| Title: | Development of simplified kinetics models of the hydrocarbon fuel for oblique detonation wave phenomena based on detailed mechanism and shock tube data |
| Time: | 11:00:00 - 12:00:00 |
| Place: | Room 4504 (Lift 25/26) |
| Abstract: | This study develops simplified chemical kinetics mechanisms for hydrocarbon fuels to efficiently simulate oblique detonation wave (ODW) flows. The mechanisms demonstrate that controlling ignition delay time and heat release based on Chapman-Jouguet (CJ) conditions is crucial for successful ODW simulations. Key findings include: (1) computational mesh size determines whether cellular structures stabilize or shift downstream; (2) intermediate species and fuel-air ratios significantly influence CJ plane formation, affecting detonation energy and stability. The proposed ATM reconstruction method combined with AUSM+ effectively captures flow discontinuities. These results provide insights for optimizing oblique detonation wave engine (ODWE) designs. |
| Title: | Tuning-free Estimation and Inference of Cumulative Distribution Function under Local Differential Privacy |
| Time: | 15:00:00 - 16:00:00 |
| Place: | Room 2302 (Lift 17/18) |
| Abstract: | We present a new algorithm for estimating Cumulative Distribution Function (CDF) values under Local Differential Privacy (LDP), leveraging an unexpected connection between LDP and the classical current status problem in survival analysis. Our approach develops constrained isotonic estimation tools using binary queries, achieving uniform and L₂ error bounds for full CDF curve estimation. The method exhibits three key properties: (1) Error bounds improve with denser grids, with the estimator asymptotically normal; (2) Theoretical analysis reveals smooth variation in error bounds as grid density increases relative to sample size n; (3) The constrained isotonic estimator enables deterministic computation without hyperparameter tuning or stochastic optimization. Numerical experiments and mathematical proofs validate these theoretical and computational advantages. |
| Title: | Knots and Primes, and a Pro-2 Tensor Product of Vector Spaces |
| Time: | 15:00:00 - |
| Place: | Room 222, Lady Shaw Building |
| Abstract: | The Alexander polynomial can be understood as encoding the first homology of the infinite cyclic cover of the exterior of a knot. Is there a reasonable analogous understanding of its categorification, knot Floer homology? In particular, what is the sutured Floer homology of the infinite cyclic cover of the exterior of a knot? Based on a computation using bordered Floer bimodules, it seems that the answer, if it made sense, would take the form of an infinite tensor product of bimodules. But such objects do not behave well at all. Inspired by a parallel story in algebraic number theory, we are led to consider instead profinite tensor products (corresponding to profinite cyclic covers), which, once defined, will have much better properties. In this talk, I will explain the story above, and outline the construction of a pro-2 tensor product as well as some potential future directions. This is joint work in progress with David Treumann. |