Gaussian Source Research Articles

Numerical simulation of angled surface crack detection based on laser ultrasound

As an important branch of non-destructive testing, laser ultrasonic testing has attracted increasing attention in the field of material testing because of its instantaneity, non-contact and wide adaptability. Based on the finite element method, the process of laser-excited ultrasonic signal is numerically simulated, and the influence of angled cracks on the ultrasonic signal is analyzed. In this paper, the effects of the time function, pulse width, and spot radius of a Gaussian light source are analyzed through the transient field. The different modes of the ultrasonic signal are used to fit the crack’s angle, depth, and width to complete the characteristic analysis of the surface angled crack. The results show that the displacement peak-valley difference of the direct Rayleigh wave is negatively correlated with the crack angle. The displacement extremes of the transmitted Rayleigh wave boundary are negatively correlated with crack depth and width, while the transmitted Rayleigh wave is positively correlated. This paper presents a method for the quantitative analysis of surface-angled cracks and provides a theoretical basis for further experimental verification.

Quantum limits for resolving Gaussian sources

An analytical expression that estimates the separation between two point sources in arbitrary Gaussian states determines how different resources affect the scaling of the ultimate resolution limit with the mean number of emitted photons.

Optical Uplink, D2D and IoT Links Based on VCSEL Array: Analysis and Demonstration

In this paper, vertical cavity surface emitting laser (VCSEL) array is used to establish gigabits/second (Gbps) optical uplink, device-to-device (D2D), and Internet-of-thing (IoT) links, as a supplementary for visible light communication (VLC) and ultra-low latency near-field communication in a typical indoor scenario. The mathematical model based on a modified Monte-Carlo ray-tracing (MMCR) algorithm for VCSEL-based optical wireless communication (OWC) is presented, which takes into account both accuracy and time complexity for the calculation of the channel characteristics including power distribution, impulse response, error analysis, and signal-to-noise ratio (SNR). Simulation firstly takes a global approach to the optical uplink lens design method, compared between Lambertian and Gaussian sources, and then extended six typical line-of-sight (LOS) or non-line-of-sight (NLOS) VCSEL-based OWC models. For demonstration, we adopted a 940-nm VCSEL array and 850-nm single-pixel VCSEL to establish LOS and NLOS systems after measuring the optics-electronics and bandwidth characteristics, respectively. Furthermore, multiple multi-carrier schemes are adopted to improve the OWC performance system based on a 940-nm VCSEL array including uniform-loading orthogonal frequency division multiplexing (OFDM), channel-coded OFDM, bit-loading/ power-allocation OFDM, and OFDM access (OFDMA). Results show that OFDM can effectively decrease the inter-symbol interference (ISI) of the indoor channel and increase the data rate, and the bit/ power-loading method achieves the highest 7.2 Gbps transmission with the bit error rate (BER) within the forward error correction (FEC). All the theoretical and experimental results, for the first time, provide a comprehensive design and optimizing process of VCSEL-based indoor high-capacity OWC systems for future optical uplink, D2D, and IoT applications.

Noise experiments in BRAHMMA subcritical system using isotopic Poisson source and accelerator based neutron source

Reactivity measurement using noise methods have been carried out in zero power subcritical system BRAHMMA, installed in BARC, India. During noise experiments, an Am-Be neutron source (1Ci) has been placed at the centre of the subcritical system. However, the proposed external neutron source in ADS, based on particle accelerator, is different from isotopic neutron source and the inherent fluctuations in beam current and accelerating voltage makes the source non-Poisson. In this context, Degweker and Rana had postulated a noise theory based on exponentially correlated Gaussian source characteristics for ADS. In noise experiments based on this postulate, a D-T neutron generator has been used in pulsed mode and source characterisation has been carried out to determine the distribution function, source correlation factor and D+ beam pulse shape. It has been observed that the source is Gaussian in nature, the source correlation factor is very large compared to the prompt neutron decay constant and the pulsed D+ beam is rectangular in shape. In noise experiments, the time stamped data have been analysed using various noise methods. The measured prompt neutron decay constant using Poisson source and correlated Gaussian source are in good agreement with theoretical value and amongst them.

