Advanced High-Temperature Freeze & Leak-Resistant Molten Salt Valve for 750C Reliable Operation - Poster.
Abstract not provided.
Armijo, Kenneth Miguel↗
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Preliminary Designs for a Freeze-Safe Valve Stem Heat Pipe.
Abstract not provided.
Carlson, Matthew David↗
Freeze Casting SiC-SiC Composites
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11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Occurrence of Warm Freezing Rain: Observation and Modelling Study
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54 ENVIRONMENTAL SCIENCES↗
Ice-nucleating agents in sea spray aerosol identified and quantified with a holistic multimodal freezing model
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54 ENVIRONMENTAL SCIENCES↗
Improved Diagnosis of Precipitation Type with LightGBM Machine Learning
Abstract Existing precipitation-type algorithms have difficulty discerning the occurrence of freezing rain and ice pellets. These inherent biases are not only problematic in operational forecasting but also complicate the development of model-based precipitation-type climatologies. To address these issues, this paper introduces a novel light gradient-boosting machine (LightGBM)-based machine learning precipitation-type algorithm that utilizes reanalysis and surface observations. By comparing it with the Bourgouin precipitation-type algorithm as a baseline, we demonstrate that our algorithm improves the critical success index (CSI) for all examined precipitation types. Moreover, when compared with the precipitation-type diagnosis in reanalysis, our algorithm exhibits increased F1 scores for snow, freezing rain, and ice pellets. Subsequently, we utilize the algorithm to compute a freezing-rain climatology over the eastern United States. The resulting climatology pattern aligns well with observations; however, a significant mean bias is observed. We interpret this bias to be influenced by both the algorithm itself and assumptions regarding precipitation processes, which include biases associated with freezing drizzle, precipitation occurrence, and regional synoptic weather patterns. To mitigate the overall bias, we propose increasing the precipitation cutoff from 0.04 to 0.25 mm h −1 , as it better reflects the precision of precipitation observations. This adjustment yields a substantial reduction in the overall bias. Finally, given the strong performance of LightGBM in predicting mixed precipitation episodes, we anticipate that the algorithm can be effectively utilized in operational settings and for diagnosing precipitation types in climate model outputs. Significance Statement Freezing rain can have significant impacts on transportation and infrastructure, making accurate prediction of precipitation types crucial. In this study, we use a machine learning method known as LightGBM to predict precipitation types. We show that the new algorithm performs better than the existing methods for all precipitation types examined. Additionally, we compute a freezing-rain climatology over the eastern United States. Although the resulting climatology pattern corresponds well to observations, the algorithm overpredicts freezing-rain occurrence. We argue that this bias can be substantially reduced by increasing the precipitation cutoff from 0.04 to 0.25 mm h −1 . Overall, this work highlights the potential of the LightGBM algorithm for both weather forecasting and diagnosing precipitation types in climate models.
Meteorology & Atmospheric Sciences↗
Analysis of Experimental Ice Accretion Data and Assessment of a Thermodynamic Model During Ice Crystal Icing
This paper evaluates a thermodynamic ice crystal icing model that has been previously presented to describe the possible mechanisms of icing within the core of a turbofan jet engine. The model functions between two distinct ice accretions based on a surface energy balance: freeze-dominated icing and melt-dominated icing. Freeze-dominated icing occurs when liquid water (from melted ice crystals) freezes and accretes on a surface along with the existing ice of the impinging water and ice mass. This freeze-dominated icing is characterized as having strong adhesion to the surface. The amount of ice accretion is partially dictated by a freeze fraction, which is the fraction of impinging liquid water that freezes. Melt-dominated icing occurs as unmelted ice on a surface accumulates. This melt-dominated icing is characterized by weakly bonded surface adhesion. The amount of ice accumulation is partially dictated by a melt fraction, which is the fraction of impinging ice crystals that melts. Experimentally observed ice growth rates suggest that only a small fraction of the impinging ice remains on the surface, implying a mass loss mechanism such as splash, runback, bounce, or erosion. The fraction of mass loss must be determined in conjunction with the fraction of freezing liquid water or fraction of melting ice on an icing surface for a given ice growth rate. This mass loss parameter, however, along with the freeze fraction and melt fraction, are the only experimental parameters that are currently not measured directly. Using icing growth rates from ice crystal icing experiments, a methodology that has been previously proposed is used to determine these unknown parameters. This work takes ice accretion data from tests conducted by the National Aeronautics and Space Administration (NASA) at the Glenn Research Center in 2018 that examined the fundamental physics of ice crystal icing. This paper continues evaluation of the thermodynamic model from a previous effort, with additions to the model that account for sub-freezing temperatures that have been observed at the leading edge of the airfoil during icing. The predicted temperatures were generally in good agreement with measured temperatures. Other key findings include the total wet-bulb temperature being a good first order indicator of whether icing is freeze-dominated (sub-freezing values) or melt-dominated (above freezing). Maximum sticking efficiency values, the fraction of impinging mass that adheres to a surface, was calculated to be about 0.2, and retained this maximum value for a range of melt ratios (0.3 to 0.65 and possibly higher), which is defined as the ratio of liquid water content to total water content. Higher air velocities reduced the maximum sticking efficiency and shifted the icing regime to higher melt ratio values. Finally, the leading edge ice accretion angle was found to be related to ice growth (lower growth rates for smaller angles) and melt ratio (smaller melt ratios resulted in smaller angles, likely due to erosion effects).
