Scholar iON
Academic Synthesis
The scholarly papers on "math.DS" explore distinct yet significant technological and methodological advancements in their respective fields. Nakazawa et al. (2019) contribute to experimental physics by developing a versatile analog front-end for TPCs, which is crucial for detecting dark matter and studying neutrino oscillations, showcasing the need for innovative ASIC designs to meet stringent electronic requirements in varying operational environments. Conversely, Erban et al. (2007) provide a foundational guide to stochastic simulations in reaction-diffusion processes, emphasizing the importance of stochastic methods over deterministic models in capturing the complexities of molecular interactions. Both papers highlight the significance of advancing technological and computational methodologies to enhance the precision and applicability of scientific research in physics and chemistry, underscoring the interdisciplinary nature of contemporary scientific inquiries.
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.