Direct Transition Research Articles

A comprehensive investigation of the synthesis, spectral, DFT, and optical properties of a novel oxadiazolyl-pyrano[3,2-c]quinoline for photosensor applications

The condensation reaction of pyranoquinoline-3-carbaoxldehyde 1 with benzohydraide afforded hydrazone 2 which upon oxidative cyclization yielded 6-ethyl-4‑hydroxy-3-(5-phenyl-1,3,4-oxadiazol-2-yl)-2H-pyrano[3,2-c]quinoline-2,5(6H)‑dione (EHPOPQ, 3). The DFT and B3LYP/6–311++G(d,p) basis set were used to compute the optimized molecular geometry. The global reactivity descriptors were examined and showed that hydrazone 2 exhibited high softness while aldehyde 1 had more electronegativity and high global electrophilicity. Subsequently, the reactive sites of the present compounds were located by tracing the MEP map. The GIAO method was used to calculate the 1H and 13C NMR. The current comprehensive investigation of the novel (EHPOPQ) reveals its significant potential for applications in nonlinear optics (NLO) and photovoltaics. Through high-level computational methods, EHPOPQ has an exceptionally high first hyperpolarizability (βtot) of 950 × 10−30 esu, which is substantially higher than that of the conventional NLO material urea. This high βtot value suggests that EHPOPQ could dramatically enhance the efficiency and performance of NLO devices such as frequency converters and optical modulators. In parallel, the detailed spectroscopic analysis of EHPOPQ's optical properties provided critical insights for photovoltaic applications. The optical band gap was measured to be 3.07 eV, indicating a direct band gap transition suitable for efficient light harvesting in solar cells. Additionally, dispersion parameters were carefully analyzed, which are essential for understanding the interaction of light with the material. The experimental characterization of EHPOPQ-based photovoltaic devices showed promising results. Current-voltage (J-V) measurements under varying illumination intensities revealed significant enhancements in the device's short-circuit current (from 1.2 µA to 4.3 µA) and open-circuit voltage (from 0.25 V to 0.47 V) as light intensity increased. These findings demonstrate the material's heightened photoresponsivity and suggest its potential as an efficient light conversion material for solar energy applications. These specific findings underline the importance of EHPOPQ in advancing both NLO and photovoltaic technologies, offering a pathway to more efficient and effective devices.

Structural, morphological, optical and electrical characterization of MgO thin films grown by sputtering technique on different substrates

Magnesium Oxide (MgO) thin film structures were deposited on glass and n-Si substrates by means of RF magnetron sputtering technique. Structural, morphological, optical characteristics of MgO thin film were determined by XRD, AFM and UV–Vis spectrometer techniques. The optical properties like absorption coefficient and optical band gap were extracted using optical transmittance and absorption spectra. The band-gap of MgO thin film was determined for direct electronic transition. Additionally, electric parameters like ideality factor, saturation current and barrier height of the Au/MgO/n-Si device were computed from the forward I–V data in dark state. The ideality factor was found to be greater than one. This indicates that the I–V characteristics of the device exhibits non-ideal attitude. The results show that the MgO thin film can be applied to both optical and electronic device applications.

Discontinuous transition to chaos in a canonical random neural network.

We study a paradigmatic random recurrent neural network introduced by Sompolinsky, Crisanti, and Sommers (SCS). In the infinite size limit, this system exhibits a direct transition from a homogeneous rest state to chaotic behavior, with the Lyapunov exponent gradually increasing from zero. We generalize the SCS model considering odd saturating nonlinear transfer functions, beyond the usual choice ϕ(x)=tanhx. A discontinuous transition to chaos occurs whenever the slope of ϕ at 0 is a local minimum [i.e., for ϕ^{'''}(0)>0]. Chaos appears out of the blue, by an attractor-repeller fold. Accordingly, the Lyapunov exponent stays away from zero at the birth of chaos.

Berry curvature signatures in chiroptical excitonic transitions

The topology of the electronic band structure of solids can be described by its Berry curvature distribution across the Brillouin zone. We theoretically introduce and experimentally demonstrate a general methodology based on the measurement of energy- and momentum-resolved optical transition rates, allowing to reveal signatures of Berry curvature texture in reciprocal space. By performing time- and angle-resolved photoemission spectroscopy of atomically thin WSe 2 using polarization-modulated excitations, we demonstrate that excitons become an asset in extracting the quantum geometrical properties of solids. We also investigate the resilience of our measurement protocol against ultrafast scattering processes following direct chiroptical transitions.

