Grad's Method Research Articles

Retraction Note to: Comparative Measurements of Plasma Position Using Multipole Moments Method and Analytical Solution of Grad–Shafranov Equation in IR-T1 Tokamak

Retraction Note to: Comparative Measurements of Plasma Position Using Multipole Moments Method and Analytical Solution of Grad–Shafranov Equation in IR-T1 Tokamak

Validation of oscillometric ratio and maximum gradient methods for non-invasive blood pressure measurement with intra-arterial blood pressure measurements as reference.

Most non-invasive blood pressure (BP) measurements are carried out using instruments which implement either the Ratio or the Maximum Gradient oscillometric method, mostly during cuff deflation, but more rarely during cuff inflation. Yet, there is little published literature on the relative advantages and accuracy of these two methods. In this study of 40 lightly sedated individuals aged 64.1 ± 9.6 years, we evaluate and compare the performance of the oscillometric ratio (K) and gradient (Grad) methods for the non-invasive estimation of mean pressure, SBP and DBP with reference to invasive intra-arterial values. There was no significant difference between intra-arterial estimates of mean pressure made via Korotkoff sounds (MP-OWE) or the gradient method (MP-Grad). However, 17.7% of MP-OWE and 15% of MP-Grad were in error by more than 10 mmHg. SBP-K and SBP-Grad underestimated SBP by 14 and 18 mmHg, whilst accurately estimating DBP with mean errors of 0.4 ± 5.0 and 1.7 ± 6.1 mmHg, respectively. Relative to the reference standard SBP-K, SBP-Grad and DBP-Grad were estimated with a mean error of -4.5 ± 6.6 and 1.4 ± 5.6 mmHg, respectively, noting that using the full range of recommended ratios introduces errors of 12 and 7 mmHg in SBP and DBP, respectively. We also show that it is possible to find ratios which minimize the root mean square error (RMSE) and the mean error for any particular individual cohort. We developed linear models for estimating SBP and SBP-K from a range of demographic and non-invasive OWE variables with resulting mean errors of 0.15 ± 5.6 and 0.3 ± 5.7 mmHg, acceptable according to the Universal standard.

An Integrated Kernel PCA Neural Network and EGM for Number of Sources Estimation in Wireless Communication

The present work argues estimating number of sources in communication system using an integrated model of Principal Component Analysis (PCA) neural network and kernel method to produce Eigenvalue Grads Method (EGM). The essential advantage of this new suggested model is that, PCA neural is used to determine the covariance matrix instead of the traditional computation process which is time consuming. Simulation outcomes of this adopted model demonstrate wonderful responses through effectiveness, fast converge speed for (PCA) neural network, as well as achieving correct number of sources.

A novel hybrid framework coupling the discrete velocity based-method, the particle-based method and the Grad's distribution function-based method for supersonic rarefied flows

Supersonic rarefied flow has an intrinsically multiple-scale nature due to the large variations of density and characteristic length of the flow structures. Although particle-based methods such as direct Monte Carlo simulation (DSMC) present efficient performance in supersonic rarefied flows, the statistical noise as the nature of stochastic method causes a large amount of averaging steps to be required. To minimise the contamination of statistical noise and preserve the efficiency of capturing the multiscale rarefied effects, a finite volume based hybrid framework is proposed to couple the discrete velocity method (DVM), the particle-based method and the Grad's distribution function-based moment gas kinetic method (G13-MGKS). Benefiting from the coupled treatment both in the spatial and velocity space, the DVM-based method is applied to low-velocity areas close to the wall, which greatly eases the statistical noise and numerous steps of statistical averages can be avoided. Besides, the partition of different sub-methods conveniently determined by the initial flow field from conventional CFD solver has been verified without compromising any accuracy. Further applying the Grad's distribution function-based method in the area with moderate rarefied effect, the present hybrid DVM-Particle-Grad (HDPG) method exhibits the high efficiency and achieves a tenfold speedup ratio compared to the DVM.

