From Derrida's random energy model to branching random walks: from 1 to 3

We study the extremes of a class of Gaussian fields with in-built hierarchical structure. The number of scales in the underlying trees depends on a parameter alpha in [0,1]: choosing alpha=0 yields the random energy model by Derrida (REM), whereas alpha=1 corresponds to the branching random walk (BRW). When the parameter alpha increases, the level of the maximum of the field decreases smoothly from the REM- to the BRW-value. However, as long as alpha<1 strictly, the limiting extremal process is always Poissonian.Comment: 12 pages, 1 figur

On concavity of TAP free energy in the SK model

We analyse the Hessian of the Thouless-Anderson-Palmer (TAP) free energy for the Sherrington-Kirkpatrick model, below the de Almeida-Thouless line, evaluated in Bolthausen's approximate solutions of the TAP equations. We show that while its empirical spectrum weakly converges to a measure with negative support, positive outlier eigenvalues occur for some $(\beta,h)$ below the AT line. In this sense, TAP free energy may lose concavity in the order parameter of the theory, i.e. the random spin-magnetisations, even below the AT line. Possible interpretations of these findings within Plefka's expansion of the Gibbs potential are not definitive and include the following: i) either higher order terms shall not be neglected even if Plefka's first convergence criterion (yielding, in infinite volume, the AT line) is satisfied, ii) Plefka's first convergence criterion (hence the AT line) is necessary yet hardly sufficient, or iii) Bolthausen's magnetizations do not approximate the TAP solutions sufficiently well up to the AT line.Comment: 29 pages, 1 figur

AMP algorithms and Stein's method: Understanding TAP equations with a new method

We propose a new iterative construction of solutions of the classical TAP equations for the Sherrington-Kirkpatrick model, i.e. with finite-size Onsager correction. The algorithm can be started in an arbitrary point, and converges up to the AT line. The analysis relies on a novel treatment of mean field algorithms through Stein's method. As such, the approach also yields weak convergence of the effective fields at all temperatures towards Gaussians, and can be applied, upon proper alterations, to all models where TAP-like equations and a Stein-operator are available.Comment: 38 page

Analysis of the interaction of Spray G and in-cylinder flow in two optical engines for late gasoline direct injection

