Gaussian Density Distribution Research Articles

Ti–6Al–4V TIG Weld Analysis Using FEM Simulation and Experimental Characterization

This study involves thermal, metallurgical and mechanical analysis during tungsten inert gas welding of Ti–6Al–4V alloy aiming at optimizing the welding current to enhance the mechanical properties. Firstly, a 3D transient FEM simulation of TIG Ti–6Al–4V weld using ABAQUS software, based on a Gaussian distribution of power density in space, has been built to predict the effect of welding current on the heat input, weld bead geometry, temperature and residual stresses distribution across the welding line. Secondly, a validation of FEM with the experimentally measured temperature distribution and welding bead geometries has been presented. Finally, experimental study of the effect of TIG welding current, the suitable range predicted from FEM, on the microstructure, hardness and tensile strength of 12-mm-thick alloy plate is discussed. Using FEM, the suitable range of welding current was predicted to be 130–170 A. There was a close agreement among the experimental results and the FEM simulation data. It has been found that low welding current of 130 A results in high tensile strength and hardness of the welding joint. This is attributed to low heat input, high cooling rate and the formation of a fine grain structure containing martensite-phase with low values of residual stresses.

A data-driven framework for sparsity-enhanced surrogates with arbitrary mutually dependent randomness

The challenge of quantifying uncertainty propagation in real-world systems is rooted in the high-dimensionality of the stochastic input and the frequent lack of explicit knowledge of its probability distribution. Traditional approaches show limitations for such problems, especially when the size of the training data is limited. To address these difficulties, we have developed a general framework of constructing surrogate models on spaces of stochastic input with arbitrary probability measure irrespective of the mutual dependencies between individual components of the random inputs and the analytical form. The present Data-driven Sparsity-enhancing Rotation for Arbitrary Randomness (DSRAR) framework includes a data-driven construction of multivariate polynomial basis for arbitrary mutually dependent probability measures and a sparsity enhancement rotation procedure. This sparsity enhancement method was initially proposed in our previous work (Lei et al., 2015) for Gaussian density distributions, which may not be feasible for non-Gaussian distributions due developed a new data-driven approach to construct orthonormal polynomials for arbitrary mutually dependent randomness, ensuring the constructed basis maintains the orthogonality/near-orthogonality with respect to the density of the rotated random vector, where directly applying the regular polynomial chaos including arbitrary polynomial chaos (aPC) Oladyshkin and Nowak (2012) shows limitations due to the assumption of the mutual independence between the components of the random inputs. The developed DSRAR framework leads to accurate recovery, with only limited training data, of a sparse representation of the target functions. The effectiveness of our method is demonstrated in challenging problems such as partial differential equations and realistic molecular systems within high-dimensional (O(10)) conformational spaces where the underlying density is implicitly represented by a large collection of sample data, as well as systems with explicitly given non-Gaussian probabilistic measures.

Molecular Dynamics Study on the Deformation Behaviors of Nanostructures in the Demolding Process of Micro-Injection Molding.

Polymer parts with nanostructures have broad applications, possessing excellent optical, electrochemical, biological, and other functions. Injection molding technology is one of the main methods for mass production of polymer parts with various shapes and sizes. The demolding process is vital to the replication quality of molded parts with nanostructures. For this study, molecular dynamics simulations of polypropylene (PP), polymethyl methacrylate (PMMA), and cycloolefin copolymer (COC) were conducted for the demolding process. The average velocity, density distribution, adhesion energy, and demolding resistance were introduced to analyze the deformation behaviors of polymer nanostructure from a nickel nano-cavity with an aspect ratio of 2:1. The shoulders of nanostructures were firstly separated from the nickel mold insert in the simulation. Under the external demolding force of 0.07 nN, PP and PMMA could be successfully demolded with some deformations, while COC could not be completely demolded due to the greater adhesion energy between COC and Ni. It was found that the maximum adhesion energy occurred in the separation process between the shoulder of the nanostructure and Ni and the huge adhesion energy was the main cause of demolding defects. The velocity difference of the whole polymer layer and polymer nanostructure was further analyzed to explain the nanostructure deformation. In order to improve the quality of demolding, the external force applied on polymers should be properly increased.