A regularized high-order moment model to capture non-Maxwellian electron energy distribution function effects in partially ionized plasmas

A model for electrons in partially ionized plasmas that self-consistently captures non-Maxwellian electron energy distribution function (EEDF) effects is presented. The model is based on the solution of scalar and vectorial velocity moments up to the contracted fourth-order moment. The set of fluid (macroscopic) equations is obtained with Grad's method and exact expressions for the collision production terms are derived, considering the electron–electron, electron–gas, and electron–ion elastic collisions as well as for electron–gas excitation and ionization collisions. A regularization of the equations is proposed in order to avoid spurious discontinuities, existing in the original Grad's moment model, by using a generalized Chapman–Enskog expansion that exploits the disparity of mass between the electrons and the heavy particles (ions and atoms) as well as the disparity of plasma and gas densities, typical of gas discharges. The transport model includes non-local effects due to spatial gradients in the EEDF as well as the impact of the EEDF in the calculation of the elastic and inelastic collision rates. Solutions of the moment model under spatially homogeneous conditions are compared to direct simulation Monte Carlo and a two-term Boltzmann solver under conditions that are representative of high plasma density discharges at low-pressure. The moment model is able to self-consistently capture the evolution of the EEDF, in good quantitative agreement with the kinetic solutions. The calculation of transport coefficients and collision rates of an argon plasma in thermal non-equilibrium under the effect of an electric field is in good agreement with the solutions of a two-term Boltzmann solver, largely improving models with a simplified Bhatnagar–Gross–Krook collisional operator.

Generalized Fluid Models of the Braginskii Type

Several generalizations of the well-known fluid model of Braginskii (1965) are considered. We use the Landau collisional operator and the moment method of Grad. We focus on the 21-moment model that is analogous to the Braginskii model, and we also consider a 22-moment model. Both models are formulated for general multispecies plasmas with arbitrary masses and temperatures, where all of the fluid moments are described by their evolution equations. The 21-moment model contains two “heat flux vectors” (third- and fifth-order moments) and two “viscosity tensors” (second- and fourth-order moments). The Braginskii model is then obtained as a particular case of a one ion–electron plasma with similar temperatures, with decoupled heat fluxes and viscosity tensors expressed in a quasistatic approximation. We provide all of the numerical values of the Braginskii model in a fully analytic form (together with the fourth- and fifth-order moments). For multispecies plasmas, the model makes the calculation of the transport coefficients straightforward. Formulation in fluid moments (instead of Hermite moments) is also suitable for implementation into existing numerical codes. It is emphasized that it is the quasistatic approximation that makes some Braginskii coefficients divergent in a weakly collisional regime. Importantly, we show that the heat fluxes and viscosity tensors are coupled even in the linear approximation, and that the fully contracted (scalar) perturbations of the fourth-order moment, which are accounted for in the 22-moment model, modify the energy exchange rates. We also provide several appendices, which can be useful as a guide for deriving the Braginskii model with the moment method of Grad.

Eu's generalized hydrodynamics with its derived constitutive model: Comparison to Grad's method and linear stability analysis

Recently, the generalized hydrodynamic equations (GHE) and nonlinear coupled constitutive relation (NCCR) model have been successfully utilized for the practical application in stable numerical computations of the non-equilibrium flows. However, their stability property has never been studied theoretically, and the inherent connection with classical Grad's moment still remains unclear. In order to clarify these issues, Eu's method, including the modeling of the non-equilibrium distribution function and the cumulant expansion for collision terms, is revisited to derive the modified moment system. A comparison of Eu's moment method with existing Grad's is presented in detail from the perspectives of distribution function and closure theory. The original infinite system of Eu's distribution function is first truncated into a finite system with 13 moments. Then through our attempt of Taylor expanding the truncated distribution function, a connection between Eu's distribution and Maxwellian and Grad's is established. Subsequently, a truncated closure method is conducted to clarify the relation between Eu's moment and Grad's moment equations. Finally, linear stability analysis of GHE and NCCR model is performed in one-dimensional and multi-dimensional processes, which shows that the equations are unconditionally stable for all wavenumbers and frequencies in the equilibrium rest state (ui0=0) and uniform-moving state (ui0≠0). The linear stability of GHE and NCCR model assures their numerical stability in the multi-dimensional computations, which can be deemed as one of the major benefits of Eu's theory.

