Increasing Block Size Research Articles

Field evidence and indicators of rockfall fragmentation and implications for mobility

Rockfall fragmentation can play an important role in hazard studies and the design of protective measures. However, the current lack of modeling tools that incorporate rock fragmentation mechanics is a limitation to enhancing studies and design. This research investigates the fragmentation patterns of rockfalls and analyzes the resulting distribution of fragment sizes within corresponding rockfall deposits. We focus on small rock fragments, which provide insights into the dynamics of the rockfall event and can be used as input for numerical modeling. We analyzed multiple rockfall events from locations worldwide, each exhibiting different degrees of fragmentation. Using image analysis techniques, we mapped all visible blocks, determined their volumes, and measured the distances they travelled from the initial point of impact. A key finding is the identification of three indicators of fragmentation. First, in cases where fragmentation was largely absent, we observed a trend of increasing block size with distance from the impact point or source area, which aligns with previously published findings. However, for energetic rockfall events characterized by intense fragmentation, we observed that small fragments exhibited longer travel distances compared to larger fragments. This distinction allowed us to differentiate blocks primarily resulting from the disaggregation process from those primarily resulting from dynamic fragmentation, with implications for rockfall mobility. Second, although the size distribution of rockfall deposits exhibits a power-law scaling for volumes larger than a minimum size threshold corresponding to a rollover of the distribution, in some case studies a deviation from power-law scaling is observed, indicating a process of larger block comminution due to fragmentation. Third, we found that rockfalls with fragmentation experience reduced mobility, indicated by higher reach angles, and higher lateral dispersion showing a wider distribution of trajectories. We interpret these findings as being directly related to the energy-consuming nature of fragmentation, which prevents farther deposition of fragmented rock blocks.

The Influence of Rock Slope Scales of Joint Network and Slope Height on the Stability and Failure Mechanisms

This paper demonstrates the influence of slope geometry and scale of the joint networks on the stability and failure mechanisms in discontinued rock masses. These analyses are based on the finite element method (FEM) to calculate the factor of safety (FOS) and to simulate the explicit discontinuity deformations for different scales of rock masses. The study was carried out through examples of regular jointed models having different slope heights and irregular jointed dry rock slopes. Joints usually decrease the strength of the slopes and suggestively increase slope stability problems. The result shows that the slope stability decreases with increased block size and shape and that the irregular columnar joints are more unfavorable to the slope stability than the regular joints. Furthermore, with dropping the factor of safety and randomly distributed joints the rock failure mechanism appears to shift from structurally controlled for the 50 m slopes towards a step-like failure path for the 100 m and 200 m slopes.

Lithium-Ion Diffusivity Increases with Block Size in Niobium Tungsten Oxide Shear Structures

Nb16W5O55 emerged as a high-rate anode material for Li-ion batteries in 2018 (Griffith et al.,Nature 2018, 559 (7715), 556–563). This exciting discovery ignited research in Wadsley-Roth (W-R) compounds, but systematic experimental studies have not focused on how to tune material chemistry and structure to achieve desirable properties for energy storage applications. In this work, we systematically investigate how structure and composition influences capacity, Li-ion diffusivity, charge-discharge profiles, and capacity loss in a series of niobium tungsten oxide W-R compounds: (3×4)-Nb12WO33, (4×4)-Nb14W3O44, and (4×5)-Nb16W5O55. Potentiostatic intermittent titration (PITT) data confirmed that Li-ion diffusivity increases with block size, which can be attributed to an increasing number of tunnels for Li-ion diffusion. The small (3×4)-Nb12WO33 block size compound with preferential W ordering on tetrahedral sites exhibits single electron redox and, therefore, the smallest measured capacity despite having the largest theoretical capacity. This observation signals that introducing cation disorder (W occupancy at the octahedral sites in the block center) is a viable strategy to access multi-electron redox behavior in (3×4) Nb12WO33. The asymmetric block size compounds (i.e., (3×4) and (4×5) blocks) exhibit the greatest capacity loss after the first cycle, possibly due to Li-ion trapping at a unique low energy pocket site along the shear plane. Finally, the slope of the charge-discharge profile increases with increasing block size, likely because the total number of energy-equivalent Li-ion binding sites also increases. This unfavorable characteristic prohibits the large block sizes from delivering constant power at a fixed C-rate more so than the smaller block sizes. Based on these findings, we discuss design principles for Li-ion insertion hosts made from W-R materials.

