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A thermal and mechanical framework is presented for analysis of pressure‐temperature (P‐T) data and structural observations from high‐pressure‐low‐temperature (HPLT) terrains. P‐T data from 281 HPLT rocks exhibit two regimes separated at a pressure of ∼1.5 GPa, which corresponds to the modal maximum depth of thrust faulting in subduction zones. At pressures ≲1.5 GPa, interpreted as recording conditions on the plate interface, temperatures increase at about 350°C/GPa and are consistent with conditions calculated for shear stresses of ∼30–100 MPa on the interface. Such shear stresses are high enough to carry several kilometers' thickness of sediment at least to the base of the plate interface. Burial of material on plate interfaces occurs predominantly during large‐to‐great earthquakes; the exhumation phase involves contrasts in ascent rates of adjacent units, because of their differing buoyancies and strengths. In consequence, juxtaposition of unrelated rock types is expected to be ubiquitous, during both descent and ascent. The scarcity of temperatures higher than ∼650°C at pressures ≳1.5 GPa may reflect loss of material from the wedge‐slab interface by buoyant ascent. Exhumation of rocks in the subduction interface requires substantial reduction in shear stress, most plausibly by (near‐)cessation of subduction. During prograde metamorphism temperatures increase smoothly with depth in the plate interface, with almost isothermal compression in the wedge‐slab interface. Following cessation of subduction, rocks rising along the wedge‐slab interface are likely to heat slightly during decompression. Within the plate interface, temperatures drop following the cessation of shear heating, and rocks follow counter‐clockwise hairpin PT paths. Key Points A simple thermal and mechanical framework is presented for the interpretation of P‐T data from high‐pressure‐low‐temperature (HPLT) terrains PT data from HPLT terrains are consistent with thermal regimes of present‐day plate interfaces (PI), with shear stresses of ∼30–100 MPa Stresses are great enough that earthquakes can carry sediments to base of PI. Exhumation requires (near‐)cessation of subduction

Up to the beginning of the twenty-first century, most of quasi-brittle structures, in particular the ones composed by concrete or masonry frames and walls, were designed and built according to codes that totally ignored fracture mechanics theory. The structural load capacity predicted by strength-based theories, such as plastic analysis and limit analysis, do not exhibit size-effect. Within the framework of fracture mechanics theory, this paper deals with the analysis of the effect of non proportional loadings on the strength reduction with the structural scaling. In particular, this study investigates the size-effect of quasi-brittle materials subjected to self-weight. Although omnipresent, gravity-load is often considered negligible in most studies in the field of fracture mechanics. This assumption is obviously not valid for large structures and in particular for geometries in which the dead load is a major driving force leading to fracture and structural failure. In this study, an analytical formulation expressing the relation between the strength-reduction and the structural scaling and accounting for self-weight, was derived for both notched and unnotched bodies. More specifically, a closed form expression for size and self-weight effects was first derived for notched specimens from equivalent linear elastic fracture mechanics. Next, equivalent linear elastic fracture mechanics theory being not applicable to unnotched bodies, a cohesive model formulation was considered. Particularly, the cohesive size effect curve and the generalized cohesive size effect curves, originally obtained via cohesive crack analysis for weightless bodies with sharp and blunt/unnotched notches, respectively, were equipped of an additional term to account for the effect of gravity. All the resulting formulas were compared with the predictions of numerical simulation resulting from the adoption of the Lattice Discrete Particle Model. The results point out that the analytical formulas match very well the results of the numerical model for both notched and unnotched samples. Furthermore, the analytical formulas predict a vertical asymptote for increasing size, in the typical double-logarithm strength versus structural size representation. The asymptote corresponds to a characteristic size at which the structure fails under its own weight. For large structural sizes approaching this characteristic size, the newly developed formulas deviate significantly from previously proposed size-effect formulas. The practical relevance of this finding was demonstrated by analyzing size and self-weight effect for several quasi-brittle materials such as concrete, wood, limestone and carbon composites. Most importantly, the proposed formulas were applied to the failure of semi-circular masonry arches under spreading supports with different slenderness ratios. Results show that analytical formulas well predict numerical simulations and, above all, that for vaulted structures it is mandatory accounting for the effect of self-weight.