This is the author's version of a work that was accepted for publication in International Journal of Engine Research. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published as https://doi.org/10.1177/1468087419881535.[EN] An investigation of the interaction between the in-cylinder flow and the spray topology in two spray-guided direct injection optical engines is reported. The bulk flow field in the combustion chamber is characterized using particle image velocimetry. Geometrical parameters such as the axial penetration and the spray angle of the liquid spray are measured using Mie scatter imaging and/or diffuse back-illumination. The measured parameters are compared with data from a constant volume chamber available in the literature. For a late injection strategy, the so-called ECN Spray G standard condition, the mean values of the spray penetration do not seem to be significantly perturbed by the in-cylinder flow motion until the plumes approach the piston surface. However, spray probability maps reveal that cycle-to-cycle fluctuations of the spatial distribution of the liquid spray are affected by the magnitude of the in-cylinder flow. Particle image velocimetry during injection shows that the flow field in the vicinity of the spray plumes is heavily influenced by air entrainment, and that an upward flow in-between spray plumes develops. Consistent with previous research that demonstrated the importance of the latter flow structure for the prevention of spray collapse, it is found that increased in-cylinder flow magnitudes due to increased intake valve lifts or engine speeds enhance the spray-shape stability. Compared with cases without injection, the influence of the spray on the in-cylinder flow field is still noticeable approximately 2.5 ms after the start of injection.The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The work at UDE was funded by the Research Association for Combustion Engines eV (FVV, Frankfurt/Main, project 1203). TUD kindly acknowledges generous support by Deutsche Forschungsgemeinschaft through SFB/Transregio 150 (project number 237267381-TRR150).Geschwindner, C.; Kranz, P.; Welch, C.; Schmidt, M.; Bohm, B.; Kaiser, SA.; De La Morena, J. (2020). Analysis of the interaction of Spray G and in-cylinder flow in two optical engines for late gasoline direct injection. International Journal of Engine Research. 21(1):169-184. https://doi.org/10.1177/1468087419881535S169184211Alkidas, A. C. (2007). Combustion advancements in gasoline engines. Energy Conversion and Management, 48(11), 2751-2761. doi:10.1016/j.enconman.2007.07.027Costa, M., Marchitto, L., Merola, S. S., & Sorge, U. (2014). Study of mixture formation and early flame development in a research GDI (gasoline direct injection) engine through numerical simulation and UV-digital imaging. Energy, 77, 88-96. doi:10.1016/j.energy.2014.04.114Zhao, F., Lai, M.-C., & Harrington, D. . (1999). Automotive spark-ignited direct-injection gasoline engines. Progress in Energy and Combustion Science, 25(5), 437-562. doi:10.1016/s0360-1285(99)00004-0Moreira, A. L. N., Moita, A. S., & Panão, M. R. (2010). Advances and challenges in explaining fuel spray impingement: How much of single droplet impact research is useful? Progress in Energy and Combustion Science, 36(5), 554-580. doi:10.1016/j.pecs.2010.01.002Oh, H., & Bae, C. (2013). Effects of the injection timing on spray and combustion characteristics in a spray-guided DISI engine under lean-stratified operation. Fuel, 107, 225-235. doi:10.1016/j.fuel.2013.01.019Park, C., Kim, S., Kim, H., & Moriyoshi, Y. (2012). Stratified lean combustion characteristics of a spray-guided combustion system in a gasoline direct injection engine. Energy, 41(1), 401-407. doi:10.1016/j.energy.2012.02.060Stiehl, R., Schorr, J., Krüger, C., Dreizler, A., & Böhm, B. (2013). In-Cylinder Flow and Fuel Spray Interactions in a Stratified Spray-Guided Gasoline Engine Investigated by High-Speed Laser Imaging Techniques. Flow, Turbulence and Combustion, 91(3), 431-450. doi:10.1007/s10494-013-9500-xPiock, W. F., Befrui, B., Berndorfer, A., & Hoffmann, G. (2015). Fuel Pressure and Charge Motion Effects on GDi Engine Particulate Emissions. SAE International Journal of Engines, 8(2), 464-473. doi:10.4271/2015-01-0746Fansler, T. D., Reuss, D. L., Sick, V., & Dahms, R. N. (2015). Invited Review: Combustion instability in spray-guided stratified-charge engines: A review. International Journal of Engine Research, 16(3), 260-305. doi:10.1177/1468087414565675Drake, M. C., & Haworth, D. C. (2007). Advanced gasoline engine development using optical diagnostics and numerical modeling. Proceedings of the Combustion Institute, 31(1), 99-124. doi:10.1016/j.proci.2006.08.120Fansler, T. D., Stojkovic, B., Drake, M. C., & Rosalik, M. E. (2002). Local fuel concentration measurements in internal combustion engines using spark-emission spectroscopy. Applied Physics B: Lasers and Optics, 75(4-5), 577-590. doi:10.1007/s00340-002-0954-0Peterson, B., Reuss, D. L., & Sick, V. (2014). On the ignition and flame development in a spray-guided direct-injection spark-ignition engine. Combustion and Flame, 161(1), 240-255. doi:10.1016/j.combustflame.2013.08.019Schiffmann, P., Reuss, D. L., & Sick, V. (2017). Empirical investigation of spark-ignited flame-initiation cycle-to-cycle variability in a homogeneous charge reciprocating engine. International Journal of Engine Research, 19(5), 491-508. doi:10.1177/1468087417720558Sementa, P., Maria Vaglieco, B., & Catapano, F. (2012). Thermodynamic and optical characterizations of a high performance GDI engine operating in homogeneous and stratified charge mixture conditions fueled with gasoline and bio-ethanol. Fuel, 96, 204-219. doi:10.1016/j.fuel.2011.12.068Song, J., & Park, S. (2015). EFFECT OF INJECTION STRATEGY ON THE SPRAY DEVELOPMENT PROCESS IN A SINGLE-CYLINDER OPTICAL GDI ENGINE. Atomization and Sprays, 25(9), 819-836. doi:10.1615/atomizspr.2015012018Parrish, S. E., Zhang, G., & Zink, R. J. (2012). Liquid and Vapor Envelopes of Sprays from a Multi-Hole Fuel Injector Operating under Closely-Spaced Double-Injection Conditions. SAE International Journal of Engines, 5(2), 400-414. doi:10.4271/2012-01-0462Rachakonda, S. K., Paydarfar, A., & Schmidt, D. P. (2018). Prediction of spray collapse in multi-hole gasoline direct-injection fuel injectors. International Journal of Engine Research, 20(1), 18-33. doi:10.1177/1468087418819527Blessinger, M., Manin, J., Skeen, S. A., Meijer, M., Parrish, S., & Pickett, L. M. (2014). Quantitative mixing measurements and stochastic variability of a vaporizing gasoline direct-injection spray. International Journal of Engine Research, 16(2), 238-252. doi:10.1177/1468087414531971Sphicas, P., Pickett, L. M., Skeen, S. A., & Frank, J. H. (2017). Inter-plume aerodynamics for gasoline spray collapse. International Journal of Engine Research, 19(10), 1048-1067. doi:10.1177/1468087417740306Lacey, J., Poursadegh, F., Brear, M. J., Gordon, R., Petersen, P., Lakey, C., … Ryan, S. (2017). Generalizing the behavior of flash-boiling, plume interaction and spray collapse for multi-hole, direct injection. Fuel, 200, 345-356. doi:10.1016/j.fuel.2017.03.057Westlye, F. R., Penney, K., Ivarsson, A., Pickett, L. M., Manin, J., & Skeen, S. A. (2017). Diffuse back-illumination setup for high temporally resolved extinction imaging. Applied Optics, 56(17), 5028. doi:10.1364/ao.56.005028Payri, R., Salvador, F. J., Martí-Aldaraví, P., & Vaquerizo, D. (2017). ECN Spray G external spray visualization and spray collapse description through penetration and morphology analysis. Applied Thermal Engineering, 112, 304-316. doi:10.1016/j.applthermaleng.2016.10.023Kranz, P., & Kaiser, S. A. (2019). LIF-based imaging of preferential evaporation of a multi-component gasoline surrogate in a direct-injection engine. 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A Wide-field High Resolution HI Mosaic of Messier 31: I. Opaque Atomic Gas and Star Formation Rate Density

