Abstract
To enhance the sensitivity of detecting Cu and Zn in aluminum alloys, we incorporated a spark discharge unit into the femtosecond laser-induced breakdown spectroscopy (fs-LIBS) system, forming a femtosecond laser ablation spark-induced breakdown spectroscopy (fs-LA-SIBS) system. We utilized both fs-LA-SIBS and fs-LIBS techniques to detect Cu and Zn in various aluminum alloy samples with different contents. Our results reveal that the spark discharge extends the duration of laser-induced plasma atomic radiation and amplifies the peak intensity of atomic radiation, thereby significantly increasing the time-integrated signal intensity of laser-induced plasma. Under the present experimental conditions, the limits of detection (LoDs) of Cu and Zn in aluminum alloy by fs-LA-SIBS are 16 and 12 ppm, respectively. In contrast, the LoDs of Cu and Zn by fs-LIBS technique under the same laser pulse energy are 96 and 84 ppm, respectively. Hence, for Cu, the LoDs by the fs-LA-SIBS technique are 1/6 of those by the fs-LIBS technique, and for Zn, the LoDs by the fs-LA-SIBS technique are 1/7 of those by the fs-LIBS technique. Our findings demonstrate that the fs-LA-SIBS technique is more sensitive than the fs-LIBS technique in the quantitative analysis of elements and may be a practical approach for elemental analysis in alloys.
1 Introduction
Laser ablation (LA) technology uses pulsed lasers to rapidly heat a localized area on a sample surface, creating a transient plasma that provides a good basis for spectroscopic analysis [1,2]. Laser-induced breakdown spectroscopy (LIBS) has made significant progress in element analysis in various fields over the past few decades [3,4,5]. Los Alamos National Laboratory et al. have developed the ChemCam LIBS instrument onboard Curiosity which can be used to both identify and analyze rock surface alteration features [6,7,8], and the Chinese-developed Mars rover “Zhurong” successfully landed on the Martian surface carrying a surface composition detector which uses LIBS technology in 2021 [9]. The most commonly used laser in the LIBS system is a Q-switched Nd:YAG laser with pulse widths ranging from a few nanoseconds to over a hundred nanoseconds. The wide pulse range makes the interaction between laser and matter very complex. In contrast, ultrashort pulse lasers such as femtosecond (fs) lasers exhibit a series of advantages in their interaction with matter [10]. Therefore, LIBS with fs laser, that is, femtosecond laser-induced breakdown spectroscopy (fs-LIBS), has gradually become the mainstream of LIBS [11]. fs-LIBS is especially suitable for 2D surface analysis with high lateral resolution, 3D element mapping analysis, depth profile study with high depth resolution, and biological sample analysis with less damage [12,13,14]. Early studies of fs-LIBS showed that the intensity of line emission and continuous background spectrum and the temperature of plasma decrease rapidly after laser excitation. Since the duration of line emission is usually less than 1 μs [15], time-resolved signal detection is required to improve analysis sensitivity [16]. Although intensified charge-coupled device detectors have the advantages of fast gating and high detection sensitivity, the cost of these detectors is usually high.
To improve the signal intensity of laser-induced plasma, dual-pulse LIBS (DP-LIBS) technology has developed [17]. There are usually two types of DP-LIBS: one is based on two fs laser pulses, namely fs-fs DP-LIBS, and the other is based on the combination of fs and nanosecond laser pulses, namely fs-ns DP-LIBS. In fs-ns DP-LIBS, the fs laser pulse is used as the ablation laser, and the nanosecond laser pulse is used as the reheating laser, and they are arranged orthogonally. The signal is enhanced and can reach hundreds of times [18].
Although fs-ns DP-LIBS can achieve high signal enhancement factors, in some cases, there is a need to operate LIBS at a high repetition rate due to requirements for data acquisition speed or size limitations of the spectrometer. Nanosecond lasers that operate at high repetition rates have very low pulse energy, resulting in a lower practical signal enhancement factor in fs-ns DP-LIBS under such conditions. Therefore, it is necessary to find a suitable method to enhance the plasma emission signal of high-repetition-rate fs-LIBS. Spark discharge can effectively enhance laser-induced plasma emission. This discharge can be triggered by laser-induced plasma [19] or external discharge methods [20]. The start time of spark discharge is controlled by a quick switch, or the start time and pulse width are controlled by a gated high-voltage power supply. Spark discharge can operate at a high repetition rate and obtain a strong elemental spectrum signal. This mechanism of spark discharge-assisted signal enhancement is also known as spark-induced breakdown; hence, the LIBS enhanced by fs LA and spark-induced breakdown spectroscopy (fs-LA-SIBS) are referred to as fs-LA-SIBS.
