Performance of similarity explicit group iteration for solving 2D unsteady convection-diffusion equation

In this paper, a similarity finite difference (SFD) solution is addressed for thetwo-dimensional (2D) parabolic partial differential equation (PDE), specifically on the unsteady convection-diffusion problem. Structuring the similarity transformation using wave variables, we reduce the parabolic PDE into elliptic PDE. The numerical solution of the corresponding similarity equation is obtained using a second-order central SFD discretization schemeto get the second-order SFD approximation equation. We propose a four-point similarity explicit group (4-point SEG) iterative methodasa numericalsolution of the large-scale and sparse linear systems derived from SFD discretization of 2D unsteady convection-diffusion equation (CDE). To showthe 4-point SEG iteration efficiency, two iterative methods, such as Jacobiand Gauss-Seidel (GS) iterations, are also considered. The numerical experiments are carried out using three different problems to illustrate our proposed iterative method's performance. Finally, the numerical results showed that our proposed iterative method is more efficient than the Jacobiand GS iterations in terms of iteration number and execution time.

Wave-Like Exact Models with Symmetry of Spatial Homogeneity in the Quadratic Theory of Gravity with a Scalar Field

Exact solutions are obtained in the quadratic theory of gravity with a scalar field for wave-like models of space–time with spatial homogeneity symmetry and allowing the integration of the equations of motion of test particles in the Hamilton–Jacobi formalism by the method of separation of variables with separation of wave variables (Shapovalov spaces of type II). The form of the scalar field and the scalar field functions included in the Lagrangian of the theory is found. The obtained exact solutions can describe the primary gravitational wave disturbances in the Universe (primary gravitational waves).

Operational Wave Forecast Selection in the Atlantic Ocean Using Random Forests

The existence of multiple wave forecasts leads to the question of which one should be used in practical ocean engineering applications. Ensemble forecasts have emerged as an important complement to deterministic forecasts, with better performances at mid-to-long ranges; however, they add another option to the variety of wave predictions that are available nowadays. This study developed random forest (RF) postprocessing models to identify the best wave forecast between two National Centers for Environmental Protection (NCEP) products (deterministic and ensemble). The supervised learning classifier was trained using National Data Buoy Center (NDBC) buoy data and the RF model accuracies were analyzed as a function of the forecast time. A careful feature selection was performed by evaluating the impact of the wind and wave variables (inputs) on the RF accuracy. The results showed that the RF models were able to select the best forecast only in the very short range using input information regarding the significant wave height, wave direction and period, and ensemble spread. At forecast day 5 and beyond, the RF models could not determine the best wave forecast with high accuracy; the feature space presented no clear pattern to allow for successful classification. The challenges and limitations of such RF predictions for longer forecast ranges are discussed in order to support future studies in this area.

Multi-complexiton solutions of the (2+1)-dimensional asymmetrical Nizhnik-Novikov-Veselov equation

In this paper, the (2+1)-dimensional asymmetrical Nizhnik-Novikov-Veselov equation (ANNV) is investigated to acquire the complexiton solutions by the Hirota direct method. It is essential to transform the equation in to Hirota bilinear form and to build N-compilexiton solutions by pairs of conjugate wave variables.

Exact Traveling Wave Solutions of One-Dimensional Parabolic-Parabolic Models of Chemotaxis

In this chapter we consider several different parabolic-parabolic systems of chemotaxis which depend on time and one space coordinate. For these systems we obtain the exact analytical solutions in terms of traveling wave variables. Not all of these solutions are acceptable for biological interpretation, but there are solutions that require detailed analysis. We find this interesting, since chemotaxis is present in the continuous mathematical models of cancer growth and invasion (Anderson, Chaplain, Lolas, et al.) which are described by the systems of reaction–diffusion-taxis partial differential equations, and the obtaining of exact solutions to these systems seems to be a very interesting task, and a more detailed analysis is possible in a future study.

Resonant absorption: Transformation of compressive motions into vortical motions

This paper investigates the changes in spatial properties when magnetohydrodynamic (MHD) waves undergo resonant damping in the Alfvén continuum. The analysis is carried out for a 1D cylindrical pressure-less plasma with a straight magnetic field. The effect of the damping on the spatial wave variables is determined by using complex frequencies that arise as a result of the resonant damping. Compression and vorticity are used to characterise the spatial evolution of the MHD wave. The most striking result is the huge spatial variation in the vorticity component parallel to the magnetic field. Parallel vorticity vanishes in the uniform part of the equilibrium. However, when the MHD wave moves into the non-uniform part, parallel vorticity explodes to values that are orders of magnitude higher than those attained by the transverse components in planes normal to the straight magnetic field. In the non-uniform part of the equilibrium plasma, the MHD wave is controlled by parallel vorticity and resembles an Alfvén wave, with the unfamiliar property that it has pressure variations even in the linear regime.

The Association of Radial Artery Pulse Wave Variables with the Pulse Wave Velocity and Echocardiographic Parameters in Hypertension

This study aims at exploring the cardiovascular pathophysiological mechanism of TCM (traditional Chinese medicine) pulse by detecting the correlation between radial artery pulse wave variables and pulse wave velocity/echocardiographic parameters. Two hundred Chinese subjects were enrolled in this study, which were grouped into health control group, hypertension group, and hypertensive heart disease group. Physical data obtained in this study contained TCM pulse images at “Guan” position of the left hand, pulse wave velocity, and echocardiographic parameters. Linear and stepwise regression analysis was performed to assess the association of radial artery pulse wave variables with pulse wave velocity and echocardiographic parameters in the total population and in each different group. After adjusting for related confounding factors, decrease of t1, t5 and increase of h1, h3/h1 were statistically associated with arterial stiffness in the total population (P<0.05). Moreover, the correlation study in each group showed that the decrease of both t3 and h5 was also related to arterial stiffness (P<0.05). In terms of echocardiographic parameters, the height of dicrotic wave indicated by h5 was the most relevant pulse wave variable. For the health control, h5 was negatively associated with interventricular septal thickness (VST) and left ventricular posterior wall thickness (PWT) (P<0.05), while for the hypertension population and those with target-organ damage to heart, increase of h5 might be associated with decrease of ejection fraction (EF) and increase of all the remaining echocardiographic parameters especially for left ventricular end-systolic diameter (LVDs) and Left ventricular end-diastolic diameter (LVDd) (P<0.05). In conclusion, we found radial artery pulse wave variables were in association with the arterial stiffness and echocardiographic changes in hypertension, which would provide an experimental basis for cardiovascular pathophysiological mechanism of radial artery pulse wave variables.