Logarithmic Decay Function Research Articles

Experimental investigation and strength model of rough ice-filled joints under tensile and shear loading

Warming softening of ice-filled joints has caused many rockfall disasters in cold regions. A series tensile and shear strength tests were conducted to investigate the thawing softening mechanism of ice-filled joints by considering the effect of the joint opening, temperature and roughness. The joint opening has little influence on the tensile strength of ice-filled joints, but the temperature is a remarkable influencing factor. When the temperature increases from −15 °C to −0.5 °C, the average tensile strength of ice-filled joint reduces from 0.64 MPa to 0.22 MPa, which displays a constant logarithmic decay function against the freezing temperature and it is similar to the change rule of pure ice. The shear strength of the ice-filled joint decreases with increasing the infill thickness, and tends to be the shear strength of pure ice beyond the critical infilling thickness. In addition, all the tensile failures are inside the joint ice, however, the shear failure is mainly caused by the debonding of ice-rock interface when the temperature increases to −0.5 °C. It implies that the tensile bonding strength of ice-rock interface also is larger than that of the solid ice itself even at a high freezing temperature. Based on the experimental results, a new shear strength model of the ice-filled joint is proposed for Barton's joint profiles by considering the effect of temperature and infill thickness. It has been validated that this model is accurate to predict the shear strength of ice-filled joint, which may be used to estimate the stability of freezing joint rock slope in cold regions.

A dynamic Bayesian-based comprehensive trust evaluation model for dispersed computing environment

Dispersed computing is a new resource-centric computing paradigm. Due to its high degree of openness and decentralization, it is vulnerable to attacks, and security issues have become an important challenge hindering its development. The trust evaluation technology is of great significance to the reliable operation and security assurance of dispersed computing networks. In this paper, a dynamic Bayesian-based comprehensive trust evaluation model is proposed for dispersed computing environment. Specifically, in the calculation of direct trust, a logarithmic decay function and a sliding window are introduced to improve the timeliness. In the calculation of indirect trust, a random screening method based on sine function is designed, which excludes malicious nodes providing false reports and multiple malicious nodes colluding attacks. Finally, the comprehensive trust value is dynamically updated based on historical interactions, current interactions and momentary changes. Simulation experiments are introduced to verify the performance of the model. Compared with existing model, the proposed trust evaluation model performs better in terms of the detection rate of malicious nodes, the interaction success rate, and the computational cost.

Long-term temperature evolution of neutron stars undergoing episodic accretion outbursts

Context. Transient neutron star low-mass X-ray binaries undergo episodes of accretion, alternated with quiescent periods. During an accretion outburst, the neutron star heats up due to exothermic accretion-induced processes taking place in the crust. Besides the long-known deep crustal heating of nuclear origin, a likely non-nuclear source of heat, dubbed “shallow heating”, is present at lower densities. Most of the accretion-induced heat slowly diffuses into the core on a timescale of years. Over many outburst cycles, a state of equilibrium is reached when the core temperature is high enough that the heating and cooling (photon and neutrino emission) processes are in balance.Aims. We investigate how stellar characteristics and outburst properties affect the long-term temperature evolution of a transiently accreting neutron star. For the first time the effects of crustal properties are considered, particularly that of shallow heating.Methods. Using our codeNSCool, we tracked the thermal evolution of a neutron star undergoing outbursts over a period of 105yr. The outburst sequence is based on the regular outbursts observed from the neutron star transient Aql X-1. For each model we calculated the timescale over which equilibrium was reached and we present these timescales along with the temperature and luminosity parameters of the equilibrium state.Results. We performed several simulations with scaled outburst accretion rates, to vary the amount of heating over the outburst cycles. The results of these models show that the equilibrium core temperature follows a logarithmic decay function with the equilibrium timescale. Secondly, we find that shallow heating significantly contributes to the equilibrium state. Increasing its strength raises the equilibrium core temperature. We find that if deep crustal heating is replaced by shallow heating alone, the core would still heat up, reaching only a 2% lower equilibrium core temperature. Deep crustal heating may therefore not be vital to the heating of the core. Additionally, shallow heating can increase the quiescent luminosity to values higher than previously expected. The thermal conductivity in the envelope and crust, including the potentially low-conductivity pasta layer at the bottom of the crust, is unable to significantly alter the long-term internal temperature evolution. Stellar compactness and nucleon pairing in the core change the specific heat and the total neutrino emission rate as a function of temperature, with the consequences for the properties of the equilibrium state depending on the exact details of the assumed pairing models. The presence of direct Urca emission leads to the lowest equilibrium core temperature and the shortest equilibrium timescale.