Aluminum alloys are widely used in daily life and industrial production. Many aluminum alloys contain elements Cu and Zn [21]. The physical properties of aluminum alloys with different compositions vary greatly, such as ADC12 being suitable for making die castings [22] and A356 having high corrosion resistance [23]. There are clear regulations on the content of Cu and Zn in aluminum alloys of different grades. Therefore, by accurately measuring the content of Cu and Zn in aluminum alloys, it is possible to determine the type and quality of aluminum alloy material. In this article, the spark discharge is applied as a signal enhancement method in fs-LIBS with a pulse repetition frequency of 1 kHz, and the limits of detection (LoDs) and other analytical performance parameters of copper and zinc in several aluminum alloy samples are evaluated and discussed.
2 Experimental methods
The experimental setup for fs-LA-SIBS is shown in Figure 1. A Ti:Sapphire laser (Astrella, Coherent Inc., USA) was used as the ablation laser source, with a pulse width of 35 fs, a maximum output pulse energy of 6 mJ, and a repetition rate of 1 kHz. The laser wavelength used in the experiment was 800 nm, and the output laser beam diameter was 10 mm. The laser beam was tightly focused on the sample surface (numerical aperture: 0.25, working distance: 15 mm) through 10 high-power focusing lenses (LMU-10X-266, Thorlabs Inc., USA) to ablate the sample and generate the laser-induced plasma. In the experiment, a polarizer and an aperture were used to attenuate the pulse energy to less than 1.0 mJ.

Setup of fs-LA-SIBS.
As shown in Figure 1, the energy of the laser pulse was adjusted by rotating the angle between two Glan-Taylor polarizers. The residual laser was received by a fast photodiode after passing through a beamsplitter (BS) and converted into a corresponding electrical signal, which served as a synchronous trigger signal for monitoring ion emission by using an oscilloscope. The percentage of the residual laser signal after passing through the BS is about 20%. The aluminum alloy sample was fixed on a two-dimensional X–Y moving platform. During the experiment, the platform maintained a movement speed of 2 mm/s to ensure that the surface hit by each laser pulse was new. A ceramic plate was placed between the sample and the platform to keep the sample electrically insulated from the platform.
Figure 1 also shows the spark discharge device used for spark-induced breakdown. A DC power supply (4 kV, 50 mA) charges the high voltage capacitor C (5 nF) through the current limiting resistor R2 (80 kΩ). The anode of the spark discharge is a tungsten needle with a diameter of 2 mm, while the cathode is the tested aluminum alloy sample plate. The tip of the anode tungsten wire is polished into a cone shape and installed on the sample surface at a 45° angle. Once the fs laser pulse generates plasma, the gap resistance between the tip of the tungsten wire and the sample surface will immediately decrease, thus producing a spark discharge at the same repetition frequency as the laser pulse. The electric energy stored in the capacitor is released into the laser-induced plasma through the current limiting resistor R1 (4 Ω), further decomposing the ablated sample and enhancing the atomic emission spectrum intensity of the plasma.
The plasma radiation was collected by a lens system and focused onto the input port of a fiber optic spectrometer for spectral analysis. A monochromator (Omni-λ3017i, Zolix Inc., CN) was used to select the emission line for analysis, and a 500 MHz digital storage oscilloscope (GDS3502, GW Inc., CN) was used to record the output signal of the photomultiplier tube. The data stored in the oscilloscope were transferred to a personal computer for further processing. A multi-channel fiber optic spectrometer (1202156U3, 1202157U3, and 1202158U3, Avantes Inc., NLD) was used to record the spectrum in the wavelength range of 200–500 nm. The fiber optic spectrometer includes three channels, which cover the wavelength ranges of 200–317, 317–415, and 415–500 nm, respectively. Each channel’s linear charge-coupled device (CCD) detector has 2,048 pixels, and the spectral resolution of these channels is less than 0.1 nm.