Unveiling a New 2D Semiconductor: Biphenylene-Based InN.

The two-dimensional (2D) materials class earned a boost in 2021 with biphenylene synthesis, which is structurally formed by the fusion of four-, six-, and eight-membered carbon rings, usually named 4-6-8-biphenylene network (BPN). This research proposes a detailed study of electronic, structural, dynamic, and mechanical properties to demonstrate the potential of the novel biphenylene-like indium nitride (BPN-InN) via density functional theory and molecular dynamics simulations. The BPN-InN has a direct band gap energy transition of 2.02 eV, making it promising for optoelectronic applications. This structure exhibits maximum and minimum Young modulus of 22.716 and 22.063 N/m, Poisson ratio of 0.018 and -0.008, and Shear modulus of 11.448 and 10.860 N/m, respectively. To understand the BPN-InN behavior when subjected to mechanical deformations, biaxial and uniaxial strains in armchair and zigzag directions from -8 to 8% were applied, achieving a band gap energy modulation of 1.36 eV over tensile deformations. Our findings are expected to motivate both theorists and experimentalists to study and obtain these new 2D inorganic materials that exhibit promising semiconductor properties.

Synthesis of thermochromic CdHgI4 thin film: Insight into the thickness-dependent structural, morphological, linear, and nonlinear spectroscopic properties

This study introduces an in-depth exploration of structural, morphological, linear, and nonlinear optical properties of CdHgI4 thin films deposited by the thermal evaporation technique. In this study, cadmium tetra iodomercurate (CdHgI4) nanopowder was synthesized by fusion method from which thin films of various thicknesses (150 to 450 nm) were deposited on glass substrates by thermal evaporation technique. The Structural investigation conducted by X-ray diffractometer (XRD) established that both CdHgI4 nanopowder and thin film formed in a single phase with a tetragonal crystallographic system. However, the CdHgI4 nanopowder and films display a different preferred orientation as corroborated by texture coefficient determination (Tc). The microstructural features obtained by High-resolution transmission electron microscopy (HRTEM) revealed that the powder particles were agglomerated; however, the particles of thin film were well-defined with high compactness and uniform size. The purity as well as stoichiometry were judged by energy dispersive X-ray analysis confirming the absence of any impurities and samples adopted near stoichiometry features. The surface morphology done by field emission scanning electron microscope revealed that films constituted of nanostructured grains with noticeable growth particles with increasing thickness. The CdHgI4 nanopowder had a direct optical transition of band gap of about 1.41 eV evaluated from diffuse reflectance spectroscopy. The band gap of thin films determined from specular optical spectroscopy varied from 2.20 to 1.58 eV, as the thickness changed from 150 to 450 nm. The thickness dependence of other linear optical parameters, such as Urbach energy (Eu), refractive index (n), optical dielectric constants (ε1, ε2), the surface and volume energy loss (SELF, VELF), were elaborately discussed. The nonlinear optical properties including first-order linear susceptibility, third-order susceptibility (χ(1), χ(3)), NL refractive index (n2), and two-photon absorption coefficients (βc) were greatly dependent on the film thickness.

Optical properties and antimicrobial of ionic chitosan-MgO-SiO2@ aminolsilane nanocomposites

This investigation involved synthesizing a nanocomposite heterostructure, Chitosan-MgO-SiO2@aminosilane, using the physical blending of chitosan-MgO-silica with aminosilane using the sol–gel technique. The prepared nanocomposites were characterized using x-ray diffraction (XRD), Scanning/Transmission Electron Microscope (SEM-EDX/TEM), Fourier Transform Infrared Spectroscopy (FTIR), and optical analysis to investigate the microstructural and spectroscopic properties. XRD results confirmed the formation of orthorhombic Mg2SiO4 within the fabricated system. FTIR analysis verified interactions among chitosan, MgO-silica, and aminosilane, leading to the development of diverse functional groups, including M-O bonds, silanol-hydroxyl ions, and heteropolymeric-O-M within the chitosan-MgO-SiO2@aminosilane nanocomposite. Optical studies demonstrated that aminosilane-incorporated samples have two distinct absorption bands around 215 nm and 419 nm, corresponding to the electronic transitions π–π* (k-band) and n–π* (R-band), respectively. The absorption band at 400 nm is ascribed to localized surface plasmon resonance (SPR). The incorporation of aminosilane resulted in a decrease in the direct transition energy gap from 2.677 to 2.399 eV. The nanocomposites displayed significant antimicrobial activity against pathogenic microorganisms such as Gram-positive Staphylococcus aureus, Gram-negative Pseudomonas aeruginosa, and pathogenic fungi Candida albicans and Aspergillus niger. The positive antimicrobial response of the fabricated nanocomposites candidates them for various applications, including wound dressings and food packaging.

