Scholar iON
Academic Synthesis
The scholarly papers on "math.SP" present significant advancements in the fields of detector technology and stochastic simulations, highlighting both the engineering and mathematical aspects of scientific investigations. Nakazawa et al. (2019) detail the development of a versatile analog front-end for TPCs, which is crucial for enhancing the detection capabilities in dark matter searches and neutrino studies, underscoring the importance of ASIC design for accommodating diverse operating conditions. Meanwhile, Erban et al. (2007) provide a foundational guide to stochastic simulations in reaction-diffusion processes, bridging the gap between stochastic and deterministic models and offering essential tools like the Gillespie algorithm for chemical reactions. Together, these studies underscore the multidisciplinary nature of scientific research, where advances in electronics and mathematical modelling play pivotal roles in expanding the frontiers of particle physics and chemical kinetics.
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.