Before applying fs-LA-SIBS technology to analyze the content of Cu and Zn in aluminum alloys, it is necessary to establish a standard curve using standard samples. In this study, five different standard samples (being purchased from Fushun Aluminum Factory Standard Sample Research Institute, China) with varying Cu and Zn contents (as shown in Table 1) were used to establish the standard curves for different trace elements, and the LoDs were also evaluated.
Contents of Cu and Zn in standard aluminum alloy samples (wt%)
Sample no. | GB215 | GB216 | GB217 | GB218 | GB219 |
---|---|---|---|---|---|
Contents of Zn | 0.011 | 0.046 | 0.089 | 0.140 | 0.200 |
Contents of Cu | 0.190 | 0.150 | 0.100 | 0.053 | 0.016 |
Aluminum | 98.639 | 98.843 | 99.062 | 99.257 | 99.360 |
3 Results and discussion
3.1 Signal enhancement observation
The emission spectra of Al exhibit peaks at 390.1, 394.4, 396.2, and 466.3 nm [24]. To compare the enhancement effect of spark-induced breakdown on the spectra, plasma radiation at 394.4 and 393.0 nm was monitored under two different excitations (as shown in Figure 2): fs-LIBS and fs-LA-SIBS. The first excitation is generated by fs laser pulse-induced breakdown, while the second excitation is generated by fs-LA-SIBS. The spectrum at 393.0 nm is close to the Al I 394.4 nm line and can be used to evaluate the continuous spectrum background. Al ion radiation and continuous background can be observed at 394.4 nm, while only continuous background can be observed at 393.0 nm. The following parameters were selected to record these results: pulse energy of 0.4 mJ, capacitor of 5 nF, and discharge voltage of 1.6 kV, as shown in Figure 2.

Time domain diagram of plasma emission at 394.4 and 393.0 nm in (a) fs-LIBS and (b) fs-LA-SIBS, respectively. The laser pulse energy is 0.4 mJ and the discharge voltage is 1.6 kV.
Figure 2 shows that under fs-LIBS excitation conditions (Figure 2(a)), the atomic radiation of Al at 394.4 nm lasts less than 2.15 μs, and the continuum background at 393.0 nm lasts less than 0.43 μs. Therefore, for time-resolved signal detection in fs-LIBS, the time window of the data acquisition gate was set to 0.43–2.15 μs. Under fs-LA-SIBS excitation conditions (Figure 2b), the duration of atomic emission of Al at 394.4 nm is extended to 22.5 μs, and the duration of the continuum background at 393.0 nm is extended to 5.5 μs. For time-resolved signal detection in fs-LA-SIBS, the time window of the data acquisition gate was set to 5.5–22.5 μs, and the time-integrated signal intensity was significantly enhanced. It can be seen that the extension of the duration of the spark-induced breakdown plasma emission makes it easier to achieve time-resolved signal detection.
Plasma emission spectra generated by fs-LIBS and fs-LA-SIBS in non-gated mode of operation were recorded with an AVANTES multi-channel spectrometer, the sample analyzed was standard aluminum alloy GB216. Figure 3a shows the emission spectra in the wavelength range of 260–500 nm recorded by fs-LIBS and fs-LA-SIBS operating at a repetition rate of 1 kHz. The laser pulse energy and high voltage for spark discharge were the same as mentioned earlier. The integration time of the spectrometer was 20 ms, i.e., an average of 20 discharges was accumulated for each measurement.

Plasma emission spectra recorded in fs-LIBS and fs-LA-SIBS, respectively. (a) Spectra in the wavelength range of 260–500 nm; (b) Spectra in the wavelength range of 322–342 nm.
