Mar

23

Thu

Title: Simulating Rotating Detonation Rocket Engines

Abstract: Most rocket engines are designed to avoid the formation of detonation waves, due to the tendency of such waves to cause damage inside the engine. However, incorporating detonations into rocket design has the potential to improve engine performance — rotating detonation rocket engines aim to harness this potential, but the associated rapid fluctuations in temperature and pressure make the devices difficult to analyze experimentally. These challenges increase the importance of models that are capable of reproducing and explaining the large-scale behavior that can be observed in experiments. We use a series of simulations to explore how changing nozzle geometries affects detonation dynamics inside the combustion chamber, and show that the simulations capture experimentally-observed wave behavior. The simulations further demonstrate that, although the addition of a nozzle increases engine thrust, the changes in engine behavior can be detrimental to overall engine performance.

Apr

3

Mon

Location: **KELLER 313**

**Title:** SEQUENT CALCULUS FOR CLASSICAL LOGIC PROBABILIZED

**Abstract:** Gentzen’s approach to deductive systems, and Carnap’s and Popper’s treatment of probability in logic were two fruitful ideas that appeared in logic of the mid-twentieth century. By combining these two concepts, the notion of sentence probability, and the deduction relation formalized in the sequent calculus, we introduce the notion of ‘probabilized sequent’ $\Gamma\vdash_a^b\Delta$ with the intended meaning that “the probability of truthfulness of $\Gamma\vdash\Delta$ belongs to the interval $[a,b]$”. This method makes it possible to define a system of derivations based on ‘axioms’ of the form $\Gamma_i\vdash_{a_i}^{b_i}\Delta_i$, obtained as a result of empirical research, and then infer conclusions of the form $\Gamma\vdash_a^b\Delta$. We discuss the consistency, define the models, and prove the soundness and completeness for the defined

probabilized sequent calculus.

## University of Hawaiʻi at Mānoa