Application of Omori’s Decay Law to the 2001 Bhuj Aftershock Sequence for Kachchh Region of Western India

In the present study, the temporal behavior of 2001 Bhuj aftershock sequence in Kachchh region of western peninsular India is studied by the modified Omori law. The Omori law parameters p, c and K are determined with the standard errors by the maximum likelihood estimates using ZMAP algorithm in MatLab environment. The entire aftershock sequence is analyzed by diving it into three separate series with respect to time to weigh up the bigger earthquake of magnitude M 5.7 occurring on March 7, 2006 at Gedi fault. This study helps to understand the cumulative effect of the aftershocks generated by this bigger earthquake of the mainshock sequence. The results of this analysis are discussed with other studies of the different earthquake sequence for the different parts of the world and suggest that all the three series of Bhuj aftershock sequence follow the Omori relation. Values of parameter p vary significantly from series 1 to series 3, i.e., p-value varies significantly with time. Similarly, other two Omori law parameters K and c are also found to change significantly with time. These parameters are useful to describe temporal behavior of aftershocks and to forecast aftershock activity in time domain. Aftershock decay rate provides insight into stress release processes after the mainshock, thus helping to understand the heterogeneity of the fault zone properties and evaluate time-dependent seismic hazard analysis over the region.

Large-time Behavior of Solutions for Parabolic Conservation Laws with Large Initial Data

In this paper,we study the large-time behavior of periodic solutions for parabolic conservation laws.There is no smallness assumption on the initial data.We firstly get the local existence of the solution by the iterative scheme,then we get the exponential decay estimates for the solution by energy method and maximum principle,and obtain the global solution in the same time.

Pointwise Estimates on Travelling Wave Solution of the Scalar Viscous Conservation Laws

This paper research on the pointwise behavior of perturbations from a viscous shock solution to a scalar viscous conservation law by introducing an approximate Green’s function. The authors obtain not only the pointwise decay of the perturbation and but also the high derivative of it. Stability in anyL(p≥1) norm is a direct consequence.

Time Decay Rate of Solutions Toward the Viscous Shock Waves under Periodic Perturbations for the Scalar Conservation Law with Nonlinear Viscosity

In this paper,it is proved that the weak solution to the Cauchy problem for the scalar viscous conservation law,with nonlinear viscosity,different far field states and periodic perturbations,not only exists globally in time,but also converges towards the viscous shock wave of the corresponding Riemann problem as time goes to infinity.Furthermore,the decay rate is shown.The proof is given by a technical energy method.

On the Approximation of Fractal-Fractional Differential Equations Using Numerical Inverse Laplace Transform Methods

Laplace transform is one of the powerful tools for solving differential equations in engineering and other science subjects.Using the Laplace transform for solving differential equations,however,sometimes leads to solutions in the Laplace domain that are not readily invertible to the real domain by analyticalmeans.Thus,we need numerical inversionmethods to convert the obtained solution fromLaplace domain to a real domain.In this paper,we propose a numerical scheme based on Laplace transform and numerical inverse Laplace transform for the approximate solution of fractal-fractional differential equations with orderα,β.Our proposed numerical scheme is based on three main steps.First,we convert the given fractal-fractional differential equation to fractional-differential equation in Riemann-Liouville sense,and then into Caputo sense.Secondly,we transformthe fractional differential equation in Caputo sense to an equivalent equation in Laplace space.Then the solution of the transformed equation is obtained in Laplace domain.Finally,the solution is converted into the real domain using numerical inversion of Laplace transform.Three inversion methods are evaluated in this paper,and their convergence is also discussed.Three test problems are used to validate the inversion methods.We demonstrate our results with the help of tables and figures.The obtained results show that Euler’s and Talbot’s methods performed better than Stehfest’s method.

General Decay for a Thermoelastic Problem of a Microbeam with Gurtin-Pipkin Thermal Law

In this paper,we study the well-posedness and the asymptotic stability of a one-dimensional thermoelastic microbeam system,where the heat conduction is given by Gurtin-Pipkin thermal law.We first establish the well-posedness of the system by using the semigroup arguments and Lumer-Phillips theorem.We then obtain an explicit and general formula for the energy decay rates through perturbed energy method and some properties of the convex functions.

GROUND STATES OF A NONLINEAR ELLIPTICSYSTEM IN R^N

We investigate existence of ground states of nonlinear elliptic systems in R-N and establish decaying laws for solutions of the systems at infinity.