From Figure 3, it can be seen that the spectra recorded by the fs-LA-SIBS technique are significantly enhanced compared to those recorded by the fs-LIBS technique. For example, in the fs-LIBS spectra, the emission intensity at 466.3 (spectrum of Al plasma emission) nm is about 3.5 × 104, much higher than that in the fs-LA-SIBS spectrum (about 1.1 × 104). In the fs-LIBS spectrum, the intensity of emissions from Cu ions at 324.8 nm is about 390, and that from Zn ions at 334.5 nm is about 480, while in the fs-LA-SIBS spectrum, the corresponding emissions from Cu ions and Zn ions are about 0.85 × 104 and 1.20 × 104 (Figure 3b).
3.2 Comparison of LoDs
To evaluate the analytical sensitivity of fs-LA-SIBS technology and compare it with fs-LIBS technology, LoDs of Cu and Zn elements in aluminum alloys were selected for comparison. The LoD of an element was determined using the widely accepted 3σ rule [25], that is:
where σ B is the standard deviation (SD) of the background and S is the slope of the calibration curve.
Figures 4 and 5 show the calibration curves for Cu and Zn, respectively, elements in aluminum alloys obtained using fs-LIBS and fs-LA-SIBS technologies, and the data are listed in Table 2. In the experiments, the pulse energy of the fs laser was set to 0.4 mJ, the discharge voltage was 1.6 kV, the capacitance was 5 nF, and the CCD in the fiber spectrometer was set to an integration time of 20 ms. The final spectrum was the average of 20 overlapped spectra, and the net peak height of the analysis line was used as the signal intensity. The selected spectral lines were the emission lines of Cu ions at 324.8 nm and Zn ions at 334.5 nm, with errors determined from the signal deviation of 10 measurements.

Calibration curves of cuprum in aluminum alloy by fs-LA-SIBS and fs-LIBS.

Calibration curves of zinc in aluminum alloy by fs-LA-SIBS and fs-LIBS.
The data corresponding to the calibration curve obtained by the fs-LA-SIBS and the fs-LIBS techniques
Conc. of Cu (wt%) | Mean counts of fs-LA-SIBS | SD | Relative deviation (%) | Mean counts of fs-LIBS | SD | Relative deviation (%) |
---|---|---|---|---|---|---|
0.016 | 946 | 62 | 6.5 | 38.1 | 12.3 | 32.4 |
0.053 | 3,002 | 110 | 3.7 | 121.8 | 22.1 | 18.1 |
0.100 | 5,594 | 150 | 2.7 | 197.9 | 28.1 | 14.2 |
0.150 | 8,452 | 184 | 2.2 | 289.2 | 34.0 | 11.8 |
0.190 | 10,632 | 206 | 1.9 | 372.9 | 38.6 | 10.4 |
From these figures and Table 2, it can be seen that although the SD of the data points corresponding to the calibration curve obtained by the fs-LA-SIBS technique was larger than that obtained by the fs-LIBS technique, the relative deviation was much smaller than that of the fs-LIBS technique. The standard curve was obtained by fitting the measured data points using the least-squares method, with the fitted parameters listed in Table 3. To evaluate the LoD, the SD of the background corresponding to the analysis line, σ B, is needed. Here, σ B was evaluated based on the SD of the background in a 1-nm wavelength range near the analysis line. Table 3 lists the corresponding background SD σ B and the LoDs of copper and zinc elements calculated by formula (1).
LoDs of cuprum and zinc in aluminum alloy obtained by fs-LIBS and fs-LA-SIBS techniques
Intercept distance | Slop/100 | Determination coefficient (R) | σ B | LOD (ppm) | ||
---|---|---|---|---|---|---|
Cu | fs-LA-SIBS | 45 ± 25 | 55,790 ± 211 | 0.99994 | 29 | 16 |
fs-LIBS | 12 ± 6 | 1,878 ± 52 | 0.99700 | 6 | 96 | |
Zn | fs-LA-SIBS | 95 ± 166 | 85,219 ± 1,403 | 0.99892 | 33 | 12 |
fs-LIBS | –1 ± 24 | 3,176 ± 204 | 0.98361 | 9 | 85 |
As shown in Table 3, the LoDs of Cu and Zn obtained by the fs-LA-SIBS technique were only about 1/6 to 1/7 of those obtained by the fs-LIBS technique, indicating a significantly improved detection sensitivity. Due to the interaction between spark discharge and laser-induced plasma, the signal emitted by the plasma could be enhanced, thereby increasing the analytical sensitivity. Therefore, the fs-LA-SIBS technique could be a highly useful elemental analysis technique and may have widespread applications.
