Gaussian Source Research Articles

Holographic Einstein rings of an AdS black hole in massive gravity

In the context of holography, the Einstein ring of an AdS black hole (BH) in massive gravity (MG) is depicted. An oscillating Gaussian source on one side of the AdS boundary propagates in bulk, and we impose a response function to explain it. Using a wave optics imaging system, we obtain the optical appearance of the Einstein ring. Our research reveals that the ring can change into a luminosity-deformed ring or light spots depending on the variation of parameters and observational positions. When observers are positioned at the north pole, the holographic profiles always appear as a ring with concentric stripe surroundings, and a bright ring appears at the location of the photon sphere of the BH. To investigate the distinct features of the MG AdS BH from previous studies, we discussed the relation between the temperature T and the event horizon ue , which shows the decaying behavior with the increasing values of the event horizon ue , when the graviton parameter m is fixed. These in turn influence the behavior of the response function and the Einstein ring. For example, the amplitude of the lensed response function |〈O〉| increases with the increasing values of the graviton parameter m, for the fixed value of the horizon ue . On the other hand, the amplitude of the lensed response function |〈O〉| decreases with the increasing values of the horizon ue , for the fixed value of graviton parameter m. These differences are also reflected in the Einstein ring, where the intensities and the locations of the Einstein ring significantly vary according to the numerical values of the involved parameters. These findings are also observed in the brightness profiles and the best fit comparison between the results obtained by wave optics and geometric optics for different values of graviton parameter m. In this perspective, our study contributes to a better understanding of the analytical studies of holographic theory, which can be used to evaluate different types of BHs for a fixed wave source and optical system.

An analytical model and experimental validation of annular heat source during scanning electron beam treatment

In this investigation, the maximum depth of penetration and power density coefficient are calculated by simulating the motion trajectories of electrons in surface layer of 5CrNiMo steel using Monte Carlo method, and the number of electrons is 500,000 in simulation. Then tomographic calculation is used to determine the distribution of power density coefficient on the section perpendicular to electron incidence direction, and a Gaussian columnar heat source model that matches the properties of electron beam is established. Finally, a mobile annular heat source model of scanning electron beam is then derived, combining it with the real operating mode. The temperature field during surface modification is simulated by using the mobile annular heat source model, and the simulation findings are compared to experimental data. The findings of Monte Carlo simulation demonstrate that the power density coefficient is Gaussian distributed on the section perpendicular to the depth of electron incidence and the peak power density at the center of each section changes with depth. The thickness and microstructure of re-melting layer predicted from the temperature field simulation is very close to the one from experimental findings. In our investigation, on top of deriving a model for the heat source of a single beam spot, we have also solved the problem of mathematical representation of the beam spot when it is doing high-speed rotational and linear composite motions. The aforementioned findings demonstrate that our study can provide methodological references for the construction of heat source models for different materials during electron beam treatment.

Belief Propagation Optimization for Lossy Compression Based on Gaussian Source

In the Internet of Things, sensor nodes collect environmental information and utilize lossy compression for saving storage space. To achieve this objective, high-efficiency compression of the continuous source should be studied. Different from existing schemes, lossy source coding is implemented based on the duality principle in this work. Referring to the duality principle between the lossy source coding and the channel decoding, the belief propagation (BP) algorithm is introduced to realize lossy compression based on a Gaussian source. In the BP algorithm, the log-likelihood ratios (LLRs) are iterated, and their iteration paths follow the connecting relation between the check nodes and the variable nodes in the protograph low-density parity-check (P-LDPC) code. During LLR iterations, the trapping set is the main factor that influences compression performance. We propose the optimized BP algorithms to weaken the impact of trapping sets. The simulation results indicate that the optimized BP algorithms obtain better distortion–rate performance.

Study of melt pool dynamics and porosity forming mechanism of laser beam oscillation welding of titanium and aluminum

In this study, a numerical model of oscillation weld butt joint is developed to investigate the welding of titanium alloy with aluminum alloy. Three oscillation paths, namely, straight, sine, and circular, are used to study the distribution of force in the molten pool, the welding temperature field, and the formation and evolution of porosity within the weld. A 3D Gaussian heat source is used to represent the laser beam. The volume of the fluid method is employed to track the gas-liquid free surface, and the gas-liquid interface force is transformed by using the continuous surface force model. The mechanism of keyhole collapse and pore formation was examined along with the fluid flow, surface tension, and recoil pressure on the molten pool. The results confirmed that the highest welding quality is acquired by using a laser welding circular path. Notably, numerical simulation results are validated through experimental data, and circular oscillating laser welding significantly reduced weld seam porosity in the welding of Ti–Al dissimilar alloys. The circular oscillation path with an offset of 0.6 mm and an oscillation amplitude of 0.6 mm is identified as the optimal approach for suppressing pores in the weld joint. This research provides valuable insights into the fundamental mechanisms of keyhole collapse and pore formation in laser welding, which contributes to the advancement of effective welding strategies for dissimilar alloys.