SO(5) Deconfined Phase Transition under the Fuzzy-Sphere Microscope: Approximate Conformal Symmetry, Pseudo-Criticality, and Operator Spectrum

The deconfined quantum critical point (DQCP) is an example of phase transitions beyond the Landau symmetry-breaking paradigm that attracts wide interest. However, its nature has not been settled after decades of study. In this paper, we apply the recently proposed fuzzy-sphere regularization to study the SO(5) nonlinear sigma model with a topological Wess-Zumino-Witten term, which serves as a dual description of the DQCP with an exact SO(5) symmetry. We demonstrate that the fuzzy sphere functions as a powerful microscope, magnifying and revealing a wealth of crucial information about the DQCP, ultimately paving the way toward its final answer. In particular, through exact diagonalization, we provide clear evidence that the DQCP exhibits approximate conformal symmetry. The evidence includes the existence of a conserved SO(5) symmetry current, a stress tensor, and integer-spaced levels between conformal primaries and their descendants. Most remarkably, we identify 23 primaries and 76 conformal descendants. Furthermore, by examining the renormalization group flow of the lowest symmetry singlet as well as other primaries, we provide numerical evidence in favor of DQCP being pseudo-critical, with the approximate conformal symmetry plausibly emerging from nearby complex fixed points. The primary spectrum we compute also has important implications, including the conclusion that the SO(5) DQCP cannot describe a direct transition from the Néel to valence bond solid phase on the honeycomb lattice. Published by the American Physical Society 2024

Compositional dependence of direct transition energies in SixGe1−x−ySny alloys lattice-matched to Ge/GaAs

SixGe1−x−ySny ternary alloys are a candidate material system for use in solar cells and other optoelectronic devices. We report on the direct transition energies and structural properties of Ge-rich SixGe1−x−ySny alloys with six different compositions (up to 10% Si and 3% Sn), lattice-matched to Ge or GaAs substrates. The direct interband transitions occurring at energies between 0.9 and 5.0 eV were investigated using spectroscopic ellipsometry, and the resulting data were used to obtain the dielectric functions of the SixGe1−x−ySny layer by fitting a multilayer model. Values for the E0, E1, Δ1, E0′, and E2 transition energies were then found by identifying critical points in the dielectric functions. Structurally, the composition of the samples was measured using energy-dispersive x-ray measurements. The lattice constants predicted from these compositions are in good agreement with reciprocal space maps obtained through x-ray diffraction. The results confirm that a 1 eV absorption edge due to direct interband transitions can be achieved using relatively low Si and Sn fractions (<10% and <3%, respectively), although the bandgap remains indirect and at lower energies. The higher-energy critical points show smaller shifts relative to Ge and match results previously observed or predicted in the literature.

Light emission from ion-implanted SiGe quantum dots grown on Si substrates

We report on electroluminescence spectroscopy experiments demonstrating room-temperature light emission from heavily alloyed SiGe quantum dots, for which the light emission properties are enhanced by incorporated split-[110] self-interstitials. The quantum dots are formed during molecular beam epitaxy deposition of Si0.6Ge0.4 alloys on n-doped silicon-on-insulator substrates. To create the split-[110] self-interstitials the quantum dots were co-implantated in-situ using Si and Ge ions. The hybrid emitters were further embedded into the intrinsic region of a p-i-n diode structure to enable electrical pumping. Similar to previous theoretical results on unstrained Ge-based quantum dots containing these defects, radiative direct transitions are possible for these SiGe light emitters. However, in SiGe dots these transitions are not at the Brillouin zone center. Instead, first-principles calculations indicate that the presence of the split-[110] self-interstitial defect in strained and unstrained SiGe can lead to optically direct transitions in momentum space in the X-direction of the Brillouin zone.