Structure–Property Relationships in High-Rate Anode Materials Based on Niobium Tungsten Oxide Shear Structures

Nb16W5O55 emerged as a high-rate anode material for Li-ion batteries in 2018 [Griffith et al., Nature2018, 559 (7715), 556–563]. This exciting discovery ignited research in Wadsley–Roth (W–R) compounds, but systematic experimental studies have not focused on how to tune material chemistry and structure to achieve desirable properties for energy storage applications. In this work, we systematically investigate how structure and composition influences capacity, Li-ion diffusivity, charge–discharge profiles, and capacity loss in a series of niobium tungsten oxide W–R compounds: (3 × 4)-Nb12WO33, (4 × 4)-Nb14W3O44, and (4 × 5)-Nb16W5O55. Potentiostatic intermittent titration (PITT) data confirmed that Li-ion diffusivity increases with block size, which can be attributed to an increasing number of tunnels for Li-ion diffusion. The small (3 × 4)-Nb12WO33 block size compound with preferential W ordering on tetrahedral sites exhibits single electron redox and, therefore, the smallest measured capacity despite having the largest theoretical capacity. This observation signals that introducing cation disorder (W occupancy at the octahedral sites in the block center) is a viable strategy to assess multi-electron redox behavior in (3 × 4) Nb12WO33. The asymmetric block size compounds [i.e., (3 × 4) and (4 × 5) blocks] exhibit the greatest capacity loss after the first cycle, possibly due to Li-ion trapping at a unique low energy pocket site along the shear plane. Finally, the slope of the charge–discharge profile increases with increasing block size, likely because the total number of energy-equivalent Li-ion binding sites also increases. This unfavorable characteristic prohibits the large block sizes from delivering constant power at a fixed C-rate more so than the smaller block sizes. Based on these findings, we discuss design principles for Li-ion insertion hosts made from W–R materials.

About the return period of a catastrophe

Abstract. When a natural hazard event like an earthquake affects a region and generates a natural catastrophe (NatCat), the following questions arise: how often does such an event occur? What is its return period (RP)? We derive the combined return period (CRP) from a concept of extreme value statistics and theory – the pseudo-polar coordinates. A CRP is the (weighted) average of the local RP of local event intensities. Since CRP's reciprocal is its expected exceedance frequency, the concept is testable. As we show, the CRP is related to the spatial characteristics of the NatCat-generating hazard event and the spatial dependence of corresponding local block maxima (e.g., annual wind speed maximum). For this purpose, we extend a previous construction for max-stable random fields from extreme value theory and consider the recent concept of area function from NatCat research. Based on the CRP, we also develop a new method to estimate the NatCat risk of a region via stochastic scaling of historical fields of local event intensities (represented by records of measuring stations) and averaging the computed event loss for defined CRP or the computed CRP (or its reciprocal) for defined event loss. Our application example is winter storms (extratropical cyclones) over Germany. We analyze wind station data and estimate local hazard, CRP of historical events, and the risk curve of insured event losses. The most destructive storm of our observation period of 20 years is Kyrill in 2002, with CRP of 16.97±1.75. The CRPs could be successfully tested statistically. We also state that our risk estimate is higher for the max-stable case than for the non-max-stable case. Max-stable means that the dependence measure (e.g., Kendall's τ) for annual wind speed maxima of two wind stations has the same value as for maxima of larger block size, such as 10 or 100 years since the copula (the dependence structure) remains the same. However, the spatial dependence decreases with increasing block size; a new statistical indicator confirms this. Such control of the spatial characteristics and dependence is not realized by the previous risk models in science and industry. We compare our risk estimates to these.