Holographic Einstein rings of a Gauss–Bonnet AdS black hole

Based on the AdS/CFT correspondence, we study the holographic Einstein image of a Gauss–Bonnet AdS black hole in the framework of wave optics. Our results show that for the absolute amplitude of total response function, there always exists the interference pattern when the scalar wave passes through black hole. And, the value of the amplitude depends closely on the properties of Gaussian source and spacetime geometry. More importantly, we also find that the holographic images always appears as a ring surrounded by the concentric stripe when observer located at the north pole. At other positions, this ring will change into a luminosity-deformed ring, or two light points. In addition, the influence of Gauss–Bonnet parameter alpha , wave source and optical system on the holographic image have been carefully addressed and the results show that the radius of ring is dependent of the Gauss–Bonnet parameter alpha but not dependent of wave source and optical system. The holographic images that different types of black holes have different features may shed deep insights on the existence of a gravity dual for a given material.

Gray–Wyner and Mutual Information Regions for Doubly Symmetric Binary Sources and Gaussian Sources

Gray–Wyner and Mutual Information Regions for Doubly Symmetric Binary Sources and Gaussian Sources

Phase and thermodynamics-informed predictive model for laser beam additive manufacturing of a multi-principal element alloy

The complex solidification cycles experienced by multi-principal element alloys (MPEAs) during laser-based additive manufacturing (LBAM) often lead to structural defects that affect the build quality. The underlying thermal processes and phase transformations are a function of the process parameters employed. With a moving Gaussian heat source to mimic LBAM and leveraging material thermodynamics guidelines from CALculation of PHAse Diagrams (CALPHAD), we estimate the temperature-dependent thermal properties, phase fractions, and melt pool geometry using an experimentally validated computational fluid dynamics model. The results substantiate that the peak temperatures are inversely correlated to the scan speeds, and the melt pool dimensions can assist in the predictive selection of process parameters such as hatch distance and layer thickness. A relatively low cooling rate recorded during the process is ascribed to the preheating of the substrate to ensure printability of the alloy.

Optimal Rate-Limited Secret Key Generation From Gaussian Sources Using Lattices

We propose a lattice-based scheme for secret key generation from Gaussian sources in the presence of an eaves-dropper, and show that it achieves the strong secret key capacity in the case of degraded source models, as well as the optimal secret key / public communication rate trade-off. The key ingredients of our scheme are the use of the modulo lattice operation to extract the channel intrinsic randomness, based on the notion of flatness factor, together with a randomized lattice quantization technique to quantize the continuous source. Compared to previous works, we introduce two new notions of flatness factor based on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> distance and KL divergence, respectively, which might be of independent interest. We prove the existence of secrecy-good lattices under <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> distance and KL divergence, whose <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> and KL flatness factors vanish for volume-to-noise ratios up to 2πe. This improves upon the volume-to-noise ratio threshold 2π of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sup> flatness factor.

Comprehensive Simulation Research on Microprocess and Macroscopic Electromagnetic Signals of Surface Discharge in SF6

The surface discharge on the dielectric is a common type of partial discharge in GIS, but the microscopic development process of surface discharge in SF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> is unclear. To find out the micro-process of surface discharge and its correlation mechanism with the partial discharge detection signals of GIS, the fluid-chemical simulation model of the streamer is used to simulate the micro-process of surface discharge in SF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> . Then the current signal obtained by the micro-process simulation is used as the excitation to simulate the electromagnetic signals based on the FITD method. A close connection between the microscopic discharge and the macroscopic signals is established. The results show that the electron concentration at the streamer head and the streamer velocity decrease first and then increase during the discharge, with an average velocity of about 9.84×105m/s. The discharge current reached a peak value of about 0.22A when the surface streamer reaches the cathode. In terms of waveform correlation, the absolute value of the average correlation coefficient between the electric field signals simulated in this paper and the actual measured signals is above 0.7, which is much higher than the simulated signal excited by the Gaussian source. By changing the applied voltage and comparing with the experiment results, it is found that the simulation method in this paper can reflect the change of signals under the influence of external conditions. As the applied voltage rises, the amplitude of the electric field signals increases, and the main frequency component on the frequency spectrum grows, with the main frequency value at about 1.2 GHz. The research in this paper is an effective supplement to the existing study on the microscopic mechanism of partial discharge signals.