We have undertaken a deep, wide-field HI imaging survey of M31, reaching a maximum resolution of about 50 pc and 2 km/s across a 95x48 kpc region. The HI mass and brightness sensitivity at 100 pc resolution for a 25 km/s wide spectral feature is 1500 M_Sun and 0.28 K. Our study reveals ubiquitous HI self-opacity features, discernible in the first instance as filamentary local minima in images of the peak HI brightness temperature. Local minima are organized into complexes of more than kpc length and are particularly associated with the leading edge of spiral arm features. Just as in the Galaxy, there is only patchy correspondence of self-opaque features with CO(1-0) emission. Localized opacity corrections to the column density exceed an order of magnitude in many cases and add globally to a 30% increase in the atomic gas mass over that inferred from the integrated brightness under the usual assumption of negligible self-opacity. Opaque atomic gas first increases from 20 to 60 K in spin temperature with radius to 12 kpc but then declines again to 20 K beyond 25 kpc. We have extended the resolved star formation law down to physical scales more than an order of magnitude smaller in area and mass than has been possible previously. The relation between total-gas-mass- and star-formation-rate-density is significantly tighter than that with molecular-mass and is fully consistent in both slope and normalization with the power law index of 1.56 found in the molecule-dominated disk of M51 at 500 pc resolution. Below a gas-mass-density of about 5 M_Sun/pc^2, there is a down-turn in star-formation-rate-density which may represent a real local threshold for massive star formation at a cloud mass of about 5x10^4 M_Sun.Comment: Accepted for publication in ApJ, 34 pages, 20 figure