Note on the single-shock solutions of the Korteweg-de Vries-Burgers equation

The well-known shock solutions of the Korteweg-de Vries-Burgers equation are revisited, together with their limitations in the context of plasma (astro)physical applications. Although available in the literature for a long time, it seems to have been forgotten in recent papers that such shocks are monotonic and unique, for a given plasma configuration, and cannot show oscillatory or bell-shaped features. This uniqueness is contrasted to solitary wave solutions of the two parent equations (Korteweg-de Vries and Burgers), which form a family of curves parameterized by the excess velocity over the linear phase speed.     

Basic thermodynamic parameters of a black hole resulting from a Yukawa type of correction to the metric

There has been a renewed interest in the recent years in the possibility of deviations from the predictions of Newton’s “inverse-square law” of universal gravitation. One of the reasons for renewing this interest lies in various theoretical attempts to construct a unified elementary particle theory, in which there is a natural prediction of new forces over macroscopic distances. Therefore the existence of such a force would only coexist with gravity, and in principle could only be detected as a deviation from the inverse square law, or in the “universality of free fall” experiments. New experimental techniques such that of Sagnac interferometry can help explore the range of the Yukawa correction λ≥10¹⁴ m where such forces might be present. It may be, that future space missions might be operating in this range which has been unexplored for very long time. In this paper we derive the basic thermodynamic parameters of such a Yukawa stationary spherically symmetric black hole. First, the expression for the event horizon of such a black hole is derived, with the help of which the temperature, entropy and heat capacity of this particular black hole are obtained. We have also obtained analytical expressions for the change of mass of such black hole, and also its corresponding evaporation time.     

Identifying wildland fire ignition factors through sensitivity analysis of a neural network

Artificial neural networks (ANNs) show a significant ability to discover patterns in data that are too obscure to go through standard statistical methods. Data of natural phenomena usually exhibit significantly unpredictable non-linearity, but the robust behavior of a neural network makes it perfectly adaptable to environmental models such as a wildland fire danger rating system. These systems have been adopted by many developed countries that have invested in wildland fire prevention, and thus civil protection agencies are able to identify areas with high probabilities of fire ignition and resort to necessary actions. Since one of the drawbacks of ANNs is the interpretation of the final model in terms of the importance of variables, this article presents the results of sensitivity analysis performed in a back-propagation neural network (BPN) to distinguish the influence of each variable in a fire ignition risk scheme developed for Lesvos Island in Greece. Four different methods were utilized to evaluate the three fire danger indices developed within the above scheme; three of the methods are based on network’s weights after the training procedure (i.e., the percentage of influence—PI, the weight product—WP, and the partial derivatives—PD methods), and one is based on the logistic regression (LR) model between BPN inputs and observed outputs. Results showed that the occurrence of rainfall, the 10-h fuel moisture content, and the month of the year parameter are the most significant variables of the Fire Weather, Fire Hazard, and Fire Risk Indices, respectively. Relative humidity, elevation, and day of the week have a small contribution to fire ignitions in the study area. The PD method showed the best performance in ranking variables’ importance, while performance of the rest of the methods was influenced by the number of input parameters and the magnitude of their importance. The results can be used by local forest managers and other decision makers dealing with wildland fires to take the appropriate preventive measures by emphasizing on the important factors of fire occurrence.     

Fluvial stacking due to plate collision and uplift during the Early Pleistocene in Cyprus

Southern Cyprus is situated within a mosaic terrane that has been fragmented between the northward drifting African and Arabian plates and the Eurasian plate. Enormous uplift of the earth mantle in the Tróodos Mountains is explained by two models. The subduction model explains subduction along the Cyprean arc to be the driving force for uplift whereas after the restraining bend model westward squeezing of Cyprus along strike-slip faulting is responsible for the enormous uplift at restraining bends. Since its emergence as an island in early Miocene times, landscape formation on Cyprus has been strongly controlled by this uplift. Until the Plio-Pleistocene, a strait belt separated the southern unroofed ophiolitic core region-the Tróodos Mountains-from the folded Kyrenia range to the north. This former sea basin, nowadays the Mesaoría Basin, is linked with the Tróodos Mountains by a dissected glacis with a thick cover of river deposits. The highest and oldest river deposits (Apalós Formation) were studied in the Vlokkariá hill southwest of Lefkosía. The 45.5 m thick Apalós Formation of Early Pleistocene age exhibits 24 sedimentary units (Fluviatile Series). Their magnetostratigraphical characters align with the Matuyama chron including the Olduvai and Jaramillo subchrons thus comprising about 1.15 Ma within the Early Pleistocene. This fluvial stack indicates a very flat and deeply lying river environment flowing from a slowly uplifting Tróodos hinterland. It happened during the end of Early Pleistocene when the enhanced Tróodos uplift started the dissection of the stacked river plain.     

