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1. Equality cases of the Alexandrov–Fenchel inequality are not in the polynomial hierarchy

   https://doi.org/10.1017/fmp.2024.20  

   Chan, Swee Hong; Pak, Igor (January 2024, Forum of Mathematics, Pi)

   Abstract Describing the equality conditions of theAlexandrov–Fenchel inequality[Ale37] has been a major open problem for decades. We prove that in the case of convex polytopes, this description is not in the polynomial hierarchy unless the polynomial hierarchy collapses to a finite level. This is the first hardness result for the problem and is a complexity counterpart of the recent result by Shenfeld and van Handel [SvH23], which gave a geometric characterization of the equality conditions. The proof involves Stanley’s [Sta81]order polytopesand employs poset theoretic technology. 

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2. Influence of fine particle content in debris flows on alluvial fan morphology

   https://doi.org/10.1038/s41598-022-24397-x  

   Chen, Tzu-Yin Kasha; Hung, Chi-Yao; Mullenbach, Jared; Hill, Kimberly (December 2022, Scientific Reports)

   Abstract Alluvial fans are large-scale depositional structures commonly found at the base of mountain ranges. They are relatively soil-rich compared to the rocky terrains, or catchment areas, from which their material originates. When frequented by debris flows (massive, muddy, rocky flows) they contribute significantly to local hazards as they carry focused, collisional, fast-moving materials across alluvial fans, unpredictable in size, speed, and direction. We research how fine particle content in debris flows correlates with directional changes, i.e., debris flow avulsions. Toward this, we analyzed field data from two neighboring alluvial fans in the White Mountains (California, USA) that exhibit dramatically different topographies despite their proximity and associated similar long-term climates. Informed by these measurements, we performed long-term and incremental alluvial fan experiments built by debris flows with systematically-varied fine particle content. We found that (1) decreasing fine particle content increases the variability of fan slopes and associated channelization dynamics, and (2) for all mixtures longer-term continuous alluvial fan experiments form more complex surface channelizations than repeated flows for the same total time, indicating the importance ofbothparticle sizes and timescales on alluvial fan surface morphology. 

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3. Avulsion dynamics determine fluvial fan morphology in a cellular model

   https://doi.org/10.1130/G51138.1  

   Martin, Harrison K.; Edmonds, Douglas A. (June 2023, Geology)

   Abstract Fluvial fans are large, low-gradient depositional systems that occur in sedimentary basins worldwide. Fluvial fans can represent much of the geologic record of foreland basins, create hazards, and record paleoclimate and tectonic signals. However, we lack an understanding of how fluvial fans grow into the variety of shapes observed around the world. We explored this aspect using a cellular model of foreland basin landscape evolution with rules for sediment transport, river avulsion, and floodplain processes. We tested the hypothesis that avulsion dynamics, namely, avulsion trigger period and abandoned channel dynamics, are a primary control on fluvial fan development. We found that shorter trigger periods lead to rounder planform fluvial fan shapes because, between avulsions, channel aggradation (and thus avulsion setup) propagates shorter distances from the upstream boundary along channel pathways. This prioritizes lateral sediment dispersion, creating shorter, rounder fans, over sediment delivery further into the basin, which would create elongated fans. Modeled fans with abandoned channel attraction (but not repulsion) generated a commonly observed abrupt fan boundary marked by a transition from distributary to tributary channel patterns. While fluvial fans are thought to be linked to climate, they can occur anywhere that rivers aggrade, lose lateral confinement, and preserve alluvial topography. Instead, fluvial fans might be more recognizable in environments that frequently trigger avulsions and preserve abandoned channels that capture future avulsions. 

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4. Rates and processes controlling periglacial alluvial fan formation: Implications for martian fans

   https://doi.org/10.1130/B36459.1  

   Palucis, Marisa C.; Morgan, A.M.; Strauss, J.V.; Rivera-Hernandez, F.; Marshall, J.A.; Menio, E.; Miller, R. (July 2022, GSA Bulletin)

   Alluvial fans are found across a range of climates and are built from a combination of fluvial and debris flow processes. Correct identification of process is critical to reconstructing the climate and water histories of alluvial fans on Earth and Mars. Theory and data from subaerial Earth fans are often used to estimate paleoflow discharges and sediment fluxes for martian fans; however, most terrestrial work has been conducted on fans that are in hot, dry climates with runoff sourced from rainfall. This differs from the prevailing interpretation that martian fans were sourced from snowmelt under warming periglacial conditions. To characterize processes and rates of periglacial fan formation, we conducted a field-based study of the Black Mountain alluvial fan in the Aklavik Range, Canada. We observed active fluvial bedload transport as well as several small debris flows that had initiated from ice-filled gullies. Following a runoff event of ∼0.005 mm/hr to ∼0.2 mm/hr across the fan, we estimated sediment fluxes of ∼0.04 m3/hr. Under bankfull conditions, we estimated runoff rates between ∼0.01 mm/hr to ∼14 mm/hr and corresponding sediment fluxes of ∼0.3 m3/hr to ∼550 m3/hr. This suggests that moderate flow events, well below the maximum runoff production rates suggested for Mars, are capable of entraining and transporting appreciable amounts of sediment by fluvial processes. However, sedimentological and geomorphological observations suggest that ∼67% of the fan was deposited fluvially; the remainder was deposited by mass flows. Our results emphasize the need to take care in interpreting martian sedimentary processes and climate from fan surface morphology alone. 

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5. Thermal Performance Evaluation of Three Types of Novel End-of-Aisle Cooling Systems

   https://doi.org/10.1115/IPACK2017-74016  

   Sahini, Manasa; Agonafer, Dereje; Pandiyan, Vijayalan (August 2017, ASME 2017 International Technical Conference and Exhibition on Packaging and Integration of Electronic and Photonic Microsystems)

   Data centers house a variety of compute, storage, network IT hardware where equipment reliability is of utmost importance. Heat generated by the IT equipment can substantially reduce its service life if Tjmax, maximum temperature that the microelectronic device tolerates to guarantee reliable operation, is exceeded. Hence, data center rooms are bound to maintain continuous conditioning of the cooling medium becoming large energy consumers. The objective of this work is to introduce and evaluate a new end-of-aisle cooling design which consists of three cooling configurations. The key objectives of close-coupled cooling are to enable a controlled cooling of the IT equipment, flexible as well as modular design, and containment of hot air exhaust from the cold air. The thermal performance of the proposed solution is evaluated using CFD modeling. A computational model of a small size data center room has been developed. Larger axial fans are selected and placed at rack-level which constitute the rack-fan wall design. The model consists of 10 electronic racks each dissipating a heat load of 8kw. The room is modeled to be hot aisle containment i.e. the hot air exhaust exiting for each row is contained and directed within a specific volume. Each rack has passive IT with no server fans and the servers are cooled by means of rack fan wall. The cold aisle is separated with hot aisle by means of banks of heat exchangers placed on the either sides of the aisle containment. Based on the placement of rack fans, the design is divided to three sub designs — case 1: passive heat exchangers with rack fan walls; case 2: active heat exchangers (HXs coupled with fans) with rack fan walls; case 3: active heat exchangers (hxs coupled with fans) with no rack fans. The cooling performance is calculated based on the thermal and flow parameters obtained for all three configurations. The computational data obtained has shown that the case 1 is used only for lower system resistance IT. However, case 2 and Case 3 can handle denser IT systems. Case 3 is the design that can consume lower fan energy as well as handle denser IT systems. The paper also discusses the cooling behavior of each type of design. 

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