Moment method as a numerical solver: Challenge from shock structure problems

We survey a number of moment hierarchies and test their performances in computing one-dimensional shock structures. It is found that for high Mach numbers, the moment hierarchies are either computationally expensive or hard to converge, making these methods questionable for the simulation of highly nonequilibrium flows. By examining the convergence issue of Grad's moment methods, we propose a new moment hierarchy to bridge the hydrodynamic models and the kinetic equation, allowing nonlinear moment methods to be used as a numerical tool to discretize the velocity space for high-speed flows. For the case of one-dimensional velocity, the method is formulated for odd number of moments, and it can be extended seamlessly to the three-dimensional case. Numerical tests show that the method is capable of predicting shock structures with high Mach numbers accurately, and the results converge to the solution of the Boltzmann equation as the number of moments increases. Some applications beyond the shock structure problem are also considered, indicating that the proposed method is suitable for computation of transitional flows.

Local non-equilibrium phase density reconstruction with Grad and Chapman-Enskog methods

The study of the non-equilibrium velocity gas distribution function reconstruction was carried out due to extended gas dynamics methods. The bimodal Mott-Smith solution for a plane shock wave was used as a reference distribution function. The shock-wave solutions were considered in the range of Mach numbers from Ma = 2.0 to Ma = 8.0. The reconstruction of the original function was carried out using the Navier-Stokes-Fourier, 13-moment, regularized 13-moment and 26-moment approximating functions.

Equations and improved coefficients for parallel transport in multicomponent collisional plasmas: Method and application for tokamak modeling

New analytical expressions for parallel transport coefficients in multicomponent collisional plasmas are presented in this paper. They are improved versions of the expressions written in Zhdanov [Transport Processes in Multicomponent Plasma, English ed. (Taylor and Francis, London, New York, 2002)], based on Grad's 21N-moment method. Both explicit and approximate approaches for the calculation of transport coefficients are considered. Accurate application of this closure for the Braginskii transport equations is discussed. Viscosity dependence on the heat flux is taken into account. Improved expressions are implemented into the SOLPS-ITER code and tested for deuterium and neon ITER cases. Some typos found in Zhdanov [Transport Processes in Multicomponent Plasma, English ed. (Taylor and Francis, London, New York, 2002)] are corrected.

Relativistic hydrodynamics with momentum-dependent relaxation time

A second order relativistic hydrodynamic theory has been derived using momentum dependent relaxation time in the relativistic transport equation. In order to do that an iterative technique of gradient expansion approach, namely the Chapman-Enskog (CE) expansion of the particle distribution function has been employed. The key findings of this work are (i) momentum dependent relaxation time in the collision term results in an extended Landau matching condition for the thermodynamic variables, (ii) the result from the numerical solution of the Boltzmann equation lies somewhere in between the two popular extreme limits: linear and quadratic ansatz, indicating a fractional power of momentum dependence in relaxation time to be appropriate, (ii) an equivalence has been established between the iterative gradient expansion method like CE and the well known moment approach like Grad's 14-moment method.

Detection of Geothermal Anomaly Areas With Spatio-Temporal Analysis Using Multitemporal Remote Sensing Data

Thermal infrared (TIR) remote sensing is an important technology for detecting geothermal anomalies. However, detection results have been found to have a certain dependency on the distribution of ground objects and imaging conditions at different times, and pseudo-anomalous areas are easily extracted. To solve this problem, a new geothermal anomaly detection method is proposed in this article and implemented in the Jiaonan uplift in the Yishu fault zone. A temperature inversion experiment is carried out on TIR remote sensing images based on the radiation transfer equation. Then, a gradient operator is used to extract high-temperature regions in various periods, and geothermal anomaly areas are selected through the spatio-temporal analysis method proposed in this article after excluding the influence of impervious surfaces, water bodies, and vegetation. The temperature anomaly points, which are all high-temperature points in each inversion result and geothermal anomaly areas extracted by the proposed method, are compared with the five geothermal anomaly points, which are determined based on 150 geothermal wells and the geological structure in the study area. The spatial locations of the temperature anomaly points and geothermal anomaly areas are close to those of the geothermal anomaly points. Compared with the mean grad method, the proposed method is found to effectively delete some pseudo-anomaly areas under the premise of ensuring the extraction accuracy of geothermal anomaly areas.