Out-of-plane mechanism in the seismic risk of masonry façades

A framework for evaluating the risk of the out-of-plane mechanism of masonry facades subjected to earthquake excitations is presented. The effect of seismic events on masonry facades is investigated and results are presented in terms of fragility curves and seismic risk for several masonry supporting restrictions. The restrictions considered are (1) masonry facade unrestricted to rock on a firm base, (2) masonry facade restricted to rock in one direction, and (3) restrained rocking masonry facade in one-sided motion. Because the available empirical information is insufficient to obtain fragility functions for masonry facades, the study is based on numerical analysis and recent studies on seismic risk. The conceptual framework is illustrated with information from masonry facades characteristic of Mexican religious structures and within the seismic hazard areas of Mexico. Since the frequency characteristics of ground motions strongly depend on the distance from the epicenter to the site, which is of cardinal importance to the vulnerability of these structures, the impact of this distance for hard-soil sites is thoroughly investigated. The probability of failure for the three types of masonry facades was calculated. It was found that the probability of failure decreases with an increased width-to-height relation; conversely, the probability of failure (reported in terms of the reliability index) increases with increased block size dimensions. Results in this study show that restraining conditions of the facades inconsequentially affect the probability of failure. Although the reliability of freestanding masonry facades are marginally greater, this finding holds true regardless of whether or not one considers far-field ground motions. The results in this study can be useful for evaluation and reinforcement tasks of masonry facades located in areas of high seismic hazard.

Morphological comparison of blocks in chaos terrains on Pluto, Europa, and Mars

Chaotic terrains are characterized by disruption of preexisting surfaces into irregularly arranged mountain blocks with a “chaotic” appearance. Several models for chaos formation have been proposed, but the formation and evolution of this enigmatic terrain type has not yet been fully constrained. We provide extensive mapping of the individual blocks that make up different chaos landscapes, and present a morphological comparison of chaotic terrains found on Pluto, Jupiter's Moon Europa, and Mars, using measurements of diameter, height, and axial ratio of chaotic mountain blocks. Additionally, we compare mountain blocks in chaotic terrain and fretted terrain on Mars. We find a positive linear relationship between the size and height of chaos blocks on Pluto and Mars, whereas blocks on Europa exhibit a flat trend as block height does not generally increase with increasing block size. Block heights on Pluto are used to estimate the block root depths if they were floating icebergs. Block heights on Europa are used to infer the total thickness of the icy layer from which the blocks formed. Finally, block heights on Mars are compared to potential layer thicknesses of near-surface material. We propose that the heights of chaotic mountain blocks on Pluto, Europa, and Mars can be used to infer information about crustal lithology and surface layer thickness.

EFFECTS OF CHANGING SCALES ON LANDSCAPE PATTERNS AND SPATIAL MODELING UNDER URBANIZATION

Spatial scale is an eternal topic in landscape pattern related analysis. This paper examined the spatial scale effect of landscape pattern changes and their relationships with urbanization indicators in Qingdao using a series of sampling blocks. The results indicated that, with the increasing block scale, the mean patch density and aggregation within a block decreased, whereas the diversity increased. Furthermore, the expanding scale amplified the mean change ratio of landscape metrics and eliminated local drastic changes and regional variation trends along an urban-to-rural gradient, which would be obvious at a finer block scale. Meanwhile, the adjusted R2 of GWR (Geographically Weighted Regression) models increased with an increasing block size, especially when the block scale changed from 1 km to 5 km. Odd-numbered block scales performed better than even-numbered block scales.

Block-Based Optical Color Image Encryption Based on Double Random Phase Encoding

This paper investigates and presents a block-based opto-color cipher using double random phase encoding (DRPE) with different block sizes. The color plainimage is divided into equal-sized blocks and then converted to an optical signal by an optical emitter. The obtained optical signal is encrypted by employing the DRPE technique, which applies two types of phase modulation, time, and Fourier domains. Finally, the optical color cipherimage is, upon detection, converted to digital format by a charge-coupled device digital camera. Experiments and security analysis show that the proposed block-based optical color image cipher using DRPE with increased block size is secure, effective, and including a good immunity to channel noise.