About the elongation at break of unfilled natural rubber elastomers

This paper presents the characterization of the mechanical properties, of the ability to crystallize thermally or under strain, and of the Elastically Active Chains (EAC) network of Natural Rubber elastomer, whose EAC average density and length distribution were modified by thermo-oxidative ageing. EAC length distribution is not a critical parameter for λbreak in elastomers which do not crystallize (as far as the quantity of free and dangling chains stays negligible, which is the case in this study). However, it becomes important in crystallizable materials, since it controls the chains quantity which can be stretched enough to crystallize. When this quantity is large enough, the material can be stretched up to λc, and the crystallization process will enable to increase both λbreakand σbreak. Conversely when it is too low, λbreakis seemingly mainly governed by the average EAC density and a power law then links both quantities.

Chameleon field in a spherical shell system

We investigate the validity of screening mechanism of the fifth force for chameleon field in highly inhomogeneous density profile. For simplicity, we consider a static and spherically symmetric system which is composed of concentric infinitely thin shells. We calculate the fifth force profile by using a numerical method for a relatively large Compton wavelength of the chameleon field. An approximate solution is also derived for the small Compton wavelength limit. Our results show that, if the thin-shell condition for the corresponding smoothed density profile is satisfied, the fifth force is safely screened outside the system irrespective of the configuration of the shells inside the system. In contrast to the screening outside the system, we find that the fifth force can be comparable to the Newtonian gravitational force inside the system. If the system is highly inhomogeneous, the chameleon field cannot trace the potential minimum varying with the density and repeats being kicked, climbing up and rolling down the potential even when the effective mass of the chameleon field is sufficiently large in the system on average. One should not feel complacent about the wellbehavedness of the fifth force field with an averaged density distribution when we consider inhomogeneous objects.

Optimal design of helicon wave antenna and numerical investigation into power deposition on helicon physics prototype experiment

<sec>Recently, helicon plasma sources have aroused the great interest particularly in plasma-material interaction under fusion conditions. In this paper, the helicon wave antenna in helicon physics prototype experiment (HPPX) is optimized. To reveal the effect of the radial density configuration on wave field and energy flow, Maxwell's equations for a radially nonuniform plasma with standard cold-plasma dielectric tensor are solved. Helicon wave coupling and power deposition are studied under different types of antennas, different antenna lengths and driving frequencies by using HELIC. Through the numerical simulation, the optimal antenna structure and size are obtained, that is, half helix antenna, which works at 13.56 MHz and has a length of 0.4 m, can generate nonaxisymmetric radio frequency energy coupling to excite higher electron density.</sec><sec>The influences of different static magnetic fields and axis plasma densities on power deposition are also analyzed. It is found that the absorbed power of the plasma to the helicon wave has different peak power points in a multiple static magnetic field and axial plasma densities, and the overall coupling trend increases with static magnetic field increasing, but decreases with axis plasma density increasing. According to the simulation results, the ionization mechanism of helicon plasma is discussed. In order to further study the coupling of helicon wave with plasma in HPPX, the induced electromagnetic field and current density distribution are given when the plasma discharges. Under parabolic density distribution, the field intensity of the induced electric field at the edge is large, while neither the induced magnetic field nor current density changes much along the radial direction, the energy is distributed evenly in the whole plasma. Under the Gaussian density distribution, the induced electric field intensity is higher at the edge, while the induced magnetic field and current density in the center are much higher than at the edge. </sec><sec>In this paper studied are the structure and size of helicon wave antenna, the influences of static magnetic field and axial plasma density on plasma power deposition and the distribution of induced electromagnetic field and current density during plasma discharge under different density distributions. This work will provide important theoretical basis for helicon wave antena design and relevant physical experiments on HPPX.</sec>

A Numerical and Experimental Analysis of Inconel 625 Electron-Beam Welding – Thermal Aspects

Inconel 625, a nickel based superalloy, finds application in many fields. It is known to have a good weldability and it is often used in the as-welded conditions, heat treatments could be necessary to relief stresses. Numerous variables are known to affect the residual stresses field: welding process, joined geometry and clamping conditions. Since experimental measurements based on X-ray diffraction are not straightforward, expensive experimental work could be substituted by numerical simulation. Before performing an elastoplastic simulation, thermal analysis results are needed, first.This paper focus on the thermal analysis procedure. The analysis has been validated by means of macrographs and with thermocouples data. The heat source was successfully modelled using a superimposition of a spherical and a conical shape heat source with Gaussian power density distribution in order to reproduce the nail shape of the fusion zone. Heat source parameters were chosen so that the model would match with experimentally determined weld pool shape and temperatures. Preliminary results of the metallurgical analysis are also presented.