Foundation–structure systems over a rupturing normal fault: Part II. Analysis of the Kocaeli case histories

Motivated by the observed (successful and unsuccessful) performance of numerous structures on top of, or immediately next to a normal fault that ruptured during the Kocaeli 1999 earthquake, this paper: (i) develops a two-step finite element methodology to study the propagation of a fault rupture through soil and its interplay with the foundation–structure system, denoted hereafter “Fault Rupture–Soil– Foundation–Structure Interaction” (FR–SFSI), (ii) provides validation of the developed methodology through successful Class “A” predictions of centrifuge model tests, and (iii) applies the centrifuge-validated methodology to study one-by-one the Kocaeli case histories of the first paper (Part I). It is shown that the presence of a structure on top of an outcropping fault may have a significant influence on the rupture path: with heavy structures founded on continuous and rigid foundations, the fault rupture diverts substantially and may avoid rupturing underneath the structure. The latter undergoes rigid body rotation, with its foundation sometimes loosing contact with the bearing soil, but in most cases retaining its structural integrity. In stark contrast, buildings on isolated footings and, perhaps surprisingly, piles exert a smaller diversion of the rupture which is thus likely to outcrop between the footings or pile caps; the latter may thus undergo devastating differential displacements. It is shown that structures in the vicinity of faults can be designed to survive significant dislocations. The “secret” of successful performance lies on the continuity, stiffness, and rigidity of the foundation.     

Some aspects of floor spectra of 1DOF nonlinear primary structures

In this paper the influence of the nonlinear behaviour of the primary structure on floor spectra is investigated by means of simple models. The general trends of floor spectra for different types of nonlinear behaviour of one degree of freedom (1DOF) primary structure are shown and we point out their common futures and their differences. A special attention is given to the cases of elastoplastic and nonlinear elastic behaviours and methods to determine an equivalent linear oscillator are proposed. The properties (frequency and damping) of this equivalent linear oscillator are quite different from the properties of equivalent linear oscillators commonly considered in practice. In particular, in the case of elastoplastic behaviour, there is no frequency shift and damping is smaller than assumed by other methods commonly used. In the case of nonlinear elastic behaviour, the concept of an equivalent frequency which is a random variable is used. Finally, a design floor spectrum of primary structures, exhibiting energy dissipating nonlinear behaviour is proposed. Copyright © 2006 John Wiley & Sons, Ltd.     

Quantifying geomorphic evolution of earthquake-triggered landslides and their relation to active normal faults. An example from the Gulf of Corinth, Greece

Photogrammetric analysis of aerial photographs is used to investigate morphological changes in two large landslides located adjacent to the active Marathias normal fault along the Gulf of Corinth, Greece. This E–W trending fault intersects at almost right angles a series of west-verging and east-dipping thrust faults, and has a clear geomorphic expression. The fault's structural signature, such as the trace length, displacement, segmentation, and scarp freshness resembles other normal faults within the Gulf of Corinth. Along this fault we mapped a series of landslides that are mainly concentrated at the near tip areas. Two of them are hosted in the damage zone formed by the intersecting normal and reverse faults. The Marathias and Sergoula landslides show a significant geomorphic evolution on aerial photographs from 1945 to 1991.

Evolution of landslides in the study area appears to be correlated with two earthquake clusters that drive mass wasting in the order of 10⁶ m³, significant drainage adjustment, and triggering of post-landslide river incision. We infer the following process sequence for these presumably earthquake-triggered landslides in the region: eroded material in Marathias landslide and reactivation of movement within the main body of the Sergoula landslide were observed in 1969 aerial photographs. Both landslides are deep-seated rotational rockslides. Obstruction or abandonment of channels due to the landslides establishes river incision and a dramatic increase of the rate of fan-delta progradation in the order of 1 m/yr. These large landslides are related to strong (M > 6.5) earthquakes concentrated along faults, and their reactivation period is almost a century, based on seismological or paleoseismological analyses.     

Remediation of Sea Water Intrusion: A Case Study

Sea water intrusion and remediation in the Upper Floridan Aquifer in South Carolina is simulated using the finite-element model SUTRA developed by the U.S. Geological Survey. A sensitivity analysis of the effect of the hydrogeologic parameters on the sea water recharge and seepage velocities is performed. An increase in confining unit and/or in aquifer conductivity results in an increase of the sea water recharge. An increase in aquifer porosity results in a decrease of the sea water recharge. Among the three remedial techniques simulated—reduced aquifer withdrawals, an injection well, and a combined injection and capture well—the reduced aquifer withdrawals and injection well are the best methods for preventing sea water intrusion.     

Dynamic behaviour of rocking two-block assemblies

The dynamic behaviour of systems consisting of two blocks, one placed on the top of the other, and free to rock without sliding, is examined in this analysis. The equations of motion for each ‘mode’ of vibration are derived and criteria for the initiation of rocking and the transition between modes are given. During vibration, the system continuously changes from one mode to another and this makes the response non-linear. This transition may be accompanied by impact, in which case dissipation of energy occurs, the amount of which depends on the relative velocities and the dimensions of the blocks. Also, redistribution of the kinetic energy of the system in the blocks happens. In most cases, the fractional contribution from the upper block to the system energy increases, which results in a larger and longer response of the top block, compared to the vibration of the lower one.