Search

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.

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.

Garnet-bearing metapelites are cropped out in the Zanhuang metamorphic complex located in the central section of the N–S trending Trans-North China Orogen. Petrological studies indicate that these garnet-bearing metapelites preserve three distinct metamorphic assemblages (M1–M3). The cores of garnet porphyroblasts and fine-grained inclusions of plagioclase + quartz ± biotite ± apatite ± magnetite ± rutile ± ilmenite define the prograde metamorphic stage (M1). The assemblage of the peak metamorphic stage (M2) consists of biotite + plagioclase + quartz ± kyanite ± hornblende ± magnetite ± ilmenite in equilibrium with the lowest-XMn garnet rims. The peak metamorphism was followed by a near-isothermal decompressional stage (M3) and the development of symplectitic coronas of biotite + plagioclase + quartz ± hornblende ± magnetite surrounding garnet porphyroblasts. Quantitative phase equilibria modeling and traditional thermobarometric estimations were applied to yield P–T conditions of 4.5–5.9 kbar and 551–596 °C for stage M1, 9.6–12.3 kbar and 770–830 °C for stage M2, and ∼4.7 kbar and ∼635 °C for stage M3. The combination of the mineral inclusions, mineral compositions, and metamorphic reactions in the Zanhuang metapelites defines a clockwise P–T path with nearly isothermal decompression, which is considered to have been related to the amalgamation of the Eastern and Western Blocks to form the North China Craton. Abundant U–Pb spot analyses of metamorphic zircons from the gneiss and amphibolite reveal two discrete, meaningful ages of metamorphism within the Zanhuang complex: the first age dates to ∼2507 Ma, and the second age dates to ∼1839 Ma. The first age group (∼2507 Ma) was most likely associated with a regional Neoarchean granulite-facies metamorphic event within the North China Craton, whereas the second age group (∼1839 Ma) is interpreted as the result of a Paleoproterozoic orogenic event that occurred in the Trans-North China Orogen (TNCO).

This paper studies commuters' departure time choice behavior along a bottleneck constrained highway connecting a resident area and a workplace. Commuters are differentiated by their value of time, and the bottleneck capacity is assumed to follow a uniform distribution within a range. The equilibrium properties of the proposed model are derived and individual travel cost is obtained. It is found that at equilibrium, the increase of capacity variability would change the commuters' travel behavior by increasing the expected equivalent travel time and lengthening the peak period. Every commuter is better off by reducing the individual travel cost if the stochasticity of the capacity decrease, and commuters with high value of time benefit more than those with low values. Numerical results are presented to support analytic findings.

Meta-mafic rocks in the Daqingshan–Wulashan Complex, in the central segment of the Paleoproterozoic Khondalite Belt of the North China Craton, are composed predominantly of garnet-bearing mafic granulites, mafic granulites, and amphibolites. They occur mainly as irregular lenses and as a set of deformed dyke/sill swarms within dioritic–granitic orthogneisses and Al-rich paragneisses. An integrated study involving laser Raman and scanning electron microscope analyses of mineral inclusions from zircons, cathodoluminescence imaging, and LA–ICP–MS U–Pb dating of zircons, shows that magmatic zircons in these meta-mafic rocks record four age groups of 2500–2450, 2300–2100, 1970–1930, and ca. 1850 Ma, indicating multiple mafic magmatic events occurred within the Daqingshan–Wulashan Complex. In addition, four groups of metamorphic zircons with ages of ca. 2450, ca. 1950, ca. 1900, and ca. 1850 Ma are present within these meta-mafic rocks. Zircons of the first (oldest) group contain medium- to low-pressure (MLP) granulite facies mineral inclusions of orthopyroxene + clinopyoxene + amphibole + plagioclase + quartz, and yield ages of ca. 2450 Ma, representing the timing of the early MLP granulite facies metamorphic event within the Daqingshan–Wulashan reworked basement complex. In contrast, zircons of the second group are free of mineral inclusions, and yield ages of ca. 1950 Ma, which is considered to be the timing of the regional high-grade metamorphic and structural event probably caused by the collision of the Yinshan and Ordos Blocks. Zircons of the third group contain MLP granulite facies mineral inclusions of orthopyroxene + clinopyoxene + amphibole + plagioclase + quartz, similar to the zircons of the first group, but yield younger ages of ca. 1900 Ma, interpreted as the timing of the regional MLP granulite facies metamorphism that most likely occurred during the early stage of post-orogenic exhumation of the Daqingshan–Wulashan Complex. Zircons of the fourth group contain MLP amphibolite facies mineral inclusions of clinopyoxene + amphibole + plagioclase + quartz, and yield the youngest ages of ca. 1850 Ma, which probably represent the timing of the regional amphibolite facies metamorphism during the late stage of post-orogenic exhumation of the Daqingshan–Wulashan Complex. Combined with previous geological data of the Khondalite Belt, it is speculated that the multiple mafic magmatism and contemporaneous high-grade metamorphism of the Daqingshan–Wulashan Complex from the Khondalite Belt were most likely generated by an orogenic process involving early subduction–collision and late exhumation in an active continental margin arc.