Parameter Characterization of High Latitude Geomagnetic Storms in 2010

Geomagnetic storm is a kind of severe disturbance that lasts for more than ten hours to several tens of hours in the entire Earth’s magnetosphere. This paper uses the NRLMSISE-00 model to calculate the temperature and density data. According to the surveyed medium magnetic storm events, the characteristics of daily average density and temperature in the occurrence of magnetic storms in 2010 were studied. At the same time, high latitude meridians were taken as research objects. Divide the temperature and density characteristics at different heights. Results showed that the annual trend of density is the same for different heights, and there is an average of the average density every day on the six medium magnetic storm mountains. For the average daily temperature, each medium magnetic storm event corresponds to a temperature peak. The peak temperature on April 5 was the highest temperature throughout the year, consistent with the annual average density distribution. Due to the intensity of the magnetic storm, the temperature of a large area of bright areas rose sharply on April 12, which is also the highest in the year. At 18:00 on May 2, it was the peak time of the moderate magnetic storm event caused by CIR, but May 3 was the date of the peak temperature. This peak delay is reasonable.

Investigation of spatial density of public and business objects in the largest city with help of geoinformation technologies

The article reveals the study of spatial distribution of the density of public and business objects with the use of geoinformation technologies. The source of the data was data from the open geoinformation project OpenStreetMap. Earlier, we showed that for the radial component of the density of public and business facilities. This paper is a continuation of the previous one. The angular distribution of density of public and business objects is studied by example of the largest city - Ekaterinburg. Spatial density has "tails" that characterize the predominant directions of the city development. At the same time, the average spatial configuration for the average density distribution shows the radial-ring structure for urban planning. The obtained results are interpreted within the framework of the "frame-fabric".

Distributed fusion for nonlinear uncertain systems with multiplicative parameters and random delay

Abstract This paper proposes an information filtering-based distributed fusion for nonlinear uncertain systems with multiplicative random parameters and randomly delayed measurements in sensor networks. This is a typical nonlinear and non-Gaussian stochastic system with multiple uncertainties including nonlinearity, multiplicative random parameters and random delay, along with additive noises. In the criterion of minimizing the mean square error of state estimate, the centralized information-type filter via Gaussian mixture realization is put forward, by applying statistical linear regression to nonlinear measurement models to reconstruct a new and equivalent one with the linear form. Then, the distributed implementation is designed via average consensus with the corresponding weight of each component being updated distributively, in order to ensure that the Gaussian mixture distribution of the posterior probability density in each processing unit asymptotically approximates the corresponding one in the centralized fusion as closely as possible. Meanwhile, the d-step lag state smoothing is obtained to further improve the estimation precision, in terms of the proposed filtering method. An example with multiplicative random parameters and one-step/two-step random delay in the distributed processing network is simulated to validate the proposed method.

Application of SN-EMD in Mode Feature Extraction of Ship Radiated Noise

Due to the randomness of added noise, noise-assisted versions based on EMD (empirical mode decomposition) usually cause new “mode mixing” problem. In addition, these algorithms also have problems such as high time-consuming and large recovering error. For the reasons, a new method SN-EMD (Selective Noise-assisted EMD) is put forward in this paper. It determines whether to add noise as assistance by judging whether there is high frequency intermittent component contained in the signal or not. The new method was proved to have the optimal performance by comparing the performance parameters for evaluating the decomposition. In this paper, SN-EMD was used to decompose ship radiated noise. On account of the differences in the original information contained in each mode of radiated noise signals from different ship, we selected the first three modes for processing. Average instantaneous frequency, center frequency, energy density, and energy distribution ratio were extracted as mode feature of ship targets for classification and recognition. Spatial distribution of the feature quantities in three-dimensional space verified similarity of the same target and separability of different targets.

Investigation of spatial density of public and business objects in the largest city with help of geoinformation technologies

The article reveals the study of spatial distribution of the density of public and business objects with the use of geoinformation technologies. The source of the data was data from the open geoinformation project OpenStreetMap. Earlier, we showed that for the radial component of the density of public and business facilities. This paper is a continuation of the previous one. The angular distribution of density of public and business objects is studied by example of the largest city - Ekaterinburg. Spatial density has "tails" that characterize the predominant directions of the city development. At the same time, the average spatial configuration for the average density distribution shows the radial-ring structure for urban planning. The obtained results are interpreted within the framework of the "frame-fabric".