The 3D vibration model of metaconcrete single aggregate is established under the linear elastic deformation. The soft coating and mortar are replaced by equivalent spring. Their equivalent mass, length and stiffness are calculated. The nonlinear control equation of free vibration is derived. The analytical expression of solution was acquired. A kind of method for solving such equation was given. The analytical expression of non-damping and damping nonlinear frequency are obtained. The effects of material parameters, geometrical parameters and initial conditions of aggregate on vibration were analyzed. The backbone curves of free vibration are studied. The influence of elastic modulus of soft coating on the backbone curves, the time history curve of displacement, etc. are investigated. The selection of aggregates is optimized. It can provide theoretical reference for engineering design such as designing aggregates attenuating high-frequency wave, low-frequency vibrations, etc. and for the theoretical study of multiple cells aggregate vibration.

Global Navigation Satellite System (GNSS) observations are subject to various errors during their propagation process. A reasonable correction of these errors can improve the positioning, navigation, and timing (PNT) service capability. The impact of multipaths on pseudorange observations can reach a decimeters or even meters level. However, their mechanism is complex and there is currently no universally accepted high-precision correction model. The correlation between the pseudorange multipaths (MP) of BDS-2 satellites and satellite elevation has been confirmed, while there have been fewer analyses of the MP characteristics for different frequencies of BDS-3 satellites. The broadcasting of multi-frequency observations in BDS-3 should theoretically make the extracted MP more accurate compared to traditional methods. Based on this, in this contribution, a multi-frequency MP extraction algorithm based on the least squares principle is proposed, which can simultaneously eliminate the influence of higher-order ionospheric delay. The analytical expression for only eliminating first-order ionospheric delay is successfully derived. Subsequently, the characteristics of the MPs extracted from different frequency combinations and the impact of combination noise on the extraction accuracy are discussed. The influence of second-order ionospheric delay on the MPs for each frequency under different combination noises, as well as the periodic behavior exhibited in long-term observations of the BDS-3 medium earth orbit (MEO) and inclined geosynchronous orbit (IGSO) satellites, are also analyzed. Finally, the correlations between the MPs of each frequency of BDS satellite and elevation are quantitatively analyzed based on observations from 35 stations. Overall, this work has positive implications for the study of the MP characteristics of BDS-3 and subsequent modeling efforts.

In this study, the authors investigate the outage probability and bit-error rate (BER) of distributed antenna system in downlink multicell environment with blanket transmission. Different from the most existing works, the variance of interference plus noise is treated as a random variable other than constant, and it is influenced by the short term fading when propagation pathloss and transmit power are given. From the perspective of information theory, the closed-form and approximate analytical expressions of downlink outage probability and average BER in the cellular system are derived for no shadowing and shadowing scenarios, respectively. Extensive simulation results validate the theoretical analysis and demonstrate that the system performances can be significantly improved for cell-edge users. Moreover, the proposed analytical method can obtain more accurate system performances.

Currently, the extrusion process with traditional conical die or elliptic die will cause the problems of high energy consumption and stress concentration. In order to address these problems, a novel streamline die characterized by the Gaussian function is designed first. The corresponding velocity field is constructed on the basis of the condition of equal flow per second. By using the newly constructed velocity field, the energy analysis of the extrusion is conducted, and the concrete internal work rate of plastic deformation, shearing work rate, and work rate of friction are obtained by a new method, called the feature-fitting substituting method. Then, the analytical expressions of extrusion force and stress state coefficient are obtained by the upper bound method. Simultaneously, the finite element (FE) simulation is conducted to verify the accuracy of the analytical expression of extrusion force and to disclose the advantages of the present die over the existing dies. The results show that the extrusion forces obtained from the present die match well with the simulation results, and the maximum deviation is no more than 1.73%. Above all, it is proved that the present Gaussian die can consume less energy and reduce the possibility of die loss evidently.