Coseismic and Early Postseismic Deformation of the 5 January 2013 Mw 7.5 Craig Earthquake from Static and Kinematic GPS Solutions

Static (low‐rate, 30 s) and kinematic (high‐rate, 1 s) Global Positioning System solutions are employed to investigate the near‐field coseismic and early postseismic deformation associated with the 5 January 2013 Craig M w 7.5 earthquake. Based on the static solutions, the coseismic slip distribution has an average slip of ∼6 m, a geodetic moment M of 1.5×1020 N·m, and a magnitude M w of 7.4. A comparison of the static and kinematic results indicates that early (first 4 days) postseismic deformation was small compared to the coseismic deformation. The postseismic transient can be characterized by a logarithmic decay function with an average decay time constant of about 56 days. Substantial postseismic deformation is observed over the first ∼1.6 yrs of the earthquake and can be explained by afterslip on an adjacent segment of the fault to the southeast of the main coseismic rupture. Additional study will be needed to confirm whether afterslip is indeed the dominant mechanism causing postseismic motions or if another mechanism is also active. Online Material: Figures showing high‐rate Global Positioning System time series and model fits for selected sites.

Modelling post-seismic displacements in Thai geodetic network due to the Sumatra-Andaman and Nias earthquakes using GPS observations

It is evident that the 2004 Sumatra-Andaman, 2005 Nias and 2007 Bengkulu earthquakes caused significantly large co-seismic and post-seismic displacements all over the South-East Asian region. The Thai geodetic network has been severely affected by the 2004 and 2005 earthquakes. Largest post-seismic horizontal displacements were observed in the southern part of Thailand, while moderate and small displacements were seen in the central and northern parts of Thailand. This paper will analyse the GPS observations obtained by the Royal Thai Survey Department GPS campaigns up to the end of 2009. The post-seismic displacements have been shown to follow a main direction which is towards the rupture area. A simple filtering technique is proposed to remove noise from the post-seismic displacements prior to the fitting of the post-seismic displacements with the logarithmic decay function. As a result, the τ log values in the logarithmic decay function at each point were found to be more consistent in both north and east directions. The new fitting results can therefore be used to estimate the coordinate of the zero-order Thai geodetic network to any epoch with millimetre accuracy.

Coseismic and postseismic deformation related to the 2007 Chuetsu-oki, Niigata Earthquake

AbstractAn intermediate-strength earthquake of magnitudeMj6.8 occurred on July 16, 2007, centered beneath the Japan Sea a few kilometers offshore of Niigata Prefecture in central Japan. We constructed a dense GPS network to investigate postseismic deformation after this event, choosing our GPS sites carefully so as to complement the nationwide GPS GEONET array. Coseismic displacements caused by the mainshock detected at some GEONET sites were used to estimate coseismic fault parameters. The results indicate that the geodetic data can be explained by a combination of two rectangular faults dipping northwest and southeast. Minor but definite postseismic deformation was detected largely in the southern part of the dense network. The time series of site coordinates can be characterized by a logarithmic decay function, and the estimated time constant seems to be almost similar in range to that of the 2004 Mid-Niigata Prefecture Earthquake. We also found a possible site instability at 960566 (Izumo-zaki, GEONET) caused by a small, local landslide associated with the mainshock and therefore concluded that the data obtained at this site should not be used for coseismic or postseismic analysis.