This paper investigates the impact of stochastic capacity at the downstream bottleneck after a merge and the impact of merging behavior on the morning commuters’ departure-time patterns. The classic bottleneck theory is extended to include a uniformly distributed capacity and the commuters’ equilibrium departure patterns are derived for two different merging rules. The results show that uncertainty in the bottleneck capacity increases the commuters’ mean trip cost and lengthens the peak period, and that the system total cost is lower under give-way merging than under a fixed-rate merging. Capacity paradoxes with dynamic user responses are found under both merging rules.

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

The Zhifu Group exposed in the northeastern Jiaobei Terrane is subdivided from base to top into the Laoyeshan, Bingying and Dongkou formations, and comprises mainly quartzites and muscovite- and tourmaline-bearing quartz schists. In order to define its provenance and depositional age, and to constrain the crustal growth and recycling of the source regions, we have conducted LA-ICP-MS U–Pb dating and in situ Hf isotopic study of detrital zircons from three quartz schists samples collected from the Zhifu Group. Most of the analyzed zircon grains have oscillatory zoning and Th/U ratios >0.4, suggesting igneous origins. 270 detrital zircons U–Pb analyses yield U–Pb ages of 1709–3679 Ma that cluster into three major age populations of 1.7–1.9 Ga with a peak at 1844 Ma, 1.9–2.0 Ga with a peak at 1936 Ma and 2.4–2.55 Ga with a peak at 2465 Ma, and two minor age populations of 2.2–2.35 and 2.6–2.7 Ga. The peaking age of 1844 Ma for the youngest age population indicates that the Zhifu Group must be deposited after 1844 Ma. Detrital zircons with ages of 1.7–2.35 Ga can be linked to pre- and post-tectonic polyphase magmatic events along the JLJB, and most of the zircons have negative ɛ Hf( t ) values from +1.76 to −18.02 and two-stage Hf model ages ( T DM2 ) concentrating at ∼2.7–3.0 Ga, indicating that source rocks of these zircons were derived from recycling of ancient crusts. Detrital zircons with ages of 2.4–2.9 Ga may have been sourced from the Archean granitoid (mainly TTG) gneisses in the Jiaobei Terrane, and these zircons have ɛ Hf( t ) values from +6.4 to −7.53 and T DM2 of 2.6–3.4 Ga (peak at ∼2.7–3.0 Ga), suggesting that source rocks of these zircons were mainly derived from juvenile crusts associated with a major crustal growth at ∼2.7–3.0 Ga, and a limited amount of ancient crustal component. The two detrital zircons with ages of 3631 and 3679 Ma have negative ɛ Hf( t ) values of −4.42 and −1.51 and T DM2 of 4137 and 4000 Ma, respectively, implying the recycling of ancient continental crust (>3.6 Ga) and crustal growth prior to 4.1 Ga in the NCC.