Ice-Crystal Icing↗
Use of Microgravity to Control the Microstructure of Eutectics
This grant began in June of 1996. Its long term goal is to be able to control the microstructure of directionally solidified eutectic alloys, through an improved understanding of the influence of convection. The primary objective of the projects in the present grant is to test hypotheses for the reported influence of microgravity on the microstructure of eutectics. The prior experimental results on the influence of microgravity on the microstructure of eutectics have been contradictory. With lamellar eutectics, microgravity had a negligible effect on the microstructure. Microgravity experiments with fibrous eutectics sometimes showed a finer microstructure and sometimes a coarser microstructure. Most research has been done on the MnBi/Bi rod-like eutectic. Larson and Pirich obtained a two-fold finer microstructure both from microgravity and by use of a magnetic field to quench buoyancy-driven convection. Smith, on the other hand, observed no change in microgravity. Prior theoretical work at Clarkson University showed that buoyancy-driven convection in the vertical Bridgman configuration is not vigorous enough to alter the concentration field in front of a growing eutectic sufficiently to cause a measurable change in microstructure. We assumed that the bulk melt was at the eutectic composition and that freezing occurred at the extremum, i.e. with minimum total undercooling at the freezing interface. There have been four hypotheses attempting to explain the observed changes in microstructure of fibrous eutectics caused by convection: I .A fluctuating freezing rate, combined with unequal kinetics for fiber termination and branching. 2. Off-eutectic composition, either in the bulk melt due to an off-eutectic feed or at the freezing interface because of departure from the extremum condition. 3. Presence of a strong habit modifying impurity whose concentration at the freezing interface would be altered by convection. At the beginning of the present grant, we favored the first of these hypotheses and set out to test it both experimentally and theoretically. We planned the following approaches: I .Pass electric current pulses through the MnBi/Bi eutectic during directional solidification in order to produce an oscillatory freezing rate. 2. Directionally solidify the MnBi/Bi eutectic on Mir using the QUELD II gradient freeze furnace developed by Professor Smith at Queen's University. 3. Select another fibrous eutectic system for investigation using the Accelerated Crucible Rotation Technique to introduce convection. 4. Develop theoretical models for eutectic solidification with an oscillatory freezing rate. Because of the problems with Mir, we substituted ground-based experiments at Queen's University with QUELD II vertical and horizontal, with and without vibration of the furnace. The Al-Si system was chosen for the ACRT experiments. Three related approaches were used to model eutectic solidification with an oscillatory freezing rate. A sharp interface model was used to calculate composition oscillations at the freezing interface in response to imposed freezing rate oscillations.