Numerical Simulation Analysis of Temperature Distribution of NbC-Reinforced Ti-Based Composite Coating by Laser Cladding

In this article, three-dimensional numerical modeling of the laser cladding process by Ansys was proposed. The three-dimensional Gaussian heat source model was used to simulate the actual laser heat source to analyze the temperature distribution of the molten pool. The temperature distribution of the molten pool of TiAlSi + NbC coatings within different process parameters was obtained by simulation. To obtain finer simulation results, the thermophysical properties of TiAlSi + NbC powder and TiAlSi + NbC alloy were investigated, respectively. The temperature selection judgment mechanism, which is used to distinguish the powder and alloy elements, was built. The results showed that the laser power and laser scanning speed play a vital role in the temperature distribution along with the track width and the depth of the molten pool. The simulation values of the width and depth of the cladding layer under different processing parameters were obtained by using the temperature selection judgment mechanism and fitting. The results showed that the track width and depth had a positive correlation with the laser power, whereas they had a negative correlation with the laser scanning speed.

Long-distance ghost imaging with incoherent four-petal Gaussian sources in atmospheric turbulence

In this study, we investigate the use of incoherent four-petal Gaussian sources for ghost imaging (GI) through atmospheric turbulence. A GI imaging formula for incoherent four-petal Gaussian sources in turbulent conditions is derived. The impact of propagation distance, turbulence strength and beam orders on the imaging quality is analyzed numerically in detail. Our findings indicate that the use of a four-petal Gaussian source can significantly improve the quality of the GI system under long-distance imaging conditions, as compared to the commonly used Gaussian sources.

Signaling games in multiple dimensions: Geometric properties of equilibrium solutions

Signaling game problems investigate communication scenarios where encoder(s) and decoder(s) have misaligned objectives due to the fact that they either employ different cost functions or have inconsistent priors. This problem has been studied in the literature for scalar sources under various setups. In this paper, we consider multi-dimensional sources under quadratic criteria in the presence of a bias leading to a mismatch in the criteria, where we show that the generalization from the scalar setup is more than technical. We show that the Nash equilibrium solutions lead to structural richness due to the subtle geometric analysis the problem entails, with consequences in both system design, the presence of linear Nash equilibria, and an information theoretic problem formulation. We first provide a set of geometric conditions that must be satisfied in equilibrium considering any multi-dimensional source. Then, we consider independent and identically distributed sources and characterize necessary and sufficient conditions under which an informative linear Nash equilibrium exists. These conditions involve the bias vector that leads to misaligned costs. Depending on certain conditions related to the bias vector, the existence of linear Nash equilibria requires sources with a Gaussian or a symmetric density. Moreover, in the case of Gaussian sources, our results have a rate–distortion theoretic implication that achievable rates and distortions in the considered game theoretic setup can be obtained from its team theoretic counterpart.

Single-Particle Irradiation Effect and Anti-Irradiation Optimization of a JLTFET with Lightly Doped Source.

In this article, the particle irradiation effect of a lightly doped Gaussian source heterostructure junctionless tunnel field-effect transistor (DMG-GDS-HJLTFET) is discussed. In the irradiation phenomenon, heavy ion produces a series of electron-hole pairs along the incident track, and then the generated transient current can overturn the logical state of the device when the number of electron-hole pairs is large enough. In the single-particle effect of DMG-GDS-HJLTFET, the carried energy is usually represented by linear energy transfer value (LET). In simulation, the effects of incident ion energy, incident angle, incident completion time, incident position and drain bias voltage on the single-particle effect of DMG-GDS-HJLTFET are investigated. On this basis, we optimize the auxiliary gate dielectric, tunneling gate length for reliability. Simulation results show HfO2 with a large dielectric constant should be selected as the auxiliary gate dielectric in the anti-irradiation design. Larger tunneling gate leads to larger peak transient drain current and smaller tunneling gate means larger pulse width; from the point of anti-irradiation, the tunneling gate length should be selected at about 10 nm.