Design, Synthesis, and Performance of Photo-Responsive Liquid Crystal Polymers with Stepwise Deformation Capability.

Photo-responsive liquid crystal polymers (LCPs) have potential application value in flexible robots, artificial muscles, and microfluidic control. In recent years, significant progress has been made in the development of LCPs. However, the preparation of LCPs with continuous and controllable stepwise deformation capabilities remains a challenge. In this study, visible photo-responsive cyanostilbene monomer, UV photo-responsive azobenzene monomer, and multiple hydrogen bond crosslinker are used to prepare photo-responsive LCPs capable of achieving continuously and controllable stepwise deformation. The comprehensive investigation of the multiple light response ability and photo-induced deformation properties of these copolymers is conducted. The results reveal that in the first stage of photo-induced deformation under 470nm blue light irradiation, the deformation angle decreases with a reduction in cyanostilbene content in the copolymer component, ranging from 40° in AZ0-CS4 to 0° in AZ4-CS0. In the second stage of photo-induced deformation under 365nm UV irradiation, the deformation angle increases with the increase of azobenzene content, ranging from 0° of AZ0-CS4 to 89.4° of AZ4-CS0. Importantly, the deformation between these two stages occurs as a continuous process, allowing for a direct transition from the first-stage to the second-stage deformation by switching the light source from 470 to 365nm.

Entropy production from waiting-time distributions for overdamped Langevin dynamics

For a Markovian dynamics on discrete states, the logarithmic ratio of waiting-time distributions between two successive, instantaneous transitions in forward and backward direction is a measure of time-irreversibility. It thus serves as an entropy estimator, which is exact in the case of a uni-cyclic network. We adopt this framework to overdamped Langevin dynamics, where such transitions have finite duration. By introducing milestones based on the observation of a particle at at least two milestones and an additional third event, we identify an entropy estimator that becomes exact for driven motion along a one-dimensional potential.

Synthesis of Mn doped nanostructured zinc oxide thin films for H2 gas sensing

Thin films of zinc oxide and (ZnO:Mn) with 1% and 3% concentrations were created at 400 °C by spray pyrolysis. According to X-ray diffraction (XRD) investigation, ZnO films are polycrystalline and have a cubic structure with a distinct peak in one direction (101). The grain size increases as manganese content rise, from 12.66 nm to 14.66 nm. While the strain (ε) for ZnO reduced after manganese doping, it decreased from 27.36 to 23.63. Surface topography and nanostructure study reveal that as the manganese (Mn) content of ZnO films increased, cluster grain size, average roughness, and root mean square roughness (Rrms) all significantly reduced. SEM images show substantial morphological changes from flat islands to spherical nano-grains post-manganese via Mn content. The average transmittance was >70% in the visible area for Undoped ZnO and 1, 3% Manganese doping optical transmittance demonstrates exceptional optical transparency. When doping levels are increased by 1% or 3%, the absorption coefficient rises. The optical band gap widens in ZnO: Mn film for allowed direct transition has been decreased from (3.32 to 3.21) eV. Results illustrate that the films' refractive index and extinction coefficient decreases with increasing Mn Doped. Hydrogen gas decreases resistance in ZnO films, suggesting p-type behavior. Doping with 3% Mn increases resistance. Decreased sensitivity with higher Mn content after hydrogen gas exposure indicates increased electrical resistance in the film.

Comprehensive structural analysis, magnetic, elastic, and optical properties of Cu–Ni–Co spinel and its potential applications

This work investigates the Cu0·6Ni0·2Co0·2FeAlO4 (CNCFAO) spinel nanoparticle, focusing on its structural, magnetic, elastic, and optical properties. The structural analysis provided various parameters, such as lattice parameter, crystallite size, and bond lengths, which were compared to theoretical values. The force constants of the sample were used to calculate stiffness constants (C11, C12, and C44), which in turn were used to determine elastic moduli such as the bulk modulus (B), longitudinal modulus (L), and rigidity modulus (G). The calculated Pugh ratio (B/G) indicated the brittle mechanical nature of the sample, while the Poisson ratio (σ) was estimated as σ = 0.25, consistent with isotropic elasticity theory. The sample demonstrated a low coercive field, indicating its potential for soft magnetic devices. Optical characteristics were evaluated using the Tauc method, revealing a direct optical transition with estimated band-gap (Eg) and Urbach (Eu) energies of 2.38 eV and 0.59 eV, respectively. Additional optical properties, including the penetration depth, refractive index, and extinction coefficient, were thoroughly examined. These results provide valuable insights into the potential optoelectronic applications of the synthesized sample.