Wilcox. William R.↗
Laboratory and field studies of ice-nucleating particles from open-lot livestock facilities in Texas
Abstract. In this work, an abundance of ice-nucleating particles (INPs) from livestock facilities was studied through laboratory measurements from cloud-simulation chamber experiments and field investigation in the Texas Panhandle. Surface materials from two livestock facilities, one in the Texas Panhandle and another from McGregor, Texas, were selected as dust proxies for laboratory analyses. These two samples possessed different chemical and biological properties. A combination of aerosol interaction and dynamics in the atmosphere (AIDA) measurements and offline ice spectrometry was used to assess the immersion freezing mode ice nucleation ability and efficiency of these proxy samples at temperatures above −29 ∘C. A dynamic filter processing chamber was also used to complement the freezing efficiencies of submicron and supermicron particles collected from the AIDA chamber. For the field survey, periodic ambient particle sampling took place at four commercial livestock facilities from July 2017 to July 2019. INP concentrations of collected particles were measured using an offline freezing test system, and the data were acquired for temperatures between −5 and −25 ∘C. Our AIDA laboratory results showed that the freezing spectra of two livestock dust proxies exhibited higher freezing efficiency than previously studied soil dust samples at temperatures below −25 ∘C. Despite their differences in composition, the freezing efficiencies of both proxy livestock dust samples were comparable to each other. Our dynamic filter processing chamber results showed on average approximately 50 % supermicron size dominance in the INPs of both dust proxies. Thus, our laboratory findings suggest the importance of particle size in immersion freezing for these samples and that the size might be a more important factor for immersion freezing of livestock dust than the composition. From a 3-year field survey, we measured a high concentration of ambient INPs of 1171.6 ± 691.6 L−1 (average ± standard error) at −25 ∘C for aerosol particles collected at the downwind edges of livestock facilities. An obvious seasonal variation in INP concentration, peaking in summer, was observed, with the maximum at the same temperature exceeding 10 000 L−1 on 23 July 2018. The observed high INP concentrations suggest that a livestock facility is a substantial source of INPs. The INP concentration values from our field survey showed a strong correlation with measured particulate matter mass concentration, which supports the importance of size in ice nucleation of particles from livestock facilities.
58 GEOSCIENCES↗
Spatiotemporal evolution of melt ponds on Arctic sea ice
Melt ponds on sea ice play an important role in the Arctic climate system. Their presence alters the partitioning of solar radiation: decreasing reflection, increasing absorption and transmission to the ice and ocean, and enhancing melt. The spatiotemporal properties of melt ponds thus modify ice albedo feedbacks and the mass balance of Arctic sea ice. The Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) expedition presented a valuable opportunity to investigate the seasonal evolution of melt ponds through a rich array of atmosphere-ice-ocean measurements across spatial and temporal scales. In this study, we characterize the seasonal behavior and variability in the snow, surface scattering layer, and melt ponds from spring melt to autumn freeze-up using in situ surveys and auxiliary observations. We compare the results to satellite retrievals and output from two models: the Community Earth System Model (CESM2) and the Marginal Ice Zone Modeling and Assimilation System (MIZMAS). During the melt season, the maximum pond coverage and depth were 21% and 22 ± 13 cm, respectively, with distribution and depth corresponding to surface roughness and ice thickness. Compared to observations, both models overestimate melt pond coverage in summer, with maximum values of approximately 41% (MIZMAS) and 51% (CESM2). This overestimation has important implications for accurately simulating albedo feedbacks. During the observed freeze-up, weather events, including rain on snow, caused high-frequency variability in snow depth, while pond coverage and depth remained relatively constant until continuous freezing ensued. Both models accurately simulate the abrupt cessation of melt ponds during freeze-up, but the dates of freeze-up differ. MIZMAS accurately simulates the observed date of freeze-up, while CESM2 simulates freeze-up one-to-two weeks earlier. This work demonstrates areas that warrant future observation-model synthesis for improving the representation of sea-ice processes and properties, which can aid accurate simulations of albedo feedbacks in a warming climate.