Numerical Investigation of the Influence of Geometrical and Mechanical Parameters of the Intersecting Joint Sets on the Area of Failure Zones around Tunnel

Summary One of the important problems in designing underground structures is geometrical and mechanical parameters of joint sets. Therefore designing underground structures should be done according to the structural conditions of the rock mass. In this regard, it is important to consider joint condition and spatial position of joints toward the underground excavation. In this study, using UDEC software, the structural stability of a tunnel with a horseshoe cross section in an intersecting jointed rock mass is investigated. Rock mass was containing two joint sets with different joint spacing. In the numerical models, joint shear stiffness, joint dip, joint opening, joint spacing, the ratio of joint spacing to width tunnel (l/b) and in situ stress were considered as variables. The area of failure zone was calculated separately by changing abovementioned parameters and the best condition concerning the least failure zone was determined. According to results, the largest failure area will created when dip difference between joint sets is lower than 40 degree, and further increasing of dip difference between joint sets causes reduction of area of failure zone. Also, increasing the ratio of joint spacing to tunnel width, leading to increase of the area of failure zone and consequently increase of instabilities. Instability exist in the range of this ratio from 0.11 to 0.33, and increasing of the ratio more than 0.33 provides improvement of stability condition (i.e., instability approaches zero) due to increasing block size and impossibility of block caving. The safest situation regarding minimum and maximum area of failure zone will occur for l/b=0.11 and 0.33, respectively. Introduction In this research, the effective parameters of jointed rock mass, which affect the tunnel stability and the extent of the failure zone, were examined. The final shape of failure zone has presented in a table. Also the safest situation of intersecting joints has introduced. Methodology and Approaches UDEC software has the ability of modeling jointed rock masses by considering the characteristics of joints. Therefore, using this software, the extent of the failure zone were calculated. Results and Conclusions In this research, the area and the shape of failure zone of a jointed-rock are analyzed and the effect of main parameters on tunnel stability are discussed.

Sequence balance minimisation: minimising with unequal treatment allocations

BackgroundMinimisation ensures excellent balance between groups for several prognostic factors, even in small samples. However, its use with unequal allocation ratios has been problematic. This paper describes a new minimisation scheme named sequence balance minimisation for unequal treatment allocations.MethodsTreatment- and factor-balancing properties were assessed in simulation studies for two- and three-arm trials with 1:2 and 1:2:3 allocation ratios. Sample sizes were set 30, 60 and 120. The number of prognostic factors on which to achieve balance was ranged from zero (treatment totals only) to ten with two levels occurring in equal probabilities. Random elements were set at 0.95, 0.9, 0.85, 0.80, 0.7, 0.6 and 0.5. Characteristics of the randomisation distributions and the impact of changing the block size while maintaining the allocation ratio were also examined.ResultsSequence balance minimisation has good treatment- and factor-balancing capabilities, and the randomisation distribution was centred at zero for all scenarios. The mean and median number of allocations achieved were the same as the number expected in most scenarios, and including additional factors (up to ten) in the minimisation scheme had little impact on treatment balance. Treatment balance tended to depart from the target as the random element was lowered. The variability in allocations achieved increased slightly as the number of factors increased, as the random element was decreased and as the sample size increased. The mean and median factor imbalance remained tightly around zero even when the chosen factor was not included in the minimisation scheme, though the variability was greater. The variability in factor imbalance increased slightly as the random element decreased, as well as when the number of prognostic factors and sample size increased. Increasing block size while maintaining the allocation ratio improved treatment balance notably with little impact on factor imbalance.ConclusionsSequence balance minimisation has good treatment- and factor-balancing properties and is particularly useful for small trials seeking to achieve balance across several prognostic factors.

