clustering of schistosomiasis transmission risk in Jiangling county. The infection rates in humans, livestock, snails, average density of living snails and occurrence rate of frames with snails in Jiangling County decreased from 2005 to 2021 with statistically significant. The average density of living snails in Jiangling County was spatially clustered in each year, and the Moran's I varied from 0.10 to 0.26. The hot spots were mainly concentrated in some villages of Xionghe Town, Baimasi Town and Shagang Town. The mean center of the distribution of average density of living snails in Jiangling County first moved from northwest to southeast, and then returned from southeast to northwest after 2014. SDE azimuth fluctuated in the range of 111.68°-124.42°. Kernal density analysis showed that the high and medium-high risk areas of Jiangling County from 2005 to 2021 were mainly concentrated in the central and eastern of Jiangling County, and the medium-low and low risk areas were mainly distributed in the periphery of Jiangling County. The epidemic situation of schistosomiasis decreased significantly in Jiangling County from 2005 to 2021, but the schistosomiasis transmission risk still had spatial clustering in some areas. After transmission interruption, targeted transmission risk intervention strategies can be adopted according to different types of schistosomiasis risk areas.

Impacts of Random Atomic Defects on Critical Buckling Stress of Graphene under Different Boundary Conditions.

Buckled graphene has potential applications in energy harvest, storage, conversion, and hydrogen storage. The investigation and quantification analysis of the random porosity in buckled graphene not only contributes to the performance reliability evaluation, but it also provides important references for artificial functionalization. This paper proposes a stochastic finite element model to quantify the randomly distributed porosities in pristine graphene. The Monte Carlo stochastic sampling process is combined with finite element computation to simulate the mechanical property of buckled graphene. Different boundary conditions are considered, and the corresponding results are compared. The impacts of random porosities on the buckling patterns are recorded and analyzed. Based on the large sampling space provided by the stochastic finite element model, the discrepancies caused by the number of random porosities are discussed. The possibility of strengthening effects in critical buckling stress is tracked in the large sampling space. The distinguishable interval ranges of probability density distribution for the relative variation of the critical buckling stress prove the promising potential of artificial control by the atomic vacancy amounts. In addition, the approximated Gaussian density distribution of critical buckling stress demonstrates the stochastic sampling efficiency by the Monte Carlo method and the artificial controllability of porous graphene. The results of this work provide new ideas for understanding the random porosities in buckled graphene and provide a basis for artificial functionalization through porosity controlling.

Transient and periodic steady-state characteristics of the local heat transfer measurement by thermal perturbation with Gaussian power density distribution

The local heat transfer coefficient measurement with temperature oscillation induced by periodic thermal perturbation – usually via a Gaussian laser beam, was investigated for the impact of the spikiness (i.e., the standard deviation) elaborated in comparison with the analytical model for dimensional analysis. The statistically more robust technique that relies on the linearity of the spatial phase distribution of the test point array was favored when the target Biot number approaches unity in terms of its order of magnitude. The preferred upper limit for thermographic scanning was discussed as the simplification of later data processing is concerned. Nonetheless, the time elapsed for an acceptable periodic steady state, which in principle leans to the higher end of the target Biot number spectrum in a log scale, indicates the benefit from the time series of pointwise temperature measurement – as in the conventional single-blow testing, where the effect of spikiness, as well as that of the location of individual test point, holds. Note that the vicinity as the target Biot number approaches unity was again observed with higher preference.

Phase Dependent Parity Time Symmetry in a quantum dot nanostructure

We present a diamond configuration quantum dots nanostructure trapped in two-dimensional (2D) optical lattices for the investigation of parity time (PT) symmetry. We trap quantum dots in a Gaussian density distribution to examine the PT, non-PT, and anti-PT symmetry in periodic 2D optical lattices. The variation in the relative phase of the optical beams in the quantum dots spectrum indicates either PT, anti-PT, or non-PT symmetry, resulting in an intriguing modulation of imaginary and real refractive index (RI) components. Controlling the appropriate modulation of the RI leads in PT symmetry being controlled by a single parameter, the relative phase of the optical fields. Using detuning and the coupling field of Rabi frequencies, we may determine the state of PT symmetry as well as the direction of field propagation. Coherent control of PT symmetry in 2D quantum dot nanostructure trapped in optical lattices may also have applications in 2D optical devices such as diodes, modulators and photonic transistors.