Computational and experimental investigations on structural, electronic and optical properties of scheelite compounds

Oxide of tungstate has consistently been pursued for use in optoelectronic applications. This study details the synthesis of AWO4 (A = Ba, Sr and Ca) using a high-temperature solid-state method. Additionally, theoretical calculations highlight its electronic structure, density of states, photoelectric properties, and vibrational modes. The x-ray diffraction of AWO4 (A = Ba, Sr and Ca) was meticulously introduced by the utilization of Rietveld for refinement. The refined lattice parameters substantially verified AWO4 (A = Ba, Sr and Ca) as a tetragonal system of scheelite with the spatial group of I41/a, and demonstrated significant alteration with the discrepancy in the radius of alkaline earth metal (A-site) ions. The electronic configuration and optical attributes of AWO4 (A = Ba, Sr and Ca) possessing scheelite-like structure were explored using density functional theory (DFT) based computational techniques. The theoretical blueprint was derived by optimizing the structure based on defects. The postulated optical bandgap energy confirms the occurrence of direct electronic transitions at Brillouin region G points. Calculations suggested the direct band gaps of BaWO4, SrWO4, and CaWO4 at 4.385, 3.123 and 3.813 eV. This was attributed to the energy levels produced by O and A-site atoms in the valence band, and W and O atoms in the conduction band. An examination of the polarization effect and uneven electronic charge distribution between [CaO8]6− and [WO4]2− clusters brought about by structural defects in AWO4 (A = Ba, Sr and Ca) was performed. Moreover, advanced investigations have been conducted on the elastic constants and mechanical durability of AWO4 (A = Ba, Sr and Ca). This research extensively calculated the elastic moduli of various matrices utilizing DFT. The critical Pugh’s ratio value was found to be >1.75, it indicated that AWO4 (A = Ba, Sr and Ca) has significant potential as a resilient material.

Modification in the Optical and Dielectric Characteristics of Poly (Vinyl Alcohol)/Carboxymethyl Cellulose Blended Polymers Doped with Two Phases Nanocomposites for Application in Optoelectronic and Energy Storage Devices

Nanocomposite films comprised of poly (vinyl alcohol) (PVA) and carboxymethylcellulose (CMC) were fabricated via a solution casting procedure, with the incorporation of (1-x)CuCo2O4/xZnMn2O4. Our research described here was aimed to explore the impact of the (1-x)CuCo2O4/xZnMn2O4 on the structural, optical and electrical features of the PVA/CMC blended polymer, using various techniques. The different phases formed (CuCo2 O4 and/or ZnMn2O4) in (1-x) CuCo2O4/x ZnMn2O4 filler samples were identified applying Rietveld refinement analysis. The structures and morphologies of the PVA/CMC/(1-x)CuCo2O4/xZnMn2O4 blend composites were determined using X-ray diffraction and scanning electron microscopy techniques. Their various linear and nonlinear optical parameters were examined using the diffused reflectance technique. The blended polymer composite with x = 0.1 displayed the highest absorbance. The transmittance of the PVA/CMC blend declined from 91 to 69% when it was loaded with a nanocomposite containing 10% ZnMn2O4. The optical band gaps of the doped blend composites had their lowest values, 5.45 eV for direct transition and (4.83, 2.99, 2.31) eV for the indirect transition, as the blend was loaded with the fillers containing 10 and 15% ZnMn2O4. The study also explored the influence of the (1-x)CuCo2O4/x ZnMn2O4 on the fluorescence spectra and chromaticity diagram of the PVA/CMC blend. The effect of the filler on the complex dielectric constant, complex electric modulus, ac conductivity and electrical storage energy of the host blend was examined. The obtained characteristics imply potential utility of the doped blends in photocatalytic, UV-blocking, UV-filtering, optoelectronic, electrical storage, nonlinear optical and photonic applications.

Effect of disorder on phases across two-dimensional thermal melting.