4 Conclusion
In this study, trace elements copper and zinc in aluminum alloy samples were detected and analyzed using an fs-LA-SIBS system with a repetition rate of 1 kHz. Compared with the fs-LIBS technique, the assistance of spark discharge can significantly enhance the atomic emission intensity of laser-induced plasma, resulting in a much higher sensitivity of fs-LA-SIBS. Under the experimental conditions, the LoDs of copper and zinc elements in an aluminum alloy using fs-LA-SIBS were 16 and 12 ppm, respectively, which were only about 1/6 to 1/7 of the LoDs obtained by the fs-LIBS method without spark discharge. The high sensitivity of fs-LA-SIBS makes it a promising technique for the analysis of elements in alloys.
Acknowledgments
The authors would like to acknowledge helpful discussions with Dr. He Xiaoyong of Dongguan University of Technology, et al.
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Funding information: This work was supported by Special Innovation Projects of General Universities in Guangdong Province, China(2020KTSCX351), Science and Technology Planning Project of Guangdong Province, China(2015A020216020), the Education and Teaching Research Project of Guangdong Ocean University (S2020105666059), and Research Foundation for Talented Scholars of Guangdong Ocean University (060302112102).
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Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
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Conflict of interest: The authors state no conflict of interest.
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Data availability statement: The data that support the findings of this study are available from the corresponding author upon reasonable request.
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- Heat transfer performance of magnetohydrodynamic multiphase nanofluid flow of Cu–Al2O3/H2O over a stretching cylinder
- ΛCDM and the principle of equivalence
- Axisymmetric stagnation-point flow of non-Newtonian nanomaterial and heat transport over a lubricated surface: Hybrid homotopy analysis method simulations
- HAM simulation for bioconvective magnetohydrodynamic flow of Walters-B fluid containing nanoparticles and microorganisms past a stretching sheet with velocity slip and convective conditions
- Coupled heat and mass transfer mathematical study for lubricated non-Newtonian nanomaterial conveying oblique stagnation point flow: A comparison of viscous and viscoelastic nanofluid model
- Power Topp–Leone exponential negative family of distributions with numerical illustrations to engineering and biological data
- Extracting solitary solutions of the nonlinear Kaup–Kupershmidt (KK) equation by analytical method
- A case study on the environmental and economic impact of photovoltaic systems in wastewater treatment plants
- Application of IoT network for marine wildlife surveillance
- Non-similar modeling and numerical simulations of microploar hybrid nanofluid adjacent to isothermal sphere
- Joint optimization of two-dimensional warranty period and maintenance strategy considering availability and cost constraints
- Numerical investigation of the flow characteristics involving dissipation and slip effects in a convectively nanofluid within a porous medium
- Spectral uncertainty analysis of grassland and its camouflage materials based on land-based hyperspectral images
- Application of low-altitude wind shear recognition algorithm and laser wind radar in aviation meteorological services
- Investigation of different structures of screw extruders on the flow in direct ink writing SiC slurry based on LBM
- Harmonic current suppression method of virtual DC motor based on fuzzy sliding mode
- Micropolar flow and heat transfer within a permeable channel using the successive linearization method
- Different lump k-soliton solutions to (2+1)-dimensional KdV system using Hirota binary Bell polynomials
- Investigation of nanomaterials in flow of non-Newtonian liquid toward a stretchable surface
- Weak beat frequency extraction method for photon Doppler signal with low signal-to-noise ratio
- Electrokinetic energy conversion of nanofluids in porous microtubes with Green’s function
