Scholar iON
Academic Synthesis
The scholarly works on "math.FA" encompass diverse applications in physics, particularly focusing on analog front-end development for TPCs and stochastic modeling of reaction-diffusion processes. Nakazawa et al. (2019) describe the design and testing of a versatile ASIC for negative-ion and dual-phase liquid argon TPCs, crucial for dark matter detection and neutrino studies, highlighting the technological advancements in low-noise, wide-dynamic range electronics. Erban et al. (2007) provide foundational insights into stochastic simulations, emphasizing the transition from deterministic to stochastic models in reaction-diffusion processes. Both papers underscore the significance of precise modeling—whether in electronics for particle detection or biochemical simulations—for advancing experimental and theoretical understanding in their respective fields.
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.