54 ENVIRONMENTAL SCIENCES↗
Use of Microgravity to Control the Microstructure of Eutectics
This grant began in June of 1996. Its long term goal is to be able to control the microstructure of directionally solidified eutectic alloys, through an improved understanding of the influence of convection. The primary objective of the present projects is to test hypotheses for the reported influence of microgravity on the microstructure of three fibrous eutectics (MnBi-Bi, InSb-NiSb, Al3Ni-Al). A secondary objective is to determine the influence of convection on the microstructure of other eutectic alloys. Two doctoral students and a masters student supported as a teaching assistant were recruited for this research. Techniques were developed for directional solidification of MnBi-Bi eutectics with periodic application of current pulses to produce an oscillatory freezing rate. Image analysis techniques were developed to obtain the variation in MnBi fiber spacing, which was found to be normally distributed. The mean and standard deviation of fiber spacing were obtained for several freezing conditions. Eighteen ampoules were prepared for use in the gradient freeze furnace QUELD developed at Queen's University for use in microgravity. Nine of these ampoules will be solidified soon at Queen's in a ground-based model. We hope to solidify the other nine in the QUELD that is mounted on the Canadian Microgravity Isolation Mount on MIR. Techniques are being developed for directional solidification of the Al-Si eutectic at different freezing rates, with and without application of accelerated crucible rotation to induce convection. For the first time, theoretical methods are being developed to analyze eutectic solidification with an oscillatory freezing rate. In a classical sharp-interface model, we found that an oscillatory freezing rate increases the deviation of the average interfacial composition from the eutectic, and increases the undercooling of the two phases by different amounts. This would be expected to change the volume fraction solidifying and the fiber spacing. Because of difficulties in tracking the freezing interfaces of the two solid phases, a phase-field model is also being developed. A paper demonstrating application of phase field methods to periodic structures has been submitted for publication.
Wilcox, William R.↗
Evaluation of a Thermodynamic Ice Crystal Icing Model Using Experimental Ice Accretion Data
This paper presents the evaluation of a thermodynamic ice crystal icing model, previously presented to describe the possible mechanisms of icing within the core of a turbofan jet engine. It has been proposed that there are two types of distinct ice accretions based on a surface energy balance: freeze-dominated icing and melt-dominated icing. In the former, ice accretion occurs where a freeze fraction (0 to 1) of melted ice crystals freezes on a surface, along with the existing ice of the impinging water and ice mass. This freeze-dominated icing is characterized by having strong adhesion to the surface. In the latter, icing occurs from accumulated unmelted ice on a surface, where a melt fraction (0 to 1) dictates the amount of unmelted impinged ice. This melt-dominated icing is characterized by weakly bonded surface adhesion. The experimentally observed ice growth rates suggest that only a small fraction of the impinging ice remains on the surface, implying a mass loss mechanism such as splash, runback, bounce, or erosion. This mass loss parameter must be determined in conjunction with the fraction of freezing liquid water or fraction of melting ice on an icing surface. This loss parameter, however, along with the freeze and melt fraction, are the only experimental parameters that are currently not measured directly. Using reported icing growth rates from published ice crystal icing experiments, a methodology is proposed to determine these unknown parameters. This work takes reported ice accretion data from tests conducted by the National Aeronautics and Space Administration (NASA) in 2016 and tests NASA collaborated on with the National Research Council (NRC) of Canada in 2012 that examined the fundamental physics of ice crystal icing. Those research efforts sought to generate icing conditions representative of those that occur inside a jet engine when ingesting ice crystals. This paper presents the fundamental equations of the thermodynamic model, the methodology used to determine the aforementioned unknown icing parameters, and results from model evaluation using experimental data. In addition, this paper builds on the previously proposed model by adding a transient conduction term to explain ice growth behavior at the onset of experimental tests that was observed to be different from steady-state ice growth that occurred later in the test run.With the addition of this energy term, this becomes a quasi-steady model. A key finding from this work suggests that mass loss fractions can exceed 0.90 for steady ice growth periods. In addition, due to conductive heat fluxes when using a warmer-than-freezing airfoil, lower mass loss fraction values were calculated during the initial transient period.
Ice-Crystal Ice Accretion↗
Dark matter isocurvature from curvature
Isocurvature fluctuations, where the relative number density of particle species spatially varies, can be generated from initially adiabatic, or curvature, fluctuations if the various species fall out of or were never in thermal equilibrium. The freezing of the thermal relic dark matter abundance is one such case, but for modes that are still outside the horizon the amplitude is highly suppressed and originates from the small change in the local expansion rate due to the local space curvature produced by the curvature fluctuation. We establish a simple separate-universe method for calculating this generation that applies to both freeze-in and freeze-out models, identify three critical epochs for this process, and give general scaling behaviors for the amplitude in each case: the freezing epoch, the kinetic decoupling epoch and matter-radiation equality. Freeze-out models are typically dominated by spatially modulated annihilation from the latter epochs and can generate much larger isocurvature fluctuations compared with typical freeze-in models, albeit still very small and observationally allowed by cosmic microwave background measurements. Here, we illustrate these results with concrete models where the dark matter interactions are vector or scalar mediated.