- Examining the role of activation energy and convective boundary conditions in nanofluid behavior of Couette-Poiseuille flow
- Review Article
- Effects of stretching on phase transformation of PVDF and its copolymers: A review
- Special Issue on Transport phenomena and thermal analysis in micro/nano-scale structure surfaces - Part IV
- Prediction and monitoring model for farmland environmental system using soil sensor and neural network algorithm
- Special Issue on Advanced Topics on the Modelling and Assessment of Complicated Physical Phenomena - Part III
- Some standard and nonstandard finite difference schemes for a reaction–diffusion–chemotaxis model
- Special Issue on Advanced Energy Materials - Part II
- Rapid productivity prediction method for frac hits affected wells based on gas reservoir numerical simulation and probability method
- Special Issue on Novel Numerical and Analytical Techniques for Fractional Nonlinear Schrodinger Type - Part III
- Adomian decomposition method for solution of fourteenth order boundary value problems
- New soliton solutions of modified (3+1)-D Wazwaz–Benjamin–Bona–Mahony and (2+1)-D cubic Klein–Gordon equations using first integral method
- On traveling wave solutions to Manakov model with variable coefficients
- Rational approximation for solving Fredholm integro-differential equations by new algorithm
- Special Issue on Predicting pattern alterations in nature - Part I
- Modeling the monkeypox infection using the Mittag–Leffler kernel
- Spectral analysis of variable-order multi-terms fractional differential equations
- Special Issue on Nanomaterial utilization and structural optimization - Part I
- Heat treatment and tensile test of 3D-printed parts manufactured at different build orientations
Articles in the same Issue
- Regular Articles
- Dynamic properties of the attachment oscillator arising in the nanophysics
- Parametric simulation of stagnation point flow of motile microorganism hybrid nanofluid across a circular cylinder with sinusoidal radius
- Fractal-fractional advection–diffusion–reaction equations by Ritz approximation approach
- Behaviour and onset of low-dimensional chaos with a periodically varying loss in single-mode homogeneously broadened laser
- Ammonia gas-sensing behavior of uniform nanostructured PPy film prepared by simple-straightforward in situ chemical vapor oxidation
- Analysis of the working mechanism and detection sensitivity of a flash detector
- Flat and bent branes with inner structure in two-field mimetic gravity
- Heat transfer analysis of the MHD stagnation-point flow of third-grade fluid over a porous sheet with thermal radiation effect: An algorithmic approach
- Weighted survival functional entropy and its properties
- Bioconvection effect in the Carreau nanofluid with Cattaneo–Christov heat flux using stagnation point flow in the entropy generation: Micromachines level study
- Study on the impulse mechanism of optical films formed by laser plasma shock waves
- Analysis of sweeping jet and film composite cooling using the decoupled model
- Research on the influence of trapezoidal magnetization of bonded magnetic ring on cogging torque
- Tripartite entanglement and entanglement transfer in a hybrid cavity magnomechanical system
- Compounded Bell-G class of statistical models with applications to COVID-19 and actuarial data
- Degradation of Vibrio cholerae from drinking water by the underwater capillary discharge
- Multiple Lie symmetry solutions for effects of viscous on magnetohydrodynamic flow and heat transfer in non-Newtonian thin film
- Thermal characterization of heat source (sink) on hybridized (Cu–Ag/EG) nanofluid flow via solid stretchable sheet
- Optimizing condition monitoring of ball bearings: An integrated approach using decision tree and extreme learning machine for effective decision-making
- Study on the inter-porosity transfer rate and producing degree of matrix in fractured-porous gas reservoirs
- Interstellar radiation as a Maxwell field: Improved numerical scheme and application to the spectral energy density
- Numerical study of hybridized Williamson nanofluid flow with TC4 and Nichrome over an extending surface
- Controlling the physical field using the shape function technique