Analysis of wander and spreading of an optical beam by using the oceanic turbulence optical power spectrum

Variance of beam displacement and short-term and long-term spreading of a Gaussian beam propagating in the presence of underwater turbulence are examined by using the oceanic turbulence optical power spectrum (OTOPS). Analytical expressions for both beam wander displacement variance and beam spreading are presented. Results show that the underwater turbulent channel causes deflection from the on-axis mean irradiance and brings significant wander and spreading effects to the propagating Gaussian beam wave. The variations of beam wander and short- and long-term spreading are obtained depending on the underwater medium parameters such as the average temperature, average salinity concentration, temperature-salinity gradient ratio, and temperature and energy dissipation rates. In particular, the real values of the average temperature and salinity concentration of turbulent water are used to obtain the results. In addition, the effects of propagation distance, Gaussian beam source size, and wavelength are shown. The results demonstrate that the underwater turbulent channel brings displacements in the centroid and spreading of the optical beam.

NOVEL EXPONENTIAL TYPE APPROXIMATIONS OF THE Q-FUNCTION

In this paper, we propose several solutions for approximating the Q-function using one exponential function or the sum of two exponential functions. As the novel Q-function approximations have simple analytical forms and are therefore very suitable for further derivation of expressions in closed forms, a large number of applications are feasible. The application of the novel exponential type approximations of the Q-function is especially important for overcoming issues arising in designing scalar companding quantizers for the Gaussian source, which are caused by the non-existence of a closed form expression for the Q-function. Since our approximations of the Q-function have simple analytical forms and are more accurate than the approximations of the Q-function previously used for the observed problem in the scalar companding quantization of the Gaussian source, their application, especially for this problem is of great importance.

Propagation of hyperbolic sinusoidal Gaussian beam in jet engine induced turbulence

This paper investigates beam evolution and beam sizes variation of hyperbolic sinusoidal Gaussian (HSG) beam propagating in jet engine exhaust-induced turbulence. We find the received field by solving Huygens-Fresnel integral with a relevant power spectrum. Our results reveal that HSG loses its initial profile until 100 m. Besides, beam with low displacement parameter value is more resistive against turbulence. In terms of beam size, beams with low Gaussian source size expand less as compared to the beams with larger Gaussian source size. In the light of our findings, optical systems in aircrafts like directed infrared counter measure (DIRCM) and laser designators can be developed.

Noiseless linear amplification in quantum target detection using Gaussian states

Quantum target detection aims to utilise quantum technologies to achieve performances in target detection not possible through purely classical means. Quantum illumination is an example of this, based on signal–idler entanglement, promising a potential 6 dB advantage in error exponent over its optimal classical counterpart. So far, receiver designs achieving this optimal reception remain elusive with many proposals based on Gaussian processes appearing unable to utilise quantum information contained within Gaussian state sources. This paper considers the employment of a noiseless linear amplifier at the detection stage of a quantum illumination-based quantum target detection protocol. Such a non-Gaussian amplifier offers a means of probabilistically amplifying an incoming signal without the addition of noise. Considering symmetric hypothesis testing, the quantum Chernoff bound is derived and limits on detection error probability is analysed for both the two-mode squeezed vacuum state and the coherent state classical benchmark. Our findings show that in such a scheme the potential quantum advantage is amplified even in regimes where quantum illumination alone offers no advantage, thereby extending its potential use. The same cannot be said for coherent states, whose performances are generally bounded by that without amplification.

A MIG Welding Clamping Scheme for Power Battery Enclosure’s Deformation Restrain

Aiming at the inward shrinkage between the frame and the bottom plate of the power battery enclosure after MIG (melt inert-gas) welding, a welding clamping scheme with hook-pull devices was designed. By adjusting the clamping force of the hook-pull device, the MIG welding deformation force was counteracted, so the inward shrinkage deformation of the frame after welding was restrained. To obtain the deformation force during the MIG welding, the welding simulation model of power battery enclosure was established. Gaussian heat source model was selected as temperature load. Through the numerical simulation and experimental analysis of the temperature field, the numerical simulation results are in good agreement with the measured thermal cycle curve in terms of temperature value and change trend. The error between numerical simulation result curve and measured thermal cycle curve at the measurement point is no more than 10%, which can meet the simulation requirements. Based on the simulation model and the load of the temperature field, deformation force curves were obtained by simulating the welding process. To counteract the MIG welding deformation force, a pneumatic servo control system of the welding clamp was designed, which can generate equal and reversed welding deformation force. The experiments show that the actual output force of the system has a tiny time delay and fluctuates with the varies of the pneumatic servo control system. The maximum fluctuation error is 6.96 N, which is within the permitted error range. The welding experiments were carried out to verify effectiveness of the control system and the welding clamp. The field results have shown that the maximum inward shrinkage deformation after welding is 0.6 mm, which is less than 1.2 mm required by the MIG welding process.