Monitoring Deformation of Thai Geodetic Network due to the 2004 Sumatra-Andaman and 2005 Nias Earthquakes by GPS

The Thai geodetic network has been regularly observed with GPS since 1994. The continuous tectonic motions in Thailand located on the Sundaland block are well determined with uncertainties ∼1mm∕yr. The mega thrust earthquake occurred near Banda-Aceh on Dec. 26, 2004 with Mw 9.3 magnitude and caused significant surface displacements in many surrounding countries. The geodetic network within Thailand was also significantly deformed during the earthquake at the cm to dm level and the geodetic network will continue to deform for many months and possibly even years to come. The magnitude of displacements certainly has a direct impact on the Thai geodetic control network. The Royal Thai Survey Department (RTSD) has been carrying out GPS field campaigns in an attempt to monitor the postseismic displacement. However, the situation became more complicated when the second major earthquake occurred near Nias Island, Sumatra on Mar. 28, 2005 with Mw 8.7 magnitude. This paper will analyze the GPS observations obtained from the RTSD GPS campaigns and existing permanent GPS stations in Thailand up to the end of 2006 using the precise point positioning strategy of the GIPSY-OASIS II software. Results obtained from the latest campaign (Nov. 2006) indicated that the earthquakes have resulted in the horizontal displacements, ranging from 55cm in the south to about 6cm in the north of Thailand. The behavior of postseismic motions is investigated in this study and it was found that the postseismic motions can be fitted well by a logarithmic decay function. Finally, a strategy for updating the Thai geodetic network is proposed.

Dynamics of Photosynthetic Photon Flux Density and Light Extinction Coefficient to Assess Radiant Energy Interactions for Maize Canopy

Photosynthetic photon flux density (PPFD) is a measure of the rate of radiant energy per unit leaf area. Its quantification using the light extinction coefficient (K), which describes the transmissivity of light through the canopy, has been critical in predicting light interception above and beneath the canopy and the use of light interception in canopy radiation physics and plant productivity research. We measured incoming shortwave radiation (Rs), net radiation (Rn), radiation intercepted above (Rt) and beneath (Rtu) the canopy, and leaf area index (L) for a non-stressed maize canopy during partial and complete canopy periods to: (1) assess the radiation regimes and relationships between PPFD (sum of Rt and Rtu), Rt, Rtu, Rs, and Rn; (2) quantify the performance of Beer's law for estimating Rtu; (3) determine the diurnal and seasonal attenuation and augmentation of Bouguer-Lambert law-estimated variable daily maximum (Kmax) and average (Kavg) K values and compare the results with using a fixed K value; and (4) develop a relationship between Kavg and L for a non-stressed maize canopy during partial and complete canopy. The percentages of all radiation components (PPFD, Rt, Rtu, and Rn) relative to Rs were highest early in the season before the full canopy and gradually decreased as L increased. Early in the season, when L < 2.0, the amount of PPFD was as high as 43% of Rs. PPFD decreased to 31% at 64 days after planting (DAP), when L = 4.4, and stayed relatively constant until 98 DAP (L = 4.9). Similar trends were observed for Rt and Rtu with lower magnitudes. When L < 3.5, the average percentages of Rs for Rtu, Rt, PPFD, and Rn were 8.4, 29.3, 38.0, 29.2, respectively. By midsummer, when L > 3.5, the percentages had fallen to 5.2, 26.5, and 32.1 for Rtu, Rt, and PPFD, respectively, and remained the same for Rn. Rs alone explained 93% of the variability in PPFD (PPFD = 0.1827Rs1.0969) for conditions when 1.2 < L < 5.30. A strong correlation was observed between Rs and Rt, and Rs explained 94% of the variability in Rt. The correlation between the Rs and Rtu was poor (r2 = 0.28) due to diffusion of the light beneath the canopy. The Beer's law Rtu estimates were poorly correlated with the data, with scatter increasing at higher Rtu values. Beer's law underestimated Rtu in the range of 10 to 40 W m-2 and overestimated for values greater than 40 W m-2 (due to using a constant K) with an overall root mean square difference (RMSD) of 11.3 W m-2. We showed that K not only changed during the season but also fluctuated significantly within a day due to change in the sun angle and other factors. Daily Kmax varied from near zero to as high as 1.8 with a seasonal average of 0.73. Kavg ranged from 0.12 to 1.14 with a seasonal average of 0.44. Diurnal fluctuations and seasonal attenuation in Kavg were influenced by solar zenith angle (T). We made an attempt to quantify the effect of T on K and presented the results. Finally, we derived a variable Kavg equation as a function of L. There was a logarithmic and very strong dependence between the transmissivity of light through the canopy and L akin to the original logarithmic decay function of Beer's law. The derived function (K = -0.439ln(L) + 1.016) accounted for 76% of the variability in Kavg using L alone. The model represents conditions when 1.2 < L < 5.30 for non-stressed maize canopy, and extrapolating it beyond these boundaries may not provide particularly accurate estimates of K.