Field Design Factors Affecting the Precision of Ryegrass Forage Yield Estimation

Core Ideas The row‐column designs were 36% more efficient than the randomized complete block designs. The impact of block size and number of replicates on trial precision was dependent on block shape. Increasing number of replicates decreased LSD only in wider blocks compared to narrow blocks. Field‐based agronomic and genetic research relies heavily on data generated from field trials. Therefore, it is imperative to optimize the precision of yield estimates in cultivar evaluation trials. Experimental error in yield trials is sensitive to several factors, some of which are classified as experimental design factors (i.e., plot size, block size, and number of replicates). The objective of this study was to conduct a retrospective case‐study analysis of long‐term perennial ryegrass (Lolium perenne L.), Italian ryegrass [Lolium perenne L. ssp. multiflorum (Lam.) Husnot], and hybrid ryegrass (Lolium boucheanum) forage yield trials to quantify the effects of block size, block shape, plot size, and number of replicates on trial precision. A total of 142 forage yield trials sown 2001 to 2011 across five locations by the Department of Agriculture, Food and the Marine (DAFM), Ireland, were considered. The contribution of row and column sum of squares (SS) to total SS decreased with increasing block size from 6 (71% of total SS) to 33 cultivars per block (51% of total SS). Empirical estimates of LSD decreased with increasing number of replicates only for square blocks, but not for rectangular blocks. Across different block sizes from 6 to 42 plots per block, row‐column designs were 36% more efficient than complete blocks. Increasing plot size was consistently ineffective. Use of incomplete block designs would significantly improve precision for the DAFM trials. This case study provides a template by which any research with long‐term data can be used to design more efficient field trials.

Dynamic Network Control for Confidential Multi-Hop Communications

We consider the problem of resource allocation and control of multihop networks in which multiple source-destination pairs communicate confidential messages, to be kept confidential from the intermediate nodes. We pose the problem as that of network utility maximization, into which confidentiality is incorporated as an additional quality of service constraint. We develop a simple, and yet provably optimal dynamic control algorithm that combines flow control, routing and end-to-end secrecy-encoding. In order to achieve confidentiality, our scheme exploits multipath diversity and temporal diversity due to channel variability. Our end-to-end dynamic encoding scheme encodes confidential messages across multiple packets, to be combined at the ultimate destination for recovery. We first develop an optimal dynamic policy for the case in which the number of blocks across which secrecy encoding is performed is asymptotically large. Next, we consider encoding across a finite number of packets, which eliminates the possibility of achieving perfect secrecy. For this case, we develop a dynamic policy to choose the encoding rates for each message, based on the instantaneous channel state information, queue states and secrecy outage requirements. By numerical analysis, we observe that the proposed scheme approaches the optimal rates asymptotically with increasing block size. Finally, we address the consequences of practical implementation issues such as infrequent queue updates and de-centralized scheduling. We demonstrate the efficacy of our policies by numerical studies under various network conditions.

Chaotic map-embedded Blowfish algorithm for security enhancement of colour image encryption

The quest for achieving an accurate and efficient algorithm in enhancing the security of colour image encryption is never-ending. We enhance the security level of conventional Blowfish algorithm (BA) for colour image encryption by modifying it with new F-function. The dynamic S-box and XOR operator are generated from the F-function via four-dimensional hyper-chaotic map, and the number of iterations is dramatically reduced from sixteen to four to simplify the processing complexity. The block secret keys of varying space size are randomly created. The computation is performed using Matlab R2008a codes on eight images of size $$512\times 512$$ pixels obtained from standard USC-SIPI Image Database. The security of the proposed method exhibits notable enhancement with increasing block size. Performance analyses reveal a correlation coefficient less than $$-$$ 0.0016 and entropy greater than 7.9993. Furthermore, the distribution of RGB channel for image Lena displays sizeable security improvements. Correlation between image pixels is significantly decreased with higher entropy. In comparison with previous works, the proposed algorithm is found to exhibit superior performance for colour image encryption than the conventional BA.