Due to the complex mesostructure and components of composite active layers in lithium-ion battery (LIB) electrodes, coupled with the concentration-dependent material properties and eigenstrains, efficiently estimating the effective modulus of the active layers remains a great challenge. In this work, the classic Mori–Tanaka method is found to be unable to estimate the modulus of the active layer. By realizing the importance of the mesostructure feature, a rod-rod model is proposed. The resulting modulus is expressed analytically. It is shown that the rod-rod model can accurately estimate the modulus evolution of the active layer if the material properties of the components and the evolution of volume fractions are known in advance. Moreover, a simplified rod-rod model is also developed to reduce the complexity of the proposed method. By knowing the volume fractions at two arbitrary states of charge and subsequently determining two constants, the simplified model can estimate the modulus efficiently. Considering both its accuracy and its simplicity, the simplified rod-rod model is the most suitable for the estimation. Thus, the methods developed in this work provide a new perspective for analyzing the material properties of composite active layers in LIB electrodes.

The linear combination of multi-frequency carrier-phase and pseudorange observations can form the combined observations with special properties. The type and number of combined frequencies will directly affect the characteristics of the combined observations. BDS-2 and BDS-3 broadcast three and five signals, respectively, and the study of their linear combination is of great significance for precision positioning. In this contribution, the linear combination form of multi-frequency carrier-phase observations in cycles and meters is sorted out. Seven frequency combination modes are formed, and some special combinations for positioning are searched. Then, based on the principle of minimum combined noise, a simpler search method for the optimal real coefficients of ionosphere-free (IF) combination based on the least squares (LS) principle is proposed. The general analytical expressions of optimal real coefficients for multi-frequency geometry-based and ionosphere-free (GBIF), geometry-free and ionosphere-free (GFIF), and pseudorange multipath (PMP) combinations with the first-order ionosphere delay taken into account are derived. And the expression derivation process is given when both the first-order and second-order ionospheric delays are eliminated. Based on this, the characteristics of the optimal real coefficient combination in various modes are compared and discussed. The various combinations reflect that the accuracy of the combined observations from dual-frequency (DF) to five-frequency (FF) is gradually improving. The combination coefficient becomes significantly larger after taking the second-order ionospheric delay into account. In addition, the combined accuracy of BDS-3 is better than that of BDS-2. When only the first-order ionosphere is considered, the combination attribute of (B1C, B1I, B2a) is the best among the triple-frequency (TF) combinations of BDS-3. When both the first-order and second-order ionospheric delays are considered, the (B1C, B3I, B2a) combination is recommended.

Structure design is of great value for the performance improvement of solid oxide electrolysis cells (SOECs) to diminish the gap between scientific research and industrial application. A comprehensive multi-physics coupled model is constructed to conduct parameter sensitivity analysis to reveal the primary and secondary factors on the SOEC performance and optimal rib width. It is found that the parameters of the O2 electrode have almost no influence on the optimal rib width at the H2 electrode side and vice versa. The optimized rib width is not sensitive to the electrode porosity, thickness, electrical conductivity and gas composition. The optimal rib width at the H2 electrode side is sensitive to the contact resistance at the interface between the electrode and interconnect rib, while the extremely small concentration loss at the O2 electrode leads to the insensitivity of optimal rib width to the parameters influencing the O2 diffusion. In addition to the contact resistance, the applied cell voltage and pitch width also has a dramatic influence on the optimal rib width of the fuel electrode. An analytical expression considering the influence of total cell polarization loss, the pitch width and the contact resistance is further developed for the benefit of the engineering society. The maximum error in the cell performance between the numerically obtained and analytically acquired optimal rib width is only 0.14% and the predictive power of the analytical formula is fully verified.