79 ASTRONOMY AND ASTROPHYSICS↗
Cold acclimation threshold induction temperatures of switchgrass ecotypes grown under a long and short photoperiod
Abstract Plants can cold acclimate to enhance their freezing tolerance by sensing declining temperature and photoperiod cues. However, the factors influencing genotypic variation in the induction of cold acclimation are poorly understood among perennial grasses. We hypothesized that the more northern upland switchgrass ( Panicum virgatum L.) ecotype develops a higher degree of freezing tolerance by initiating cold acclimation at higher temperatures as compared with the coastal and southern lowland ecotypes. First, we determined the optimal method for assessing freezing tolerance and the length of exposure to 8/4°C required to induce the maximum level of freezing tolerance in the most northern upland and most southern lowland genotypes. We characterized the maximum freezing tolerance of eight uplands, three coastal and five lowland genotypes grown for 21 days at 8/4°C and a 10 or 16 h photoperiod. Next, we identified the temperature required to induce cold acclimation by exposing the 16 genotypes for 7 days at 20–6°C constant temperatures under a 10 or 16 h photoperiod. Cold acclimation initiated at temperatures 5 and 7°C higher in upland than in coastal and lowland genotypes. Among upland genotypes the shorter photoperiod induced cold acclimation at a 1°C higher temperature. Genotypes originating from a more northern latitude initiate cold acclimation at higher temperatures and develop higher maximum freezing tolerances. An earlier response to declining temperatures may provide the upland ecotype with additional time to prepare for winter and provide an advantage when plants are subjected to the rapid changes in fall temperature associated with injurious frosts.
60 APPLIED LIFE SCIENCES↗
Light $$Z^\prime $$ and Dirac fermion dark matter in the $$B-L$$ model
Abstract We consider a $$U(1)_{B-L}$$ U ( 1 ) B - L model with a $$Z^\prime $$ Z ′ portal Dirac fermion dark matter (DM) $$\chi $$ χ of low mass which couples very weakly to the $$B - L$$ B - L gauge boson $$Z^\prime $$ Z ′ . An arbitrary $$B-L$$ B - L charge $$Q\ne \pm 1, \pm 3$$ Q ≠ ± 1 , ± 3 of the DM $$\chi $$ χ ensures its stability. Motivated by the sensitivity reach of forthcoming “Lifetime Frontier” experiments, we focus on the $$Z^\prime $$ Z ′ mass, $$m_{Z^\prime }$$ m Z ′ , in the sub-GeV to few GeV range. To evaluate the DM relic abundance, we examine both the freeze-out and freeze-in DM scenarios. For the freeze-out scenario, we show that the observed DM abundance is reproduced near the $$Z^\prime $$ Z ′ resonance, $$m_\chi \simeq m_{Z^\prime }/2$$ m χ ≃ m Z ′ / 2 , where $$m_\chi $$ m χ is the DM mass. For the freeze-in scenario, we focus on $$m_\chi \ll m_{Z^\prime }$$ m χ ≪ m Z ′ . We show that for a fixed value of $$m_{Z^\prime }$$ m Z ′ , $$g_{BL}$$ g BL values roughly scale as 1/ Q to reproduce the observed DM abundance. For various Q values in the range between $$10^{-6}$$ 10 - 6 and $$10^2$$ 10 2 , we show that the gauge coupling values $$g_{BL}$$ g BL needed to reproduce the observed DM abundance lie in the search reach of future planned and/or proposed experiments such as FASER, Belle-II, LDMX, and SHiP. In the freeze-in case, the Q values to realize observable $$g_{BL}$$ g BL values are found to be much smaller than that in the freeze-out case.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Small field campaign: aerosol – ice formation closure pilot study. Final Report
Prediction of atmospheric ice formation from aerosol particles by heterogeneous nucleation represents one of the grand challenges in atmospheric science. Our insufficient predictive understanding of primary ice formation is the reason that climate models typically do not include heterogeneous ice nucleation with subsequent effects on climate uncertainty. Mixed-phase clouds, where supercooled water droplets and ice crystals coexist play globally an important role regulating climate. This is especially the case for the Arctic region that experiences the greatest warming due to climate change compared to other regions in the world. Immersion freezing initiated by ice-nucleating particles (INPs) in supercooled water droplets is recognized as the dominant primary ice formation pathway in mixed-phase cloud regimes. For this reason, it is crucial to evaluate our capability to predict immersion freezing for a given ambient aerosol population. The goal of this project is conducting a field-based pilot study at the U.S. DOE Atmospheric Radiation Measurement (ARM) user facility at Southern Great Plains (SGP) to evaluate