The CODE ambiguity-fixed clock and phase bias analysis products: generation, properties, and performance

The generation and use of GNSS analysis products that allow—particularly for the needs of single-receiver applications—precise point positioning with ambiguity resolution (PPP-AR) are becoming more and more popular. A general uncertainty concerns the question on how the necessary phase bias information should be provided to the PPP-AR user. Until now, each AR-enabling clock/bias representation method had its own practice to provide the necessary bias information. We have generalized the observable-specific signal bias (OSB) representation, as introduced in Villiger (J Geod 93:1487–1500, 2019) originally exclusively for pseudorange measurements, to carrier phase measurements. The existing common clock (CC) approach has been extended in a way that OSBs allowing for flexible signal and frequency handling between multiple GNSS become possible. Advantages of the proposed OSB-based PPP-AR approach are: GNSS biases can be provided in a consistent way for phase and code measurements and it is capable of multi-GNSS and suitable for standardization. This new, extended PPP-AR approach has been implemented by the Center for Orbit Determination in Europe (CODE). CODE clock products that adhere to the integer-cycle property have been submitted to the International GNSS Service (IGS) since mid of 2018 for three analysis lines: Rapid, Final, and MGEX (Multi-GNSS Extension). Ambiguity fixing is performed not only for GPS but also for Galileo. The integer-cycle property of between-satellite clock differences is of fundamental importance when comparing satellite clock estimates among various analysis lines, or at day boundaries. Both kinds of comparisons could be exploited at a very high level of consistency. Any retrieved comparison essentially indicated a standard deviation for between-satellite clocks from CODE of the order of 5 ps (1.5 mm in range). Finally, the integer-cycle property that may be recovered between the CODE Final clock and the accompanying bias product of consecutive daily sessions (using clock estimates additionally provided for the second midnight epoch) allows us to deduce GPS satellite clock and phase bias information that is consistent and continuous with respect to carrier phase observation data over two, three, or, in principle, yet more days. Phase-based clock densification from initially estimated integer-cycle-conform clock corrections at intervals of 300 s to 30 s (5 s in case of our Final clock product) is a matter of particular interest. Based on direct product comparisons and GRACE K-band ranging (KBR) data analysis, the quality of accordingly densified clock corrections could be confirmed to be on a level similar to that of “anchor” (300 s) clock corrections.

Giga-Cycle Property of a New Age-Hardened Aluminium Alloy Containing Excess Solute Magnesium

The giga-cycle property of a newly developed Al alloy, which contains 0.5wt.% excess Mg solute compared to a standard age-hardened 6061 alloy (6061-T6), was investigated by using smooth specimens subjected to ultrasonic fatigue. The fatigue strength of the new alloy was higher than that of a normal 6061 alloy particularly at relatively low stress amplitude level. Several analyses (surface crack observation, fractography, FIB cross-sectioning, etc.) were also conducted to reveal the micro-mechanism of the observed strength properties. The following results were obtained: i) No fatigue limit was confirmed for both 6061 and new alloy. ii) Total life (Nf) of 6061 and new alloys was determined by a single fatigue crack initiated from a surface PSB crack. iii) Crack initiation resistance defined by N25 (number of cycles to reach ρ = 25 mm-2, where ρ is the PSB crack number density) for new alloy was higher than that of 6061. iv) The higher fatigue strength of new alloy was explained by the effect of excess Mg solute which increased the resistance against the formation of PSB cracks.

Mixtures of TiO2·0.2H2O and LiFePO4 as Li-ion Battery Cathode Materials

Mixtures of TiO2•0.2H2O (HTO) and LiFePO4 were prepared via three main composite methods: 2-2 series model, 2-2 parallel model and 3-3 model. HTO had been reported to exhibit high specific capacity (~200 mAh/g at 1 C) as well as excellent cycle property, whereas its voltage plateau was too low (about 1.7 V vs. Li) as a cathode material. LiFePO4 was a promising cathode material for its high voltage plateau (about 3.4 V vs. Li), low cost and high specific capacity (~150 mAh/g at 1 C). However, because of its low conductivity, the rate property as well as cycle property was limited. The mixtures of HTO and LiFePO4 were considered to combine the advantages of both materials. By comparison, the 2-2 parallel model excelled in both rate property and cycle property. Its specific capacity can reach as high as 220 mAh/g with a high specific energy of 450 Wh/Kg at 0.1 C. Even after cycled 200 times at 2 C, the capacity can still be higher than 100 mAh/g. CV measurements and a combined constant current and constant voltage tests supported a two plateaus process for 2-2 parallel model. The charge-discharge voltage gap increased for the 2-2 parallel composites, which was supposed to be related to the interface. In general, the specific energy was much higher than HTO while the specific capacity as well as cycle property was much better than LiFePO4 as a cathode material. .

Monopoly Pricing over Time and the Timing of Investments

We consider a monopoly producing a good whose demand grows over time. Whatever the price policy which is adopted, the monopolist invests in order to meet the resulting demand growth. She can only invest in indivisible factory units. We identify the optimal price policy, and the ensuing optimal sequence of investment time points the monopoly selects through time. We show that this sequence satisfies the constant cycle property observed under capacity expansion for an exogenous increase in demand (Manne, 1961).