Joint formation mechanism of different laser transmission welding paths

Abstract In this study, the rectilinear, sine, and spiral paths of polymer transmission welding were used to perform welding comparative experiments, and the influence of various parameters in the polymer transmission welding of different laser paths on the joint performance and the formation of molten pool was discussed. The spiral path exhibited the highest joint strength, that increased by more than 50% compared with conventional rectilinear welding. The molten pool formed by spiral welding had a high depth-to-width ratio. Microscope observations revealed that the glass fiber flow signs in the molten pool were obvious, the glass fiber in the molten pool was abundant, and the bubble generation rate in the molten pool was lower. In this paper, Fortran language was used to construct Gaussian body heat source movement model with different paths. Results show that the spiral welding had higher welding stability than traditional rectilinear welding, welding defects caused by the lack of heat in the previous period can be properly compensated by selecting the appropriate welding period, Therefore, good joint performance can be achieved. In addition, amplitude and period are two important process parameters of spiral welding, and their sizes have important effects on joint strength and molten pool formation

Numerical Simulation of 50 mm 316L Steel Joint of EBW and Its Experimental Validation

The 316L thick plate electron beam welding (EBW) has been widely used in fusion test reactor manufacturing. Therefore, the numerical simulation of the 50 mm 316L austenitic stainless steel by two heat sources and experimental on microstructure and residual stress have been studied in this article. In the simulation study, the traditional heat source model (3D Gaussian heat source) and composite heat source (double ellipsoid heat source superimposed on the 3D Gaussian heat source) were proposed to simulate the welding of local joint. Weld cross-section, temperature curve, and residual stress after welding obtained by simulations were investigated. The experimental study involved residual stress tests and microstructure analysis. It turned out that the result of the composite heat source was closer to the actual joint. The residual stress distribution of simulation was validated and in accordance with experimental measurement. Moreover, the microstructures were studied by electro backscattered diffraction (EBSD) and compared with the temperature curve. The formation mechanism of microstructural heterogeneity was caused mainly by different thermal cycles at different positions of the thick plate. The top of the joint was more prone to stress concentration.

A combined heat source model for the prediction of residual stress post extreme high-speed laser material deposition

Extreme high-speed laser material deposition (EHLA) can be utilized for mass customization owing to its enhanced process speed and productivity. Although EHLA has multiple similarities with additive manufacturing techniques such as conventional laser metal deposition (LMD), the variation in the process speed causes different phase transformations and residual stress distributions. Therefore, a combined heat source model is proposed to evaluate the performance of structures repaired by EHLA and optimize process strategies. The model considers the unique energy input associated with the densification process compared with that of the conventionally used Gaussian heat source model. The parameters within the model were calibrated based on the residual stress distribution and molten pool morphology. The evolution of temperature and residual stress was investigated under various process conditions such as scanning speed and power input using the model. The consistency between the simulation and experimental results verified the viability of the model for determining EHLA parameters and improving the performance of repaired parts.

Transition and basin stability in a stochastic tumor growth model with immunization

The phenomenon of noise-induced transition driven by the correlated Gaussian and non-Gaussian colored noises is investigated by the first escape probability (FEP) and the mean first exit time (MFET). To derive the Markovian approximation of the original tumor growth model and obtain the analytical expressions of the FEP and MFET, we reduce the non-Gaussian colored noise and then expand the unified colored noise approximation (UCNA). Additionally, the stochastic basin of attraction (SBA), a recent geometric concept based on the FEP and MFET, is introduced to provide further insight into the effects of noisy fluctuations on the basin stability of a certain domain. A higher FEP or shorter MFET in the high tumor population region B facilitates the transition from B to the low tumor population region Bc, which indicates the weaker stability of domain B. Our main results demonstrate that (i) the transitions from B to Bc can be induced by both the Gaussian and non-Gaussian noise sources; (ii) the stronger noise intensity, especially the non-Gaussian noise intensity, with a larger deviation parameter and immune coefficient improves the FEP, shortens the MFET, and hence benefits the transitions. However, the enlargement of the correlation between noises strengthens the basin stability of domain B and impedes the transitions; (iii) the size of SBA expands due to the larger cross-correlated intensity. In contrast, the enhancements of noise intensities with a larger departure degree reduce the size of SBA, which weakens the basin stability and is less in favor of tumor treatment. Furthermore, the Monte Carlo simulations of the original system are employed to verify the feasibility and accuracy of the analytical predictions.