New Geiger-Nuttall law for cluster radioactivity half-lives

In this study,derived from Balasubramaniam’s formula[Phys.Rev.C 70,017301(2004)]and further considering the effect of the parent nucleus mass,blocking effect,and effect of reduced mass on cluster radioactivity half-lives,we propose a new Geiger-Nuttall law that is model-independent to systematically evaluate the halflives of this process for 16 even-even nuclei and 10 odd-A nuclei.For comparison,a single universal curve for cluster radioactivity andαdecay proposed by Poenaru[Phys.Rev.C 83,014601(2011)],a scaling law proposed by Horoi[J.Phys.G:Nucl.Part.Phys.30,945(2004)],an extension of the Viola-Seaborg formula fromαdecay to cluster radioactivity proposed by Ren et al.[Phys.Rev.C 70,034304(2004)],a new semi-empirical formula for exotic cluster decay proposed by Balasubramaniam et al.[Phys.Rev.C 70,017301(2004)],and a unified formula for the half-lives ofαdecay and cluster radioactivity proposed by Ni et al.[Phys.Rev.C 78,044310(2008)]are also used.The calculated results of our new Geiger-Nuttall law are in good agreement with the experimental half-lives,with the least rms being 0.606,and are better than the compared values.Moreover,we extend this formula to predict the cluster radioactivity half-lives of 51 nuclei whose decay energies are energetically allowed or observed but not yet quantified in NUBASE2020.

New look at Geiger-Nuttall law and α clustering of heavy nuclei

The Geiger-Nuttall(GN)law ofαdecay is commonly explained in terms of the quantum tunneling phenomenon.In this study,we show that such an explanation is actually not enough regarding theαparticle clustering.Such a conclusion is drawn after exploring the involved coefficients of the GN law based on the conventional description ofαdecay,namely the formation of anαcluster and its subsequent penetration.The specific roles of the two former processes,in the GN law,manifest themselves via the systematical analysis of the calculated and experimentalαdecay half-lives versus the decay energies across the Z=82 and N=126 shell closures.Theα-cluster preformation probability is then found to behave in a GN-like pattern.This previously ignored point is explicitly demonstrated as the product of an interplay between the mean-field and pairing effect,which in turn reveals the structural influence on the formation of theαcluster in a simple and clear manner.In addition to providing an effective method to evaluate the amount of surfaceαclustering in heavy nuclei,the present conjecture supports other theoretical treatments of theαpreformation probability.

Revisiting the death of geography in the era of Big Data:the friction of distance in cyberspace and real space

Many scholars have argued that the importance of geographic proximity in human interactions has been diminished by the use of the Internet,while others disagree with this argument.Studies have noted the distance decay effect in both cyberspace and real space,showing that interactions occur with an inverse relationship between the number of interactions and the distance between the locations of the interactors.However,these studies rarely provide strong evidence to show the influence of distance on interactions in cyberspace,nor do they quantify the differences in the amount of friction of distance between cyberspace and real space.To fill this gap,this study used massive amounts of social media data(Twitter)to compare the influence of distance decay on human interactions between cyberspace and real space in a quantitative manner.To estimate the distance decay effect in both cyberspace and real space,the distance decay function of interactions in each space was modeled.Estimating the distance decay in cyberspace in this study can help predict the degree of information flow across space through social media.Measuring how far ideas can be diffused through social media is useful for users of location-based services,policy advocates,public health officials,and political campaigners.

Oscillating-grid turbulence at large strokes: Revisiting the equation of Hopfinger and Toly

A quasi-isotropic, quasi-homogeneous turbulence generated by an oscillating-grid, spatially decays according to power law of u ∝ Z-nM , where u is the root mean square （rms） horizontal velocity, Z is the vertical distance from the grid and nu = 1. However, the findings of Nokes and Yi indicate that as the stroke of oscillation increases, the power law n u= 1 and does not follow the established decay law equation of Hopfinger. This paper investigates the characteristics of the turbulence that are generated using larger strokes S/M = 1.6 and 2 and compares with that obtained using a S/M = 0.8, which is the stroke used when the equation was developed. Measurements of the grid-generated turbulence in a water tank were taken using particle image velocimetry （PIV）. The results showed that the homogeneity occurred at distance beyond 2.5 mesh spacings away from the grid midplane, independent of the stroke and the frequency of oscillation. Within this region, the turbulent kinetic energy distribution was quasi-homogeneous, and the secondary mean flow is negligible. The statistical characteristics of the measured turbulence confirmed that although nu decreases as stroke increases, the grid-turbulence generated at S/M = 1.6 and 2 obeys the universal decay law.