Prospects of photon counting lidar for savanna ecosystem structural studies

Abstract. Discrete return and waveform lidar have demonstrated a capability to measure vegetation height and the associated structural attributes such as aboveground biomass and carbon storage. Since discrete return lidar (DRL) is mainly suitable for small scale studies and the only existing spaceborne lidar sensor (ICESat-GLAS) has been decommissioned, the current question is what the future holds in terms of large scale lidar remote sensing studies. The earliest planned future spaceborne lidar mission is ICESat-2, which will use a photon counting technique. To pre-validate the capability of this mission for studying three dimensional vegetation structure in savannas, we assessed the potential of the measurement approach to estimate canopy height in a typical savanna landscape. We used data from the Multiple Altimeter Beam Experimental Lidar (MABEL), an airborne photon counting lidar sensor developed by NASA Goddard. MABEL fires laser pulses in the green (532 nm) and near infrared (1064 nm) bands at a nominal repetition rate of 10 kHz and records the travel time of individual photons that are reflected back to the sensor. The photons’ time of arrival and the instrument’s GPS positions and Inertial Measurement Unit (IMU) orientation are used to calculate the distance the light travelled and hence the elevation of the surface below. A few transects flown over the Tejon ranch conservancy in Kern County, California, USA were used for this work. For each transect we extracted the data from one near infrared channel that had the highest number of photons. We segmented each transect into 50 m, 25 m and 10 m long blocks and aggregated the photons in each block into a histogram based on their elevation values. We then used an expansion window algorithm to identify cut off points where the cumulative density of photons from the highest elevation resembles the canopy top and likewise where such cumulative density from the lowest elevation resembles mean ground elevation. These cut off points were compared to DRL derived canopy and mean ground elevations. The correlation between MABEL and DRL derived metrics ranged from R2 = 0.70, RMSE = 7.9 m to R2 = 0.83, RMSE = 2.9 m. Overall, the results were better when analysis was done at smaller block sizes, mainly due to the large variability of terrain relief associated with increased block size. However, the increase in accuracy was more dramatic when block size was reduced from 50 m to 25 m than it was from 25 m to 10 m. Our work has demonstrated the capability of photon counting lidar to estimate canopy height in savannas at MABEL's signal and noise levels. However, analysis of the Advanced Topography Laser Altimeter System (ATLAS) sensor on ICESat-2 indicate that signal photons will be substantially lower than those of MABEL while sensor noise will vary as a function of solar illumination, altitude and declination, as well as the topographic and reflectance properties of surfaces. Therefore, there are reasons to believe that the actual data from ICESat-2 will give poorer results due to a lower sampling rate and use of only the green wavelength. Further analysis using simulated ATLAS data are required before more definitive results are possible, and these analyses are ongoing.

The effect of block length upon structure, physical properties, and transport within a series of sulfonated poly(arylene ether sulfone)s

The gas transport and physical properties of sulfonated poly(arylene ether sulfone) was studied as a function of sulfonated and unsulfonated block length (5k:5k, 10k:10k, and 15k:15k). Viscoelastic properties were evaluated using Dynamic Mechanical Analysis (DMA) to observe polymer relaxations and domain compatibility. A decrease in glass transition temperature Tg was observed with increasing block length. 5k:5k had a single Tg (241°C), while micro-phase separation between 10k:10k and 15k:15k domains create two Tg's that are slightly merged (191°C, 236°C and 182°C, 233°C). Swelling measurements revealed that film dimensional changes were greater in the plane normal to the film than parallel with increasing block size. He, H2, CO2, and O2 permeability decreased with increasing sulfonated block length with no interchain spacing dependence. The apparent activation energy for permeation Ep increased with gas kinetic diameter size and had a maximum value for 15k:15k. A trade-off relationship between sulfonated and unsulfonated polymer block length is linked to phase separation, water swelling, and gas permeability.

Secret image sharing scheme with adaptive authentication strength

Transmission of secret messages or images over the Internet using Shamir’s secret sharing scheme has become popular. Some researchers use steganography with Shamir’s method to hide noise like share images into natural looking cover images to improve secrecy. Stego images are authenticated against accidental or deliberate changes before recovering the secret. Authentication by a parity bit stream calculated by a keyed hash of stego images is commonly used. Researchers aim to increase the number of authentication bits to improve the authentication strength of their methods. Eslami and Ahmadabadi (2011) proposed a method with dynamic embedding strategy in 2011. They use a concatenated string of four bits, two from the current and two from previous block, to authenticate individual blocks. Even though chaining performs block based authentication, it cannot detect individual fake stego blocks and cannot authenticate the rest of the stego image blocks if it faces a changed block. This paper proposes a new secret image sharing method by selecting the number of authentication bits proportional to block size, contrary to Eslami and Ahmadabadi (2011) method which uses four bits to authenticate blocks regardless of block size. The proposed method has improved authentication for increased block size and can authenticate individual stego blocks as well. It produces good quality stego images and can still authenticate the rest of the stego image even after an altered stego block is encountered as shown in the experimental results.