EVALUATION OF THE EFFICACY OF DADRU VIDRAVANA MALAHARA IN DADRU KUSHTA- A RANDOMISED CONTROLLED CLINICAL STUDY

Skin disorders are one among the common manifestations. Normally, 10-15% of the general practitioner’s en- counter patients with skin disorders. Ayurveda covers a number of skin manifestations under Kushta Roga. Dadru is one among Kshudra Kushta. It is identified by symptoms such as Kandu, DeerghaPratana, Utsanna, Mandala, Raaga, Pidaka with predominance of Pitta Kapha Dosha. It can be correlated with Tinea infection. Being a Twak Vikara, Bahirparimarjana Chikitsa like Lepadhi treatments plays an important role in the treatment of Kushta including Dadru Kushta. Present study was conducted on 60 diagnosed patients of Dadru Kushta who were ran- domly allocated with 30 each in two groups. Dadru Vidravana Malahara was given for local application in one group and Gandhaka Malahara, a widely used formulation in clinical practice was given for local application in another group. These local applications were advised for a duration of 7 days for under the treatment concept of Lepa. The ingredients of which are the drugs processing Shodana and Kushtahara property. The data was collect- ed from patients at baseline,4th day and 8th day (on completion). Assessment was based on KASI method of grad- ing, number of lesions, perimeter of each lesion, pidaka (present or absent). The results of the study showed that,a statistically significant difference was not seen between the effect of Dadru Vidravana Malahara and Gandhaka Malahara in Dadru Kushta. Keywords: Dadru, Tinea, Dadru Vidravana Malahara, Gandhaka Malahara

Decolorization of Crystal Violet from Aqueous Solution Using Electrofenton Process

In recent years, advance oxidation processes (AOPs) have been widely interested for treatment of industrial wastewater and organic matter. At among, Electrofenton has been proposed as a strong oxidative method. So, the aim of this work was purification of colored aqueous containing crystal violet by electrofenton process and steel mesh electrodes. All regents and methods were prepared from analytical grad and standard methods. The amounts of crystal violet were determined by colorimetric using a spectrophotometer at a maximum wavelength about 586 nm. The main parameters such as pH, applied current, dye concentration, reaction time and supporting electrolyte dose were investigated. Experimental data analysis was also performed using excel software. The results of this study showed that the better dye degradation is occurred in acidic pH (pH3), contact time of 5 minutes, initial concentration of crystal violet 50 mg/l, applied current 0.8 A and an electrolyte level about 0.1 g/L of NaCl. Higher electrical current and lower pHs were caused to generate the higher amount of oxidative radical and regeneration of Fe2+. Under optimal condition, crystal violet was removed around 99.72%. Referring to the results, it can be concluded that the electrofenton is a suitable in situ hydrogen peroxide generation technology for treatment of colored wastewater.

Shear viscosity of ultrarelativistic Boson systems in the presence of a Bose-Einstein condensate

We calculate for the first time the shear viscosity of ultrarelativistic Boson systems in the presence of a Bose-Einstein condensate (BEC). Two different methods are used. One is the Grad's method of moments and another is the Green-Kubo relation within a kinetic transport approach. In this work we consider a Boson system with isotropic elastic collisions and a gluon system with elastic scatterings described by perturbation QCD (pQCD). The results show that the presence of a BEC lowers the shear viscosity. This effect becomes stronger for the increasing proportion of the BEC in the Boson system and is insensitive to the detail of interactions.

Relativistic second order dissipative hydrodynamics from an effective fugacity quasiparticle model

In this work, a second-order relativistic viscous hydrodynamic model has been presented based on the effective fugacity quasiparticle model (EQPM). The hydrodynamic model has been derived from the effective relativistic second-order transport equation under the EQPM for a multiparticle (two-component) system and solving it in Grad's 14-moment method. The EQPM describes the strongly interacting thermal system of QCD interactions through its fugacity parameters extracted from updated lattice equations of state. The proper time evolution of temperature and pressure anisotropy is observed to be affected significantly due to the inclusion of the EQPM compared to an ideal system.

Relativistic dissipation obeys Chapman-Enskog asymptotics: Analytical and numerical evidence as a basis for accurate kinetic simulations.

We present an analytical derivation of the transport coefficients of a relativistic gas in (2+1) dimensions for both Chapman-Enskog (CE) asymptotics and Grad's expansion methods. We further develop a systematic calibration method, connecting the relaxation time of relativistic kinetic theory to the transport parameters of the associated dissipative hydrodynamic equations. Comparison of our analytical results and numerical simulations shows that the CE method correctly captures dissipative effects, while Grad's method does not, in agreement with previous analyses performed in the (3+1)-dimensional case. These results provide a solid basis for accurately calibrated computational studies of relativistic dissipative flows.