Pore pressure estimation in irradiated UMo

Image analysis was performed on SEM micrographs of recently irradiated UMo dispersion fuel plates. Detailed information on the fission gas inter-granular bubbles accompanying recrystallization, including average diameter, density and size distribution were extracted and compared with previous results on UMo and UO2. A pore density drop was notice at high fission densities and attributed mainly to a pore coarsening dominated by irradiation induced phenomena. Based on the image analysis data and theoretical considerations, a model was developed to estimate the pressure inside the pores as a function of fission density, temperature and pore radius. The developed pressure can give indications of the mechanical stability of the fuel towards the progressive building-up of fission gases. Finally, the proposed methodology was applied to the nanobubble lattice decorating the fuel grains at low fission densities in order to infer the physical state of the contained fission gases. The estimated values suggest the presence of solid xenon precipitates.

Elastic and inelastic O16+C12 rainbow scattering within the coupled-channels mechanism

Angular distributions of the differential cross section of $^{16}\mathrm{O}+^{12}\mathrm{C}$ elastic and inelastic scattering in the energy range ${E}_{\mathrm{lab}}=181\ensuremath{-}1503$ MeV were fitted with the full cluster folded approach (DFC1) using the coupled-channels (CC) method by taking into account the effect of the low-lying states, ${0}^{+}$ and ${2}^{+}$ (${E}_{\mathrm{ex}}=4.44$ MeV) for the target nucleus. The cluster transition density is generated macroscopically by deforming the cluster ground state modified Gaussian density distribution of the target nucleus. The coupled-channels calculations with the fitted parameters for the elastic scattering provide a successful description of the inelastic experimental measurements. The obtained results are compared with the finding of the phenomenological Woods-Saxon potential. It was found that the characteristic features of the nuclear rainbow phenomena can be reproduced successfully by our CC calculations with both potentials but fail to reproduce the new Airy minimum of the nuclear rainbow structure. The deduced intrinsic quadrupole moment values, ${Q}_{20}$, derived from the analyses are compared with results of previous studies. The deformation lengths, ${\ensuremath{\delta}}_{20}$, obtained by CC calculations are in agreement with those obtained from the electromagnetic measurement values and those reported in previous studies.

Experimental research on improving accuracy of electrochemical machining of deep narrow grooves

Deep narrow metal grooves have wide application prospects in the field of aeronautics and astronautics. Electrochemical machining (ECM) has a unique advantage in the fabrication of deep narrow grooves due to its advantages of no cutting heat, no cutting force, and high machining efficiency. But, there is significant stray current corrosion in the side wall of the deep narrow groove, which restricts the enhancement of the processing accuracy. In the interest of improving the processing accuracy of the deep narrow groove, the effects of compound feed and matching of pulse and oscillation (MOPAO) on the average current density distribution of the deep narrow groove side wall were studied based on finite element analysis (FEA) of the electrostatic field. The finite element simulation results show that the homogeneity of the deep narrow groove could be significantly improved with the increment of the oscillation amplitude, and the processing accuracy could be improved by prolonging the pulse turn-off time. Moreover, contrast experiments on the deep narrow groove ECM were carried out based on a self-developed ECM system. The experimental results indicate that the matching of pulse and oscillation can remarkably improve the processing accuracy, and smaller average groove width and better groove width uniformity can be obtained in comparison with the compound feed. Moreover, the maximum groove width is 2.78 mm, the minimum groove width is 2.73 mm, the length-width ratio reaches 11:1, and the depth-width ratio reaches 9:1 using the machining mode of MOPAO.

Improvement on reflectivity of tunable photonic band gap with spontaneous generated coherence

The photonic band gap is a spectral range which cannot propagate in a periodic optical nanostructure, that is, the structure itself has a “forbidden band”. It has been successfully applied to the filters, amplifiers, mixers, etc. As is well known, dynamically tunable photonic band gaps in cold atomic lattices are of great importance in various research fields. However, the photonic band gaps of a traditional photonic crystal are non-tunable because the periodic structure is determined once the photonic crystal is grown. On the other hand, a majority of previous researches focused on improving the reflectivity of photonic band gap, which can only keep approaching to 1. Due to the action of the vacuum of the radiation field, near-degenerate lower level has an additional coherence term, the spontaneously generated coherence term. In this paper, we consider a three-level ∧-type atomic system driven by a strong coherent field, a weak coherent field and an incoherent pump, in which the two ground states are of hyperfine structure. The one-dimensional photonic band gaps are formed by cold atoms trapped in a one-dimensional-ordered optical lattice and this system may create two photonic band gaps (PBGs). The trapped cold atoms have a Gaussian density distribution in each period as determined by the optical potential depth and the average atomic temperature. We investigate in detail how the reflectivities of the two PBGs are influenced by the coherent effect of spontaneously generated coherence. Then, we find that the reflectivities of the two band gaps can be significantly improved by the spontaneously generated coherence. The reflectivities of such two band gaps can be dynamically manipulated by varying the intensity of incoherent driving field and the relative phase between the probe field and the coupling field, which cannot be realized in a conventional ∧-type atomic system. Besides, by adjusting the parameters appropriately, the reflectivities of these two band gaps can be higher than 1, which is because probe field gain stems from the spontaneously generated coherence. In the future, photonic transport properties can be investigated in the three-dimensional atomic lattices and this work is meaningful for the optical routing, photodiode and transistor.