- Significance of heat and mass transport in peristaltic flow of Jeffrey material subject to chemical reaction and radiation phenomenon through a tapered channel
- Complex dynamics of a sub-quadratic Lorenz-like system
- Stability control in a helicoidal spin–orbit-coupled open Bose–Bose mixture
- Research on WPD and DBSCAN-L-ISOMAP for circuit fault feature extraction
- Simulation for formation process of atomic orbitals by the finite difference time domain method based on the eight-element Dirac equation
- A modified power-law model: Properties, estimation, and applications
- Bayesian and non-Bayesian estimation of dynamic cumulative residual Tsallis entropy for moment exponential distribution under progressive censored type II
- Computational analysis and biomechanical study of Oldroyd-B fluid with homogeneous and heterogeneous reactions through a vertical non-uniform channel
- Predictability of machine learning framework in cross-section data
- Chaotic characteristics and mixing performance of pseudoplastic fluids in a stirred tank
- Isomorphic shut form valuation for quantum field theory and biological population models
- Vibration sensitivity minimization of an ultra-stable optical reference cavity based on orthogonal experimental design
- Effect of dysprosium on the radiation-shielding features of SiO2–PbO–B2O3 glasses
- Asymptotic formulations of anti-plane problems in pre-stressed compressible elastic laminates
- A study on soliton, lump solutions to a generalized (3+1)-dimensional Hirota--Satsuma--Ito equation
- Tangential electrostatic field at metal surfaces
- Bioconvective gyrotactic microorganisms in third-grade nanofluid flow over a Riga surface with stratification: An approach to entropy minimization
- Infrared spectroscopy for ageing assessment of insulating oils via dielectric loss factor and interfacial tension
- Influence of cationic surfactants on the growth of gypsum crystals
- Study on instability mechanism of KCl/PHPA drilling waste fluid
- Analytical solutions of the extended Kadomtsev–Petviashvili equation in nonlinear media
- A novel compact highly sensitive non-invasive microwave antenna sensor for blood glucose monitoring
- Inspection of Couette and pressure-driven Poiseuille entropy-optimized dissipated flow in a suction/injection horizontal channel: Analytical solutions
- Conserved vectors and solutions of the two-dimensional potential KP equation
- The reciprocal linear effect, a new optical effect of the Sagnac type
- Optimal interatomic potentials using modified method of least squares: Optimal form of interatomic potentials
- The soliton solutions for stochastic Calogero–Bogoyavlenskii Schiff equation in plasma physics/fluid mechanics
- Research on absolute ranging technology of resampling phase comparison method based on FMCW
- Analysis of Cu and Zn contents in aluminum alloys by femtosecond laser-ablation spark-induced breakdown spectroscopy
- Nonsequential double ionization channels control of CO2 molecules with counter-rotating two-color circularly polarized laser field by laser wavelength
- Fractional-order modeling: Analysis of foam drainage and Fisher's equations
- Thermo-solutal Marangoni convective Darcy-Forchheimer bio-hybrid nanofluid flow over a permeable disk with activation energy: Analysis of interfacial nanolayer thickness
- Investigation on topology-optimized compressor piston by metal additive manufacturing technique: Analytical and numeric computational modeling using finite element analysis in ANSYS
- Breast cancer segmentation using a hybrid AttendSeg architecture combined with a gravitational clustering optimization algorithm using mathematical modelling
- On the localized and periodic solutions to the time-fractional Klein-Gordan equations: Optimal additive function method and new iterative method
- 3D thin-film nanofluid flow with heat transfer on an inclined disc by using HWCM
- Numerical study of static pressure on the sonochemistry characteristics of the gas bubble under acoustic excitation
- Optimal auxiliary function method for analyzing nonlinear system of coupled Schrödinger–KdV equation with Caputo operator
- Analysis of magnetized micropolar fluid subjected to generalized heat-mass transfer theories
- Does the Mott problem extend to Geiger counters?