Finite element analysis and experimental investigation of moving heat source model for GMAW deposited mild steel weld bead

An investigation has been done to identify the heat source model suitable for numerical modeling of the Gas Metal arc Welding (GMAW) welding process. In the present investigation, a numerical model was constructed to simulate the GMAW welding process through transient thermal analysis for different thermal heat source models for weld deposition of Mild steel considering semi-cylindrical weld bead geometry. The Gaussian heat source with radial coordinate system and double ellipsoidal thermal heat source have been considered to develop a Finite Element Analysis (FEA) model. Validation of numerical analysis results has been confirmed through experimental investigation. Numerical modeling confirms the utilization of both heat sources, i.e. Gaussian and Double ellipsoidal for the prediction of the weld bead deposition profile. However, the numerical modeling developed using a double ellipsoidal heat source has more resembles experimental investigation due to the utilization of bead profile data. However, the Gaussian heat source is found to be suitable in the case of the unavailability of experimental data. The experimental studies show a variation in the weld bead geometry, along its welding direction due to multiple environmental factors. The microstructural investigation also shows the development of a fine columnar grain structure at the welding bead & weld penetration zone, and the grain structure became coarser at the Heat Affected Zone (HAZ).

Complete Characterization of Gorbunov and Pinsker Nonanticipatory Epsilon Entropy of Multivariate Gaussian Sources: Structural Properties

This paper derives the optimal test channel distribution and the complete characterization of the classical Gorbunov and Pinsker (1973), Gorbunov and Pinsker (1974) nonanticipatory epsilon entropy of multivariate Gaussian Markov sources with square-error fidelity, which remained an open problem since 1974. The paper also formulates a state dependent nonanticipatory epsilon entropy, in which past reproductions are available to the decoder and not to the encoder, the test channel is specified with respect to an auxiliary (state) random process, and the reproduction process is a causal function of past reproduction and the auxiliary random process. This variation is analogous to the Wyner and Ziv (1976) and Wyner (1978) rate distortion function (RDF), of memoryless sources. It is shown that the operational rate of zero-delay codes, with past reproductions available to the decoder but not to the encoder is bounded below by the state dependent nonanticipatory epsilon entropy rate. For the case of multivariate Gaussian Markov sources with square-error fidelity, the optimal test channel distribution and the complete characterization of the state dependent of nonanticipatory epsilon entropy are derived, and also shown that that the two nonanticipatory epsilon entropies coincide. The derivations are new; they are based on structural properties of the stochastic realizations of the reproduction process that induce the optimal test channel distributions. They are derived using, achievable lower bounds on information theoretic measures, properties of mean-square estimation theory, Hadamard’s inequality, and canonical correlation coefficients of a tuple of multivariate jointly Gaussian random processes. Applications of the nonanticipatory epsilon entropy and its state dependent variation are discussed to the areas of control of unstable Gaussian systems over limited memory channels, design of causal estimators for Gaussian Markov sources with a fidelity criterion, computation of the rate loss of causal and zero-delay codes of Gaussian Markov sources with respect to non-causal codes.

Ensemble-Based Gravity Wave Parameter Retrieval for Numerical Weather Prediction

AbstractGravity wave (GW) momentum and energy deposition are large components of the momentum and heat budgets of the stratosphere and mesosphere, affecting predictability across scales. Since weather and climate models cannot resolve the entire GW spectrum, GW parameterizations are required. Tuning these parameterizations is time-consuming and must be repeated whenever model configurations are changed. We introduce a self-tuning approach, called GW parameter retrieval (GWPR), applied when the model is coupled to a data assimilation (DA) system. A key component of GWPR is a linearized model of the sensitivity of model wind and temperature to the GW parameters, which is calculated using an ensemble of nonlinear forecasts with perturbed parameters. GWPR calculates optimal parameters using an adaptive grid search that reduces DA analysis increments via a cost-function minimization. We test GWPR within the Navy Global Environmental Model (NAVGEM) using three latitude-dependent GW parameters: peak momentum flux, phase-speed width of the Gaussian source spectrum, and phase-speed weighting relative to the source-level wind. Compared to a baseline experiment with fixed parameters, GWPR reduces analysis increments and improves 5-day mesospheric forecasts. Relative to the baseline, retrieved parameters reveal enhanced source-level fluxes and westward shift of the wave spectrum in the winter extratropics, which we relate to seasonal variations in frontogenesis. The GWPR reduces stratospheric increments near 60°S during austral winter, compensating for excessive baseline nonorographic GW drag. Tropical sensitivity is weaker due to significant absorption of GW in the stratosphere, resulting in less confidence in tropical GWPR values.

