We propose a one-dimensional viscoelastic seismic-wave model driven by the Atangana-BaleanuCaputo fractional derivative with a non-singular Mittag-Leffler kernel. A finite-difference discretization in space and an Adams-Bashforth-Moulton predictor-corrector scheme in time are used to compute solutions for several fractional orders. Simulations indicate that fractional memory alters both attenuation and dispersion, leading to non-exponential energy decay compared with the classical integer-order case.
Here, I construct an elegant frictional brachistochrone for a mass point motion of a granular material with the Coulomb frictional energy dissipation that inherently includes the evolving path curvature. The simple model reveals several striking mechanical phenomena. It is applicable to any frictional particle. With increasing friction, the particle path becomes less and less curved until a straight brachistochrone is attained in the limit of sufficiently high friction. The existence of the straight-brachistochrone is phenomenal. Some potential industrial applications of the frictional brachistochrone are considered.
We consider solenoidal space-periodic space-analytic solutions to the equations of magnetohydrodynamics. An elementary bound shows that due to the special structure of the nonlinear terms in the equations for modified solutions, effectively they lack a half of the spatial gradient, which appears to be a novel mechanism for depletion of nonlinearity. We present a two-phase iterative procedure yielding an expanded bound for the guaranteed time of the space analyticity of the hydrodynamic solutions. Each iteration involves two regimes: In phase 1, the enstrophy of the modified solution and the bound for the radius of the analyticity of the original solution simultaneously increase (the bound is proportional to the elapsed time since the beginning of phase 1). In phase 2, the enstrophy and bound simultaneously decrease. It is straightforward to generalize this construction for the equations of magnetohydrodynamics.
Variation in the balance of forces that drive and resist tectonic plate motions allows small terrestrial planet to cooler slower than larger ones. Given that interior cooling affects surface environment, through volcanic/geologic activity, this indicates that small planets should not be down-weighted in the search for life beyond Earth.
A simplified climate model based on maximum entropy production, described by a variational principle, is revisited and an analytical solution to its Euler-Lagrange equation is found. Mindful of controversy about maximum or minimum entropy production in open thermodynamical systems, we show that the solution extremizing the action integral corresponds to a maximum.
The linear transport theory is developed to describe the time dependence of the number density of tracer particles in porous media. The advection is taken into account. The transport equation is numerically solved by the analytical discrete ordinates method. For the inverse Laplace transform, the double-exponential formula is employed.
Panagiotis Tziachris, Eirini Metaxa, Frantzis Papadopoulos
et al.
In this study, different interpolation techniques are presented, assessed, and compared for the estimation of soil iron (Fe) contents in locations where observations were not available. Initially, 400 soil samples from the Kozani area, which is near Polifitou Lake in northern Greece, were randomly collected from 2013 to 2015 and were analysed in the laboratory to determine the soil Fe concentrations and pH. The soil Fe concentrations were examined for spatial autocorrelation, and semivariograms were used to determine whether pH and Fe exhibited spatial cross correlation. Three interpolation methods, including Ordinary Kriging, Universal Kriging, and Co-Kriging, were applied, and their results were compared with the use of two different cross-validation methods. In the current study, there was evidence of spatial cross correlation of soil Fe and pH for each year, which was subsequently used to improve the interpolation results in locations where there were no measurements. In nearly all cases, Co-Kriging, which takes advantage of the covariance between the two regionalized variables (Fe and pH), outperformed the other interpolation techniques each year.
I demonstrate that the conventional seismic full-waveform inversion algorithm can be constructed as a recurrent neural network and so implemented using deep learning software such as TensorFlow. Applying another deep learning concept, the Adam optimizer with minibatches of data, produces quicker convergence toward the true wave speed model on a 2D dataset than Stochastic Gradient Descent and than the L-BFGS-B optimizer with the cost function and gradient computed using the entire training dataset. I also show that the cost function gradient calculation using reverse-mode automatic differentiation is the same as that used in the adjoint state method.
Herein I respond to the criticism and to the complains by Benestad (Pattern Recogn. Phys. 1, 91-92, 2013, http://dx.doi.org/10.5194/prp-1-91-2013) of Scafetta (Pattern Recogn. Phys. 1, 37-57, 2013, http://dx.doi.org/10.5194/prp-1-37-2013) that I found misleading and not tenable. More significantly, Benestad did not find any physical nor mathematical error in Scafetta's work. Thus, Scafetta scientific results remain fully confirmed.
The problem of hydraulic fracture for the PKN model is considered within the framework presented recently by Linkov (2011). The modified formulation is further enhanced by employing an improved regularized boundary condition near the crack tip. This increases solution accuracy especially for singular leak-off regimes. A new dependent variable having clear physical sense is introduced. A comprehensive analysis of numerical algorithms based on various dependent variables is provided. Comparison with know numerical results has been given.
The ferromagnetic material in a shipwreck on the seabed causes a modification to the earth's magnetic field which can be measured at the surface. Proton magnetometer measurements at the surface are used to locate wrecks. Here I discuss how to interpret such data to explore the shape and orientation of the shipwreck on the seabed. I give details of how to model shipwrecks and deduce the magnetic signal that results. I also discuss how to analyse data in a more general way. As examples, I present and analyse data on the shipwrecks of YSTROOM and BOUBOULINA (ex COLONEL LAMB).
It is shown that the periodic alteration of night and day provides a chaotic dissipation mechanism for the North Atlantic (NAO) and Southern (SOI) climate oscillations. The wavelet regression detrended daily NAO index for last 60 years and daily SOI for last 20 years as well as an analytical continuation in the complex time domain were used for this purpose.
In this paper we discuss the sign of helicity in the $α$-$Ω$ dynamo and propose a wave-$Ω$ model in which the $α$ effect in the geodynamo is induced by helical wave but not helical flow as in the solar dynamo. We then tentatively interpret the mechanisms of the Earth's magnetic westward drift, tilt angle, and dipole reversals.
We show here that the network averaged teleseismic P-wave spectra for Indian explosions of May 11, 1998, given by Barker et al, do not have an unambiguous interpretation. Barker et al had earlier demonstrated these were similar to the Shagan River testing site of former Soviet Union. We prove here that these are equally consistent with RUBIS (57 kt) and PILEDRIVER (62kt) explosions in French Hogger and US Nevada testing sites respectively.
This note is intended to highlight the important role of black carbon produced from biomass burning in the global carbon cycle, and encourage further research in this area. Consideration of the fundamental physical chemistry of cellulose thermal decomposition suggests that suppression of biomass burning or biasing burning practices to produce soot-free flames must inevitably transfer more carbon to the atmosphere. A simple order-of-magnitude quantitative analysis indicates that black carbon may be a significant carbon reservoir that persists over geological time scales.
Using dynamic paraboloid model of Earth's magnetosphere, a large set of particles' trajectory computations was performed. Based on its result, the numerical algorithm for calculating effective cutoff rigidity dependence on empiric parameters has been developed for further use in magnetospheric transmission calculations.
A simple method for taking into account the multiple Coulomb scattering in construction of a separatrix (the line separating the regions of runaway and decelerating electrons in an electric field) is described. The desired line is obtained by solving a simple transcendental equation.