our capability to predict the number concentration of aerosol particles that serve as INPs in the immersion freezing mode. Successful prediction of INP number concentrations is also termed “closure”. This field-observational approach represents a first-of-its kind attempt of an aerosol–ice formation closure study (AEROICESTUDY). Very few closure studies related to INPs have been conducted, and to our knowledge, none using robust size-resolved ambient aerosol composition measurements as a starting point. Achievement of aerosol–ice formation closure relies on our ability to characterize the ambient aerosol population with respect to particles size and composition and to determine INP number concentrations for specified freezing temperatures. This requires numerous online and offline instrumentation resulting in this pilot field campaign being a multi-institutional and community-collaborative effort. We chose the ARM SGP megasite for this first aerosol-ice formation closure pilot study due to its significant measurement capabilities available to obtain detailed physical characterization of the local aerosol population including size distribution, mass loading, and chemical composition of non-refractory aerosol particles. The overall objective of this project is to identify ice nucleation parameterizations that produce the most robust predictions of INP numbers and thus are best suited to be included in cloud and climate models. This objective includes the following goals for this field and laboratory-based project: i) What are the crucial aerosol physicochemical property measurements needed to accurately guide ice nucleation representations in models and long-term INP measurements? ii) What level of parameter details needs to be known to achieve aerosol–ice formation closure? iii) What are the leading causes for climate model bias in INP predictions? We found that the advances in our understanding of immersion freezing garnered over the last 20 years allowed us to yield partial and full closures of atmospheric immersion freezing from ambient aerosol particles. When the aerosol population is physicochemically complex and parameterizations for representative INP types are not yet available, we still struggle to accurately predict INP number concentrations. This project clearly demonstrates that with more laboratory and field measurements that are accompanied by particle composition analysis, the necessary datasets to achieve aerosol–ice formation closure for various locations will emerge, thus providing a robust foundation for guiding the representation of INPs in cloud and climate models.
54 ENVIRONMENTAL SCIENCES↗
Mechanisms of deterioration of nutrients phase 1
Experimental methods are studied by which freeze-dried foods of improved quality are produced. Considered are: (1) Factors effecting the loss of butanol from frozen aqueous food solutions during storage; (2) a freeze-drying microscope system for observing solidification processes in organic mixtures and aqueous inorganic salt solutions; (3) browning of high quality freeze-dried foods with minimal organoleptic and nutritional detoriation; (4) retention of PVP-n-propanol in freeze-dried food models; and (5) effects of freezing rate and sucrose immersion on taste and texture of freeze-dried apple slices.
Karel, M.↗
Development of the gametophyte of the fern Schizaea pusilla
Schizaea pusilla is a pteridophyte with several unique developmental characteristics. In contrast to most other fern species, S. pusilla gametophytes remain filamentous throughout their development, and the gametophytes are associated with an endophytic fungus which appears to be mycorrhizal. In terms of tropistic responses, apical filament cells of young gametophytes are negatively phototropic compared with germ filaments of other ferns which exhibit positive phototropism. Cryofixation (propane jet freezing and high-pressure freezing) in conjunction with freeze substitution electron microscopy was used to study young gametophytes. The results demonstrate that apical filament cells have a distinctive structural polarity and that rhizoids also can be successfully frozen by these methods. The cytoskeleton and endomembrane system were particularly well preserved in cryofixed cells. In addition, Schizaea gametophytes were used as a test system to evaluate potential artifacts of propane jet freezing and high pressure freezing. There was little apparent difference in ultrastructure between cells cryofixed by either freezing method. These gametophytes will be useful in determining the effectiveness of cryofixation techniques and as a model system in tip growth studies.
Non-NASA Center↗