Uncertainty in Measurement: Procedures for Determining Uncertainty With Application to Clinical Laboratory Calculations.

In Part II of this review we consider the very common case of multiple inputs to a measurement process. We derive, using only elementary steps and the basic mathematics covered in Part I, the formula for the propagation of uncertainties from the inputs to the output. The Gaussian density distribution is briefly explained, since an understanding of this distribution is needed for the determination of so-called expanded uncertainties at the end of a measurement process. The propagation formula in general involves correlations among the inputs, although in many cases these correlations can be considered negligible. Correlations, however, need to be taken into account in related matters such as line-fitting and have particular relevance to method comparisons. These topics are addressed briefly. We next discuss the important question of bias and its incorporation into the expression of uncertainty. We present, finally, six real-world cases in clinical chemistry where uncertainty in the estimated value of the measurand is calculated using the propagation formula.

Mobility of Two-Electron Conduction in Narrow-Gap n-type Hg₁₋ₓCdₓTe Structures

A simple method for computation of the electron mobility in n-type doped Hg1– x Cd x Te structures is proposed. The method is based on the postulate of the existence of donor bands. In our model, the donor bands are assumed to have a Gaussian distribution of density of states characterized by two fitting parameters only: mean value of energy and standard deviation. By using Kronig’s–Penney’s model, we have estimated mean values of electron’s wave vector module in donor bands. This enables the numerical estimation of the donor band electron mobility (DBEM) caused by polarized optical phonon scattering at room temperatures. At 77 K, DBEM is determined by electron scattering in smooth potential caused by fluctuations in the impurity concentration rather than in individual impurity potentials. Conduction band (CB) electron mobility (CBEM) is determined by scattering on ionized impurities (IO) and polar optical phonon scattering. In calculating of IO scattering, the Brooks-Herring theory was applied with modified values of static dielectric constant. Calculated values of DBEM are almost one order of magnitude below CBEM at 77 K.

Sky-distribution of intensity of synchrotron radio emission of relativistic electrons trapped in Earth’s magnetic field

This paper presents the calculations of synchrotron radio emission intensity from Van Allen belts with Gaussian space distribution of electron density across L-shells of a dipole magnetic field, and with Maxwell’s relativistic electron energy distribution. The results of these calculations come to a good agreement with measurements of the synchrotron emission intensity of the artificial radiation belt’s electrons during the Starfish nuclear test. We have obtained two-dimensional distributions of radio brightness in azimuth — zenith angle coordinates for an observer on Earth’s surface. The westside and eastside intensity maxima exceed several times the maximum level of emission in the meridian plane. We have also constructed two-dimensional distributions of the radio emission intensity in decibels related to the background galactic radio noise level. Isotropic fluxes of relativistic electrons (E ~ 1 MeV) should be more than 107 cm–2s–1 for the synchrotron emission intensity in the meridian plane to exceed the cosmic noise level by 0.1 dB (riometer sensitivity threshold).

О распределении по небесной сфере интенсивности синхротронного радиоизлучения релятивистских электронов, захваченных в магнитном поле Земли

This paper presents the calculations of synchrotron radio emission intensity from Van Allen belts with Gaussian space distribution of electron density across L-shells of a dipole magnetic field, and with Maxwell’s relativistic electron energy distribution. The results of these calculations come to a good agreement with measurements of the synchrotron emission intensity of the artificial radiation belt’s electrons during the Starfish nuclear test. We have obtained two-dimensional distributions of radio brightness in azimuth — zenith angle coordinates for an observer on Earth’s surface. The westside and eastside intensity maxima exceed several times the maximum level of emission in the meridian plane. We have also constructed two-dimensional distributions of the radio emission intensity in decibels related to the background galactic radio noise level. Isotropic fluxes of relativistic electrons (E ~ 1 MeV) should be more than 107 cm–2s–1 for the synchrotron emission intensity in the meridian plane to exceed the cosmic noise level by 0.1 dB (riometer sensitivity threshold).