Exponential error rates in multiple state discrimination on a quantum spin chain

We consider decision problems on finite sets of hypotheses represented by pairwise different shift-invariant states on a quantum spin chain. The decision in favor of one of the hypotheses is based on outcomes of generalized measurements performed on local states on blocks of finite size. We assume the existence of the mean quantum Chernoff distances of any pair of states from the given set and refer to the minimum of them as the mean generalized quantum Chernoff distance. We establish that this minimum specifies an asymptotic bound on the exponential rate of decay of the averaged probability of rejecting the true state in increasing block size, if the mean quantum Chernoff distance of any pair of the hypothetic states is achievable as an asymptotic error exponent in the corresponding binary problem. This assumption is, in particular, fulfilled by shift-invariant product states (independent and identically distributed states). Further, we provide a constructive proof for the existence of a sequence of quantum tests in increasing block length with an error exponent which equals, up to a factor, the mean generalized quantum Chernoff distance. The factor depends on the configuration of the hypothetic states with respect to the binary quantum Chernoff distances. It can be arbitrary close to 1 and is never less than 1/m for m being the number of different pairs of states.

Evaluation of the representative elementary volume (REV) of a fractured geothermal sandstone reservoir

The objective of this study is to evaluate a representative elementary volume (REV) in a fractured geothermal sandstone reservoir in Germany using the discrete fracture network (DFN) model approach. Due to the lack of in situ data from the deep geothermal reservoir, field measurements of outcrop reservoir analogues were conducted to get a quantitative description of the DFN. Field measurements reveal that the geometry of the DFN is largely influenced by the lithological layering (e.g. relationship between joint spacing and bed thickness). Thus, DFN models have to be completed individually for each layer since each bed is distinct compared to its neighbouring beds. Various DFNs were generated using statistical-derived fracture input data. The two-dimensional universal distinct element code UDEC was used for fracture flow simulations. In order to determine the minimum REV, the equivalent average conductivity tensors were obtained with increasing block size. Plots of conductivity tensor coefficients versus block size exhibit only minor variation of the hydraulic properties with increasing block size. Hence, an REV size of 10 m × 10 m could be determined for all studied stochastically derived discrete fracture networks.

Ventilation properties of blocky stones embankments

Abstract Blocky stones are used at slopes and in embankments as one of the measures to decrease the temperature of the embankment due to natural air convection in the construction of the Qinghai–Tibet Railway. The temperature field of a blocky stones embankment is affected directly by the size, porosity and ventilation properties of the blocky stones. Experimental results show that porosity increases with increasing block size ranges from about 42.3% for 0.04 m sized stones to 47% for 0.25 m sized blocks, moreover, the minimum porosity is that of mixed blocky stones. Experiments in a wind tunnel reveal that the wind pressure gradient in blocky stones has a nonlinear behaviour with the wind velocity, directly proportional to the square of the wind velocity. Our results also show that the resistance coefficient decreases with increasing stone size, and for mixed blocky stones the coefficient is the medium. Considering the prevailing wind velocities (≥ 3 m s− 1) on the Qinghai–Tibet plateau the airflow velocity through the blocky stones embankment of Qinghai–Tibet Railway is discussed in the paper. Our experiments and calculated results confirm that blocky stones layers have good ventilation ability. Thus it can be concluded that under the prevailing wind velocities of ≥ 3 m s− 1 the forced air convection inside the blocky stones layer has a strong influence on the temperature field within and below the embankment and should be taken into account when calculating the temperature field.