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Carpooling as one of demand management measures is effective in reducing highway congestion. Recent studies have shown that an appropriate spatial allocation of bottleneck capacity between carpool lane and general-purpose lane can lead to peak-spread of the morning commuters' departure time and reduce the system's total trip cost. What is not clear however is whether temporal allocation of bottleneck capacity can also be effective and if so, what the impact would be, and furthermore what the combined effects of temporal-spatial allocation of bottleneck capacity would be. This paper investigates the impacts of a temporal allocation of bottleneck capacity, when carpool lane is available only within a reserved time window, and a joint temporal-spatial capacity allocation, on morning commute patterns. User equilibrium commute patterns are derived for both the temporal-only and the joint temporal-spatial capacity allocation schemes, along a highway corridor with two driving modes: solo driving and carpooling. The extra costs associated with carpooling are considered alongside of travel time and schedule delay costs. We identify three different cases representing the relative barriers and attractions of carpooling to commuters, and we show that the optimal capacity allocations are sensitive to the accurate estimation of the commuters' extra carpool cost. To assist in evaluating the difference between a non-optimal and the optimal temporal-spatial allocation schemes, we derive analytically the upper bounds on the efficiency loss and present numerical illustrations on how the upper bounds vary with the different operational and behavioral variables.

Mafic granulite and amphibolite occur as boudinaged lenses in felsic and metapelitic gneiss in the Guandishan area of the southern Luliang metamorphic complex. Peak assemblages recorded by large granoblastic minerals yield pressure–temperature ( P-T ) conditions of 790 °C and 9.4 kbar in granulite and >750 °C and >6.2 kbar in amphibolite based on standard thermobarometric techniques. Retrogression produced fine-grained resorptive rims in garnet, symplectitic hornblende, orthopyroxene and plagioclase that record P-T conditions of 560–775 °C and 2.8–7.5 kbar in granulite and 740 °C and 5.7 kbar in amphibolite. Mineral inclusion patterns and major element zoning are consistent with a clockwise P-T path that ended with nearly isothermal decompression. Uranium - Pb dating of metamorphic zircons from the granulite and host metapelite reveal two discrete, meaningful age groups of metamorphism in the Guandishan area: most metamorphic zircon grains exhibit peak metamorphic growth at 1935–1920 Ma, whereas a smaller, younger group exhibit growth during retrogression between 1860 and 1815 Ma. Regional metamorphism in the Luliang metamorphic complex was related to the amalgamation of the North China Craton along the Trans-North China Orogen between c. 1.95 and 1.80 Ga.

High-pressure (HP) mafic granulites in the Daqingshan–Wulashan Complex from the central segment of the Khondalite Belt of the North China Craton occur as irregular lenses or deformed dike swarms within dioritic–granitic gneisses and meta-sedimentary rocks. The HP mafic granulites contain three distinct mineral assemblages: a peak HP granulite-facies assemblage (M1) that consists of garnet + clinopyroxene + plagioclase + amphibole ± quartz ± Fe–Ti oxides; a post-peak decompression assemblage (M2) that is characterized by symplectites of orthopyroxene + clinopyroxene + plagioclase ± amphibole ± Fe–Ti oxides; a late cooling assemblage (M3) represented by symplectites of amphibole + plagioclase + Fe–Ti oxides. Pseudosection modeling using THERMOCALC in the NCFMASHTO system and conventional thermobarometers constrain the P–T conditions of the M1, M2, and M3 assemblages to P = 1.25–1.40 GPa and T = 760–815 °C, P = 0.72–0.80 GPa and T = 825–860 °C, and P = 0.69–0.81 GPa and T = 645–730 °C, respectively. In-situ U–Pb dating of zircons show that the protolith ages of the HP mafic granulites are 2100–2000 Ma and the timing of peak HP granulite-facies metamorphism is 1960–1940 Ma. The medium- to low-pressure amphibolite- to granulite-facies retrogression occurred mainly from 1920 to 1820 Ma. Petrographic investigations, mineral compositions, metamorphic reaction histories, P–T calculations, and geochronological data define a clockwise P–T–t path involving near-isothermal decompression and near-isobaric cooling, which suggests that the Daqingshan–Wulashan Complex underwent initial crustal thickening from 1960 to 1940 Ma, followed by relatively rapid exhumation, cooling, and retrogression from 1920 to 1820 Ma. This P–T–t path was likely the result of the Paleoproterozoic continental–continental (or arc) collision during the amalgamation of the North China Craton.

