Scholar iON
Academic Synthesis
The selected scholarly papers from the "math.CO" category encompass diverse applications of mathematical concepts in physical and biological systems. San-Martรญn's work explores the intricate dynamics of saddle-node bifurcation and intermittency cascades, enhancing our understanding of chaotic systems through the Myrberg-Feigenbaum point. Nakazawa et al. focus on the development of analog front-end electronics for TPCs used in dark matter detection and neutrino research, highlighting the challenges of designing versatile electronics for different operational environments. Erban, Chapman, and Maini provide a comprehensive guide to stochastic simulations in reaction-diffusion processes, bridging stochastic and deterministic modeling paradigms. Piekarski and Rewekant present a mathematical model for drug transport post-intravenous administration, emphasizing the interplay between drug binding, transport, and elimination processes. Collectively, these studies underscore the critical role of advanced mathematical techniques in elucidating complex phenomena across disciplines, from chaos theory to particle physics and pharmacokinetics.
The presence of saddle-node bifurcation cascade in the logistic equation is associated with an intermittency cascade; in a similar way as a saddle-node bifurcation is associated with an intermittency. We merge the concepts of bifurcation cascade and intermittency. The mathematical tools necessary for this process will describe the structure of the Myrberg-Feigenbaum point.
We report on the recent development of a versatile analog front-end compatible with a negative-ion $ฮผ$-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 $ฮผ$-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.
A mathematical model of a drug transport after rapid injection is given. It takes into account three processes: - drug plasma protein binding in central compartment - transport processes between the central compartment and the peripheral compartment - elimination of a drug from the central compartment. .