Coulomb Corrections for Bose–Einstein Correlations from One- and Three-Dimensional Lévy-Type Source Functions

In the study of femtoscopic correlations in high-energy physics, besides Bose–Einstein correlations, one has to take final-state interactions into account. Amongst them, Coulomb interactions play a prominent role in the case of charged particles. Recent measurements have shown that in heavy-ion collisions, Bose–Einstein correlations can be best described by Lévy-type sources instead of the more common Gaussian assumption. Furthermore, three-dimensional measurements have indicated that, depending on the choice of frame, a deviation from spherical symmetry observed under the assumption of Gaussian source functions persists in the case of Lévy-type sources. To clarify such three-dimensional Lévy-type correlation measurements, it is thus important to study the effect of Coulomb interactions in the case of non-spherical Lévy sources. We calculated the Coulomb correction factor numerically in the case of such a source function for assorted kinematic domains and parameter values using the Metropolis–Hastings algorithm and compared our results with previous methods to treat Coulomb interactions in the presence of Lévy sources.

Study on Morphology, Microstructure and Properties of 6063-T6 Aluminum Alloy Joints in MIG Welding

In this paper, a metal inert gas (MIG) shielded welding method was used for high-quality welding of 6063-T6 aluminum alloy sheet with a thickness of 2.5 mm. The welding process of MIG welding was accurately simulated and the welding temperature field and thermal cycle curve were calculated using a combination of Gaussian body heat source and double ellipsoidal heat source. As the welding current increased from 75 A to 90 A, the reinforcing phase precipitated under the microstructure of the joint gradually became larger and re-solidified into the body, resulting in a reduction in mechanical properties. When the welding current is 85 A, the pitting resistance of weld forming and weld area reaches its optimum. At this time, the tensile strength of the joint is up to 110.9 MPa, the elongation is up to 16.3% and the Vickers Microhardness is up to 46.9 HV.

Parametric analysis of the thermal model of electric discharge machining of Al-10%SiCmicro-SiCnano hybrid composites

The authors developed a finite element model for electric discharge machining (EDM) that utilizes a Gaussian heat source. The model takes into account the spark radius and the energy distribution factor, which are both dependent on the pulse on time and pulse current. The model also incorporates latent heat, specific heat, and temperature-dependent thermal conductivity properties. The authors emphasize the paucity of study on simulating EDM of hybrid composites utilizing the energy distribution factor as a function of performance parameters, which adds novelty to the research. This study used an aluminum-based hybrid composite reinforced with micro and varying percent of nano SiC particles due to their strength-enhancing properties. The L9 orthogonal array was used for experimental design.A parametric analysis was conducted to investigate the effects of SiC nanoparticle percentage, pulse current, and pulse on time on material removal rate (MRR) and surface roughness (SR). The simulation results were compared with experimental data from previous study. The findings revealed that an increase in the percentage of SiC nanoparticles, pulse current, and pulse on time resulted in a higher MRR. Furthermore, these factors initially caused an increase in SR, followed by a subsequent decrease. Notably, the pulse current exhibited the greatest impact on both MRR and SR, while the pulse on time was the second most significant factor for MRR and the least influential factor for SR. Increasing the percentage of SiC nanoparticles in the Al-based hybrid composite had the least effect on MRR but emerged as the second most influential factor for SR. In summary, the simulation results aligned with the outcomes of prior experimental investigations.

Improved training of physics-informed neural networks for parabolic differential equations with sharply perturbed initial conditions

We propose a multi-component approach for improving the training of the physics-informed neural network (PINN) model for parabolic problems with a sharply perturbed initial condition. As an example of a parabolic problem, we consider the advection–dispersion equation (ADE) with a point (Gaussian) source initial condition. In the d-dimensional ADE, perturbations in the initial condition decay with time t as t−d/2. We demonstrate that for d≥2, this decay rate can cause a large approximation error in the PINN solution. Furthermore, localized large gradients in the ADE solution make the (common in PINN) Latin hypercube sampling of the equation’s residual highly inefficient. Finally, the PINN solution of parabolic equations is sensitive to the choice of weights in the loss function. We propose a normalized form of ADE where the initial perturbation of the solution does not decrease in amplitude and demonstrate that this normalization significantly reduces the PINN approximation error. Next, we present an adaptive sampling scheme based on the analytical estimate of the solution decay rate that significantly reduces the PINN estimation error for the same number of sampling (residual) points. Finally, we develop criteria for selecting weights based on the order of magnitude of different terms in the loss function. We demonstrate the accuracy of the proposed PINN model for forward, inverse, and backward ADEs.