The Trans-North China Orogen (TNCO) is well-known as an early Precambrian orogenic belt in the North China Craton (NCC). Three meaningful groups of metamorphic ages have been reported in the metamorphic complexes throughout the TNCO, including c. 1.85 Ga, c. 1.95 Ga, and c. 2.5 Ga. The spatial distributions and relationships of these ages provide notable insight into the formation timing and tectonic evolution of the NCC basement. The Zuoquan and Zanhuang complexes are exposed in the south&ndash, central TNCO and are adjacent to the Eastern Block. In order to place new constraints on the timing of two phases of metamorphism that occurred in the complexes, combined U&ndash, Pb and rare earth element analyses were performed on zircons from different types of metamorphic rocks. Uranium&ndash, Pb zircon dating in this study shows that two groups of metamorphic ages of 1.88&ndash, 1.85 Ga and 2.48&ndash, 2.46 Ga were commonly recorded by metamorphic rocks in the Zanhuang and Zuoquan complexes, respectively. Our previous geochronological studies showed that metamorphic ages of c. 2.51 Ga and c. 1.90 Ga were locally recorded in the Zanhuang and Zuoquan complexes, respectively. These data indicate that metamorphic rocks in the two complexes underwent at least two phases of metamorphism, i.e., 2.51&ndash, 2.46 Ga (Phase I) and 1.90&ndash, 1.85 Ga (Phase II). In combination with previous studies regarding reaction microstructures, metamorphic pressure&ndash, temperature paths, and geochronology, the Phase II metamorphic ages are interpreted to be linked to the collision between the Western and Eastern Blocks along the TNCO between 1.97 Ga and 1.80 Ga, whereas the Phase I metamorphic ages, as a result of an earlier and extensive tectono-thermal event that occurred in the Eastern and Western Blocks of the NCC, were related to underplating of mantle-derived magma. It is inferred that the rocks with c. 2.51&ndash, 2.46 Ga metamorphic ages in the two complexes formed in the Eastern Block and underwent regional metamorphism during that period, and then were tectonically involved in the TNCO and experienced c. 1.90&ndash, 1.85 Ga metamorphism. Metamorphic peaks occurred at different crustal levels in the orogen, resulting in distinct metamorphic ages and peak conditions preserved by metamorphic rocks in the two complexes.

Morning commuters choose their departure times and travel modes based on a combinational evaluation of factors associated with the chances of running into bottleneck congestion, likely schedule delays, parking space availability as well as monetary costs of traveling and parking. This study investigates a morning commute problem with carpooling behavior under parking space constraint at destination. We consider such a scenario that as a competing mode of the transit line, the highway contains a carpool lane only used by carpoolers while all solo drivers are forced to use a general purpose (GP) lane. Unlike the standard bottleneck model, the rush-hour dynamic departure patterns with a binding parking supply vary with the relative proportion of the two lanes’ capacities. The possible departure pattern domain with different parking supply and lane capacity allocation is explored in terms of the relative extra carpool cost and distinguished between the bi-mode and multi-mode equilibria. It is found that compared with solo drivers, carpoolers have shorter rush hour in order to smooth the extra carpool cost. With the decrease of parking spots, the number of solo drivers cuts down gradually, whilst the number of carpoolers climbs up firstly and then declines in the multi-mode system. Under mild assumptions, the best system performance can be realized with the joint consideration of total travel cost and vehicle emission cost through optimizing the lane capacity allocation and the parking supply.

To further understand the metamorphic evolution of the Trans-North China Orogen (TNCO), a combined study of petrography, pseudosection modeling and conventional thermobarometry was completed on garnet-sillimanite-bearing metapelitic rocks of the Jiehekou Group from the southern Luliang metamorphic complex, in the central segment of the TNCO. The Luliang metapelitic rocks preserve peak assemblages of garnet, biotite, sillimanite, plagioclase and quartz, with or without K-feldspar, that reflect c. 750 °C and 7.0 kbar. Garnet has mostly homogeneous grain cores with sparse mineral inclusions, enclosed successively by: (1) rims of higher spessartine and lower pyrope content and (2) symplectitic intergrowths of cordierite, biotite and plagioclase that present a spectacular “white-eye socket’ reaction microstructure. Quantitative phase equilibria modeling and traditional thermobarometric calculation results are consistent with this retrograde microstructure having developed during decompression to T ≈ 650 °C and P