- Stability analysis, phase plane analysis, and isolated soliton solution to the LGH equation in mathematical physics
- Effects of Joule heating and reaction mechanisms on couple stress fluid flow with peristalsis in the presence of a porous material through an inclined channel
- Bayesian and E-Bayesian estimation based on constant-stress partially accelerated life testing for inverted Topp–Leone distribution
- Dynamical and physical characteristics of soliton solutions to the (2+1)-dimensional Konopelchenko–Dubrovsky system
- Study of fractional variable order COVID-19 environmental transformation model
- Sisko nanofluid flow through exponential stretching sheet with swimming of motile gyrotactic microorganisms: An application to nanoengineering
- Influence of the regularization scheme in the QCD phase diagram in the PNJL model
- Fixed-point theory and numerical analysis of an epidemic model with fractional calculus: Exploring dynamical behavior
- Computational analysis of reconstructing current and sag of three-phase overhead line based on the TMR sensor array
- Investigation of tripled sine-Gordon equation: Localized modes in multi-stacked long Josephson junctions
- High-sensitivity on-chip temperature sensor based on cascaded microring resonators
- Pathological study on uncertain numbers and proposed solutions for discrete fuzzy fractional order calculus
- Bifurcation, chaotic behavior, and traveling wave solution of stochastic coupled Konno–Oono equation with multiplicative noise in the Stratonovich sense
- Thermal radiation and heat generation on three-dimensional Casson fluid motion via porous stretching surface with variable thermal conductivity
- Numerical simulation and analysis of Airy's-type equation
- A homotopy perturbation method with Elzaki transformation for solving the fractional Biswas–Milovic model
- Heat transfer performance of magnetohydrodynamic multiphase nanofluid flow of Cu–Al2O3/H2O over a stretching cylinder
- ΛCDM and the principle of equivalence
- Axisymmetric stagnation-point flow of non-Newtonian nanomaterial and heat transport over a lubricated surface: Hybrid homotopy analysis method simulations
- HAM simulation for bioconvective magnetohydrodynamic flow of Walters-B fluid containing nanoparticles and microorganisms past a stretching sheet with velocity slip and convective conditions
- Coupled heat and mass transfer mathematical study for lubricated non-Newtonian nanomaterial conveying oblique stagnation point flow: A comparison of viscous and viscoelastic nanofluid model
- Power Topp–Leone exponential negative family of distributions with numerical illustrations to engineering and biological data
- Extracting solitary solutions of the nonlinear Kaup–Kupershmidt (KK) equation by analytical method
- A case study on the environmental and economic impact of photovoltaic systems in wastewater treatment plants
- Application of IoT network for marine wildlife surveillance
- Non-similar modeling and numerical simulations of microploar hybrid nanofluid adjacent to isothermal sphere
- Joint optimization of two-dimensional warranty period and maintenance strategy considering availability and cost constraints
- Numerical investigation of the flow characteristics involving dissipation and slip effects in a convectively nanofluid within a porous medium
- Spectral uncertainty analysis of grassland and its camouflage materials based on land-based hyperspectral images
- Application of low-altitude wind shear recognition algorithm and laser wind radar in aviation meteorological services
- Investigation of different structures of screw extruders on the flow in direct ink writing SiC slurry based on LBM
- Harmonic current suppression method of virtual DC motor based on fuzzy sliding mode
- Micropolar flow and heat transfer within a permeable channel using the successive linearization method
- Different lump k-soliton solutions to (2+1)-dimensional KdV system using Hirota binary Bell polynomials
- Investigation of nanomaterials in flow of non-Newtonian liquid toward a stretchable surface
- Weak beat frequency extraction method for photon Doppler signal with low signal-to-noise ratio
- Electrokinetic energy conversion of nanofluids in porous microtubes with Green’s function
- Examining the role of activation energy and convective boundary conditions in nanofluid behavior of Couette-Poiseuille flow
- Review Article
- Effects of stretching on phase transformation of PVDF and its copolymers: A review
- Special Issue on Transport phenomena and thermal analysis in micro/nano-scale structure surfaces - Part IV
- Prediction and monitoring model for farmland environmental system using soil sensor and neural network algorithm
- Special Issue on Advanced Topics on the Modelling and Assessment of Complicated Physical Phenomena - Part III
- Some standard and nonstandard finite difference schemes for a reaction–diffusion–chemotaxis model
- Special Issue on Advanced Energy Materials - Part II
- Rapid productivity prediction method for frac hits affected wells based on gas reservoir numerical simulation and probability method
- Special Issue on Novel Numerical and Analytical Techniques for Fractional Nonlinear Schrodinger Type - Part III
- Adomian decomposition method for solution of fourteenth order boundary value problems
- New soliton solutions of modified (3+1)-D Wazwaz–Benjamin–Bona–Mahony and (2+1)-D cubic Klein–Gordon equations using first integral method
- On traveling wave solutions to Manakov model with variable coefficients
- Rational approximation for solving Fredholm integro-differential equations by new algorithm
- Special Issue on Predicting pattern alterations in nature - Part I
- Modeling the monkeypox infection using the Mittag–Leffler kernel
- Spectral analysis of variable-order multi-terms fractional differential equations
- Special Issue on Nanomaterial utilization and structural optimization - Part I
- Heat treatment and tensile test of 3D-printed parts manufactured at different build orientations