Simulation of residual stress in aluminum alloy welding seam based on computer numerical simulation

In order to study a reliable simulation method of residual stress in aluminum alloy welds, based on computer simulation technology, this paper combines finite element technology to construct a simulation system of residual stress in aluminum alloy welding seam. Moreover, this paper summarizes the basic theories of heat conduction and related theories of welding heat sources, and proposes related mathematical models. In order to truly reflect the influence of molten pool and keyhole in laser welding, this paper adopts a combined heat source model of Gaussian distributed surface heat source and cylindrical heat source, which is more in line with the actual situation. In addition, this paper studies the simulation results of welding residual stress and deformation under pretension and without pretension, respectively calculates them in ANSYS calculation, and compares the calculation results. Finally, this paper designs an experiment to verify the performance of the computer numerical simulation method proposed in this paper, and analyze the experimental error. The research results show that the simulation method proposed in this paper is close to the actual situation, and can provide a reference for the subsequent analysis of residual stress in aluminum alloy welding seam.

Temperature and density effects on the two-nucleon momentum correlation function from excited single nuclei

Two-nucleon momentum correlation functions are investigated for different single thermal sources at given initial temperature $(T)$ and density $(\rho)$. To this end, the space-time evolutions of various single excited nuclei at $T$ $= 1 - 20$ $MeV$ and $\rho$ = 0.2 - 1.2 $\rho_0$ are simulated by using the thermal isospin-dependent quantum molecular dynamics $(ThIQMD)$ model. Momentum correlation functions of identical proton-pairs ($C_{pp}(q)$) or neutron-pairs ($C_{nn}(q)$) at small relative momenta are calculated by $Lednick\acute{y}$ and $Lyuboshitz$ analytical method. The results illustrate that $C_{pp}(q)$ and $C_{nn}(q)$ are sensitive to the source size ($A$) at lower $T$ or higher $\rho$, but almost not at higher $T$ or lower $\rho$. And the sensitivities become stronger for smaller source. Moreover, the $T$, $\rho$ and $A$ dependencies of the Gaussian source radii are also extracted by fitting the two-proton momentum correlation functions, and the results are consistent with the above conclusions.

Photonic nanojet of a Gaussian beam illuminated low refractive index microsphere in air: A comprehensive variation of parameters

A photonic nanojet (PNJ) is a narrow beam of concentrated light emerging from the illuminated micro-scattering objects, which has attracted a lot of attention lately. However, so far the variation and the properties of the PNJ of a microsphere have been computationally investigated in a limited scope and mostly for plane wave as a source. Within the framework of the Generalized Lorenz-Mie theory (GLMT), a large-scale investigation of the PNJ properties (intensity, position, length and width) and their dependence on the parameters which influence the PNJ (beam wavelength, beam size, beam position and microsphere size) is presented. The calculations are carried out for more than 400 000 configurations of parameters, with Gaussian beam source. Computations show that each parameter plays an important role in the PNJ formation. The influence of each of the parameters and their complex interplay is studied in detail. Depending on the beam position, PNJs are classified into two types, with different characteristics and possible applications. We believe this systematic and comprehensive presentation of the widest range of PNJs so far will advance the knowledge of this phenomenon, and serve as a reference for tailoring any PNJ according to one's needs and applications.

Interface detection by picosecond Laser-Induced Breakdown Spectroscopy (LIBS): Application to a physical vapor deposited tungsten layer on a copper-chromium-zirconium substrate

The Laser-Induced Breakdown Spectroscopy (LIBS) technique is tested to control the ablation of a tungsten layer having a dozen micrometers thickness obtained by physical vapor deposition (PVD) on a CuCrZr substrate figuring plasma facing components used in the WEST tokamak. In the conditions of a Gaussian laser source with a wavelength of 532 nm, 30 ps as laser time duration and irradiance of ∼1017 W m−2 in air at atmospheric pressure, the mean ablation rate of the PVD tungsten is 90 nm per pulse, which is much lower than the one of bulk tungsten measured at 500 nm per pulse. The ablation process can lead to the formation of secondary craters not directly driven by the laser irradiance distribution.The ablation rate on CuCrZr is measured at 600 nm per pulse. Measuring the deposited layer thickness requires to spectroscopically monitor the CuCrZr components to avoid any damage of the substrate. We show that this can be performed in real time. A more secure process based on the use of a defocused laser beam is tested and leads to significantly lower ablation rate with the same precision for the thickness measurement. The increase in the ablation radius may be used to clean substrates polluted by tungsten layers.