Value Of Relaxation Parameter Research Articles

Holographic complexity for black branes with momentum relaxation

We employ the "complexity equals action" conjecture to investigate the action growth rate for the charged and neutral AdS black branes of a holographic toy model consisting of Einstein-Maxwell theory in $d + 1$-dimensional bulk spacetime with $d - 1$ massless scalar fields which is called Einstein-Maxwell-Axion (EMA) theory. From the holographic point of view, the scalar fields source a spatially dependent field theory with momentum relaxation on the boundary, which is dual to the homogeneous and isotropic black branes. We find that the growth rate of the holographic complexity within the Wheeler-DeWitt (WDW) patch saturates the corresponding Lloyd's bound at the late time limit. Especially for the neutral AdS black branes, it will be shown that the complexity growth rate at late time vanishes for a particular value of relaxation parameter $\beta_{max}$ where the temperature of the black hole is minimal. Then, we investigate the transport properties of the holographic dual theory in the minimum temperature. A non-linear contribution of the axion field kinetic term in the context of k-essence model in the four-dimensional spacetime is considered as well. We also study the time evolution of the holographic complexity for the dyonic AdS black branes in this model.

RETRACTED: Unsteady flow of three-dimensional Maxwell nanofluid with variables properties over a stretching surface

The present article focuses on the time-dependent three-dimensional Maxwell fluid flow with temperature-dependent fluid properties along the stretching sheet. The heat and mass transfer analysis are presented in the occurrence of activation energy, convective boundary condition, and non-uniform heat source/sink effect. The flow model is converted into a system of coupled ODEs with the help of a similarity transformation. The numerical built-in technique Bvp4c is employed to solve the obtained coupled ODEs. The graphical outcomes are obtained against the various parameters and discussed. It is seen from the graphs that fluid velocity diminishes for stronger values of relaxation parameter and shows an opposite trend for the variable viscosity parameter. Moreover, it is noted from the tabulated data that the heat and mass transfer rate reduces for the stronger values of unsteadiness and the variable viscosity parameter.

Theoretical treatment of radiative Oldroyd-B nanofluid with microorganism pass an exponentially stretching sheet

A transient two-dimensional radiative Oldroyd-B nanofluid flow is examined in this exploration. The flow field is subject to an exponentially stretchable permeable surface which is convectively heated. In the fluid regime microorganisms have been added in-order to improve the stability of the nanofluid. Additionally, the heat and mass transportation are influenced by heat generation and chemical reaction effects. The mathematical model is reduced incorporating self-similar transformations. The resulting non-linear equations system are solved by a numerical technique using Maplesoft. The outcomes presented in graphs and tables against various parameters are discussed in detail. A comparison of our results with previous published investigations shows a good agreement. It is depicted that for higher values of relaxation parameter the fluid velocity minimizes whereas, for retardation parameter its behavior increases. Further, higher values of relaxation parameter correspond to maximum heat and mass transfer rate, while it gives lower values against retardation parameter.

Evaluation of Polyethylene/Organoclay Nanocomposites by Low-field Nuclear Relaxation

Two polyethylene (PE) samples (named BF and ES) were blended with 5% organoclay by melt processing at different shear rates. X-ray diffraction (XRD) showed that the organoclay was incorporated into the PE matrices. From the results it was determined that the level of intercalation was very similar for both systems. The knowledge of molecular dynamics of PE nanocomposites is very important since it depends on the clay dispersion. Thus, the objective of this work was to employ a new technique to understand changes in the molecular mobility for these systems. The samples were characterized by proton nuclear spin-lattice relaxation time (T1H), which is measured in a low-field NMR spectrometer. The influence of the samples' preparation was evaluated through the relaxation data. For polyethylene resins, two values of relaxation parameter were found and they were attributed to mobile region (low value) and rigid region (high value). These values change after nanocomposite formation, confirming the changes in the resin matrix after organoclay was incorporated.

Determination of the optimal value of relaxation parameter in symmetric SOR method for rectangular coefficient matrices

In this paper, we obtain the optimal value of relaxation parameter in symmetric SOR (SSOR) method. By SSOR method we find the least square solution of minimal norm to the linear system Ax = b where A is an m by n matrix.

PERFORMANCE EVALUATION OF ITERATIVE TOMOGRAPHIC ALGORITHMS APPLIED TO RECONSTRUCTION OF A THREE-DIMENSIONAL TEMPERATURE FIELD

Iterative tomographic algorithms have been applied to the reconstruction of a three-dimensional temperature field (from its projections) for Rayleigh-Renard-type natural-convection problems. Nine distinct algorithms with varying numbers of projections and projection angles have been considered. The three-dimensional temperature field is sliced into a set of two-dimensional planes and reconstruction algorithms are applied to each individual plane. Projection of the temperature field is interpreted as a path integral along a line in the appropriate direction. The integrals are evaluated numerically and are assumed to represent exact data. Errors in reconstruction are defined with field data as reference and are used to compare one algorithm with respect to another. The algorithms used in this work can be broadly classified into three groups: additive algebraic reconstruction technique (ART), multiplicative algebraic reconstruction technique (MART), and maximization reconstruction technique (MRT). Additive ART shows a systematic convergence with respect to number of the projections and the value of the relaxation parameter. MART algorithms produce less error at convergence compared to additive ARTs but converge only at low values of relaxation parameter. In the present work the MRT algorithm shows intermediate performance when compared to ART and MART. Increasing noise level in projection data increases the error in the reconstructed fidd. The maximum and root-mean-square errors are highest in ART and lowest in MART for a given projection data. Increasing noise levels in projection data decrease the convergence rates. For all algorithms, a 20% noise level is seen as an upper limit beyond which the reconstructed field is barely recognisable.