Scholar iON
Academic Synthesis
The scholarly works presented explore distinct, yet complementary domains within the field of applied mathematics and engineering, focusing on technological advancements and computational methodologies. The first paper by Nakazawa et al. discusses the development of a prototype analog front-end designed for compatibility with both negative-ion and dual-phase liquid argon time projection chambers (TPCs), crucial for research in dark matter searches and neutrino studies. The paper highlights the engineering challenges and solutions, such as noise reduction and wide dynamic range, achieved through innovative ASIC design using 180-nm CMOS technology. In contrast, the second paper by Erban et al. provides an in-depth introduction to stochastic simulations for reaction-diffusion processes, detailing foundational techniques such as the Gillespie algorithm and exploring the interplay between stochastic and deterministic models. Together, these studies underscore the significant advancements in both hardware design for particle physics experiments and computational techniques for modeling complex biochemical processes, illustrating the interdisciplinary nature of modern applied mathematics research.
We report on the recent development of a versatile analog front-end compatible with a negative-ion $μ$-TPC for a directional dark matter search as well as a dual-phase, next-generation $\mathcal{O}$(10~kt) liquid argon TPC to study neutrino oscillations, nucleon decay, and astrophysical neutrinos. Although the operating conditions for negative-ion and liquid argon TPCs are quite different (room temperature \textit{vs.} $\sim$88~K operation, respectively), the readout electronics requirements are similar. Both require a wide-dynamic range up to 1600 fC, and less than 2000--5000 e$^-$ noise for a typical signal of 80 fC with a detector capacitance of $C_{\rm det} \approx 300$~pF. In order to fulfill such challenging requirements, a prototype ASIC was newly designed using 180-nm CMOS technology. Here, we report on the performance of this ASIC, including measurements of shaping time, dynamic range, and equivalent noise charge (ENC). We also demonstrate the first operation of this ASIC on a low-pressure negative-ion $μ$-TPC.
A practical introduction to stochastic modelling of reaction-diffusion processes is presented. No prior knowledge of stochastic simulations is assumed. The methods are explained using illustrative examples. The article starts with the classical Gillespie algorithm for the stochastic modelling of chemical reactions. Then stochastic algorithms for modelling molecular diffusion are given. Finally, basic stochastic reaction-diffusion methods are presented. The connections between stochastic simulations and deterministic models are explained and basic mathematical tools (e.g. chemical master equation) are presented. The article concludes with an overview of more advanced methods and problems.