Prioritizing Burglars: Comparing the Effectiveness of Geographical Profiling Methods

The effectiveness, in prioritizing suspects, of six geographical profiling methods are compared by determining the rank to which each of 92 prolific burglars was assigned, from the total of 400 known burglars, who were selected from a large metropolitan database because they resided in the borough in which the crimes occurred. Using mean and median ranked prioritization of actual offenders, as well as the percentages that appeared in the top 5% of rankings and the area under the curve of a specially developed ‘Ranked Prioritization Function,’ RP (f), it was found that Dragnet using a logarithmic decay function and the distance from the centre of gravity produced the lowest average ranks, with 72% of the actual offenders in the top 5% of prioritized rankings. The implications of the findings are discussed.

A dense GPS observation immediately after the 2004 mid-Niigata prefecture earthquake

AbstractTo investigate the postseismic crustal deformation associated with the 2004 mid-Niigata prefecture earthquake (M6.8), we newly started GPS observation to fill a gap of the nationwide continuous GPS network. Our GPS sites were mainly distributed in the focal region without permanent GPS site, and succeeded in obtaining the postseismic deformation. Coseismic displacements of two aftershocks were clearly detected because of immediate observation. Estimated fault parameters of the aftershock (M5.9) on November 8 occurring just beneath our GPS network indicated that geodetic data could be explained by either east- or west-dipping fault model inferred from detailed aftershock data. Moreover, clear postseismic deformation, which could be characterized by a logarithmic decay function, was observed. This signal probably suggests possible aseismic slip. Our results indicated that dense GPS observation could give important and interesting data to clarify the properties of shallow inland middle-size earthquakes.

Analytical Derivation of the Vegetation Optical Depth From the Microwave Polarization Difference Index

A numerical solution for the canopy optical depth in an existing microwave-based land surface parameter retrieval model is presented. The optical depth is derived from the microwave polarization difference index and the dielectric constant of the soil. The original procedure used an approximation in the form of a logarithmic decay function to define this relationship and was derived through a series of lengthy polynomials. These polynomials had to be recalculated when the scattering albedo or antenna incidence angle changes. The new procedure is computationally more efficient and accurate.

Rapid aseismic moment release following the 5 December, 1997 Kronotsky, Kamchatka, Earthquake

Model inversions of displacements of continuously operating GPS stations in Kamchatka show that aseismic afterslip during 2 months following the Mw=7.8, 5 December, 1997 Kronotsky subduction earthquake released as much moment as the earthquake itself. The rapidly decaying transient slip on the subduction underthrust occurred near the downdip edge of the coseismic rupture and extended laterally away from it, including a region of vigorous foreshock activity. A logarithmic decay function fit to the cumulative afterslip curve has a relaxation time of about 3 days. Rapid afterslip can contribute significantly to the moment release of partially coupled subduction zones.