We study melting in a two-dimensional system of classical particles with Gaussian-core interactions in disordered environments. The pure system validates the conventional two-step melting with a hexatic phase intervening between the solid and the liquid. This picture is modified in the presence of pinning impurities. A random distribution of pinning centers forces a hexaticlike low-temperature phase that transits into a liquid at a single melting temperature T_{m}^{RP}. In contrast, pinning centers located at randomly chosen sites of a perfect crystal anchor a solid at low temperatures which undergoes a direct transition to the liquid at T_{m}^{CP}. Thus, the two-step melting is lost in either case of disorder. We discuss the characteristics of melting depending on the nature of the impurities.

Two-photon absorption induced optical limiting action of Ag-doped lanthanum molybdate decorated reduced graphene oxide nanocomposites

In this research, we aimed to investigate the linear and non-linear optical properties of Ag-La2(MoO4)3@RGO nanocomposites. For this purpose, Graphene Oxide (GO) was synthesized by Modified Hummer’s method after which GO was chemically reduced to Reduced graphene oxide (RGO). The nanocomposite Ag-doped La2(MoO4)3 is prepared by a simple and facile co-precipitation method. The prepared nanocomposite was characterized by Fourier transform infrared (FTIR), Ultraviolet-Visible (UV-Vis) absorption, X-ray diffraction (XRD), Scanning electron microscope (SEM), and energy dispersive X-ray spectroscopy (EDX). XRD and EDX analysis indicated the reduction of GO and successful synthesis of Ag-doped La2(MoO4)3 nanocomposite. FESEM images portray the presence of thin layers of graphene sheets and Ag-doped La2(MoO4)3 on the sheets of reduced graphene oxide. Ground state absorption studies show that the reduction of graphene oxide causes a hypsochromic shift in the absorption maxima of the graphene layers. The photoluminescence of Ag- La2(MoO4)3@RGO demonstrates the utmost emission in the UV range caused by the valence band and conduction band's direct transitions in the band gap region. Z-scan method using Nd: YAG laser exposes that both nanocomposite and specific counterparts hold reverse saturable absorption behaviour. The source of optical limiting action is attributed to the excited state absorption process, emerging from the influence of the plasmon resonance state of Ag nanoparticles. Strong nonlinear absorption and lower onset limiting threshold make the Ag-La2(MoO4)3@RGO nanocomposite desirable material for laser safety devices.

High-pressure X-ray study of NbON oxynitride: direct transition from baddeleyite to cotunnite structure

Abstract The structural properties of NbON oxynitride under high pressure were investigated through in situ synchrotron X-ray diffraction (SXRD) up to 43 GPa. It was found that the bulk modulus of baddeleyite NbON (290 GPa) is larger than that of ZrO2 (150 GPa), indicating that the introduction of highly covalent nitrogen imparts greater stiffness. Furthermore, SXRD patterns reveal the emergence of a peak signaling a new crystalline phase above around 20 GPa. This is in contrast to TaON, where diffraction patterns only show an increase in background beyond 33 GPa. First-principle calculations suggest that the high-pressure phase adopts an orthorhombic cotunnite-type structure, distinguishing it from the oxide counterparts, wherein the ambient pressure phase transforms to a cotunnite structure via an orthorhombic-I structure.

Configuration uncertainty propagation of gravitational-wave observatory using a directional state transition tensor

Configuration stability is essential for a space-based Gravitational-Wave (GW) observatory, which can be impacted by orbit insertion uncertainties. Configuration uncertainty propagation is vital for investigating the influences of uncertainties on configuration stability and can be potentially useful in the navigation and control of GW observatories. Current methods suffer from drawbacks related to high computational burden. To this end, a Radial-Tangential-Ddirectional State Transition Tensor (RT-DSTT)-based configuration uncertainty propagation method is proposed. First, two sensitive directions are found by capturing the dominant secular terms. Considering the orbit insertion errors along the two sensitive directions only, a reduced-order RT-DSTT model is developed for orbital uncertainty propagation. Then, the relationship between the uncertainties in the orbital states and the uncertainties in the configuration stability indexes is mapped using high-order derivatives. The result is a semi-analytical solution that can predict the deviations in the configuration stability indexes given orbit insertion errors. The potential application of the proposed RT-DSTT-based method in calculating the feasible domain is presented. The performance of the proposed method is validated on the Laser Interferometer Space Antenna (LISA) project. Simulations show that the proposed method can provide similar results to the STT-based method but requires only half of the computational time.