Through the Novy Grad and Vekhi: Vladimir Varshavsky on Aleksandr Solzhenitsyn

This article considers the participation of Vladimir Varshavsky, an emigre writer, in the discussion around Aleksandr Solzhenitsyn’s famous journalistic manifestos, i.e. Letters to the Soviet Leaders and From under the Rubble collection published in 1974 by Paris publishing house YMCA-Press. The article focuses on the considerable influence the ideology of the Novy Grad journal had on Varshavsky’s perception of Solzhenitsyn’s journalistic works. The discourse of Novy Grad helped Varshavsky occupy an independent position regarding the long-lasting harsh debate between Andrey Sakharov and Aleksandr Solzhenitsyn which took place in the 1970s. Varshavsky considered many of the issues of the argument through the prism of the Novy Grad method, i.e. deep synthesis (or convergence), and his participation in the discussion is interesting from the point of view of his attempt to uncover the origins of the antinomy and go beyond it. Varshavsky saw the reasons for the conflict in the traditional watershed of the Russian national idea, i.e. Westernism and Slavophilism. The prerevolutionary collection Vekhi (1909) played a special role of a link between the ideas of Solzheni­tsyn and later works of Varshavsky which were succeeded by many emigre authors of the Novy Grad journal and participants of From under the Rubble in the Soviet Union. This deep influence of the Vekhi tradition of self-reflection of the Russian intelligentsia played a considerable role in the approximation of Varshavsky’s views on the development of Bolshevism and Aleksandr Solzhenitsyn’s standpoint. Varshavsky’s last book The Genealogy of Bolshevism (1982) is characterised by a complex genesis combining his fundamental prewar experience at Novy Grad and response to the topical argument about the future of Russia between Sakharov and Solzhenitsyn.

FEMPAR: An Object-Oriented Parallel Finite Element Framework

FEMPAR is an open source object oriented Fortran200X scientific software library for the high-performance scalable simulation of complex multiphysics problems governed by partial differential equations at large scales, by exploiting state-of-the-art supercomputing resources. It is a highly modularized, flexible, and extensible library, that provides a set of modules that can be combined to carry out the different steps of the simulation pipeline. FEMPAR includes a rich set of algorithms for the discretization step, namely (arbitrary-order) grad, div, and curl-conforming finite element methods, discontinuous Galerkin methods, B-splines, and unfitted finite element techniques on cut cells, combined with h-adaptivity. The linear solver module relies on state-of-the-art bulk-asynchronous implementations of multilevel domain decomposition solvers for the different discretization alternatives and block-preconditioning techniques for multiphysics problems. FEMPAR is a framework that provides users with out-of-the-box state-of-the-art discretization techniques and highly scalable solvers for the simulation of complex applications, hiding the dramatic complexity of the underlying algorithms. But it is also a framework for researchers that want to experience with new algorithms and solvers, by providing a highly extensible framework. In this work, the first one in a series of articles about FEMPAR, we provide a detailed introduction to the software abstractions used in the discretization module and the related geometrical module. We also provide some ingredients about the assembly of linear systems arising from finite element discretizations, but the software design of complex scalable multilevel solvers is postponed to a subsequent work.

Kinetic approach to relativistic dissipation.

Despite a long record of intense effort, the basic mechanisms by which dissipation emerges from the microscopic dynamics of a relativistic fluid still elude complete understanding. In particular, several details must still be finalized in the pathway from kinetic theory to hydrodynamics mainly in the derivation of the values of the transport coefficients. In this paper, we approach the problem by matching data from lattice-kinetic simulations with analytical predictions. Our numerical results provide neat evidence in favor of the Chapman-Enskog [The Mathematical Theory of Non-Uniform Gases, 3rd ed. (Cambridge University Press, Cambridge, U.K., 1970)] procedure as suggested by recent theoretical analyses along with qualitative hints at the basic reasons why the Chapman-Enskog expansion might be better suited than Grad's method [Commun. Pure Appl. Math. 2, 331 (1949)0010-364010.1002/cpa.3160020403] to capture the emergence of dissipative effects in relativistic fluids.