Heat source modeling, penetration analysis and parametric optimization of super spray MAG welding

Main drives, cutterheads and other critical components of tunnel shield machines require welding with thick plates that leave roots over 5 mm. Full penetration welds cannot be achieved by conventional Pulsed MAG welding methods. This article introduces Super Spray MAG Welding technology and investigates its penetrating regularities and mechanisms through high-speed camera images, finite element simulation, and microstructural analysis. An optimal welding procedure was generated using a combination of Genetic Algorithm and Back Propagation Neural Network. The data show that Super Spray MAG arc exhibits greater concentration and stability than traditional MAG arc, marking its strong qualities in emitting high-energy beams. The morphological solidification pattern of the molten pool closely matches the FEM simulation results of the composite Gaussian surface heat source model and peak linear attenuation Gaussian cylinder heat source. The welding current mainly affects the penetration of the weld, followed by the extension of the wire, and lastly the welding speed. Increasing the welding current can transition droplet transfer from globular to spray, as well as alter microstructure development and mechanical characteristics. Suggested parameters for penetrating the 5 mm root were put forward. The BPNN-GA model established can effectively predict weld formation, and points out the optimal welding parameters.

A Scalable Approach to Independent Vector Analysis by Shared Subspace Separation for Multi-Subject fMRI Analysis.

Joint blind source separation (JBSS) has wide applications in modeling latent structures across multiple related datasets. However, JBSS is computationally prohibitive with high-dimensional data, limiting the number of datasets that can be included in a tractable analysis. Furthermore, JBSS may not be effective if the data's true latent dimensionality is not adequately modeled, where severe overparameterization may lead to poor separation and time performance. In this paper, we propose a scalable JBSS method by modeling and separating the "shared" subspace from the data. The shared subspace is defined as the subset of latent sources that exists across all datasets, represented by groups of sources that collectively form a low-rank structure. Our method first provides the efficient initialization of the independent vector analysis (IVA) with a multivariate Gaussian source prior (IVA-G) specifically designed to estimate the shared sources. Estimated sources are then evaluated regarding whether they are shared, upon which further JBSS is applied separately to the shared and non-shared sources. This provides an effective means to reduce the dimensionality of the problem, improving analyses with larger numbers of datasets. We apply our method to resting-state fMRI datasets, demonstrating that our method can achieve an excellent estimation performance with significantly reduced computational costs.

Semi-Analytical Solution for Modelling Moving Heat Sources in a Semi-Infinite Medium with Radiative and Convective Boundary Conditions

The weld quality is highly related to the thermal history of the weld and there have been many trials to monitor the quality using an infrared (IR) sensor. To obtain the real temperature of a surface based on the brightness temperature values measured by an IR camera, the emissivity value must be derived. For an accurate assessment of the emissivity, one must be aware of the melting point isotherm. The temperature profiles only depend on three factors during laser processing, specified as constants the characteristics of the material: laser beam speed (v), laser beam diameter (d), and power (P). Predicting the width of the melted zone reached during the welding process as the parameters vary is a tool for helping a quality laser processing and for determination of true temperature in laser welding using IR camera. This study describes the semi-analytical (SA) solution of the heat conduction equation for a localized moving Gaussian heat source with constant parameters on a semi-infinite medium. The solution, simple and quick to obtain, provides information on the width of the melted zone with an average error &lt; 5 %. The outcome is assessed numerically and contrasted with FEM solutions for a Gaussian source, the latter having undergone experimental validation. With two distinct defocus values, def0 and def-6, and by varying the speed and power settings, two separate types of experiments were run. Thus, the SA solution was obtained and compared after the FEM solution had been obtained with a good approximation (max err 4.3 %, average err 2.7 %). Only in regard to the 1AL test is an error more than 5 % detected; in the other case, the average error is 3.75 %. Two more tests at the defocus values of def-4 and def-8 were conducted to confirm the model's validity as the parameters varied. Overall, the average error between the semi-analytical and the FEM solution is 4.1%. The SA solution may be used to effectively estimate the isotherms related to the melting point of aluminum (770 K). This allows to obtain a tool which helps restoring the real temperature based on the brightness values measured by the IR camera during laser welding. At the same time, this effective tool allows to investigate the importance of different processing parameters in laser manufacturing.