We present a terahertz quasi time domain spectroscopy (QTDS) system setup which is improved regarding cost and compactness. The diode laser is mounted directly onto the optical delay line, making the optical setup more compact. The system is operated using a Raspberry Pi and an additional sound card. This combination replaces the desktop/laptop computer, the lock-in-amplifier, the stage controller and the signal generator. We examined not only a commercially available stepper motor driven delay line, but also the repurposed internal mechanics from a DVD drive. We characterize the performance of the new system concept.
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http://dx.doi.org/10.1364/OE.23.021972 | DOI Listing |
Qual Theory Dyn Syst
November 2024
Division of Computational Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University, ul. St. Łojasiewicza 6, 30-348 Kraków, Poland.
Motivated by the study of recurrent orbits and dynamics within a Morse set of a Morse decomposition we introduce the concept of Morse predecomposition of an isolated invariant set within the setting of both combinatorial and classical dynamical systems. While Morse decomposition summarizes solely the gradient part of a dynamical system, the developed generalization extends to the recurrent component as well. In particular, a chain recurrent set, which is indecomposable in terms of Morse decomposition, can be represented more finely in the Morse predecomposition framework.
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April 2023
College of Mathematics and Systems Science, Xinjiang University, Ürümqi, 830017 People's Republic of China.
A tuberculosis (TB) epidemic model with Beddington-DeAngelis incidence and distributed delay is proposed to characterize the interaction between latent period, endogenous reactivation, treatment of latent TB infection, as well as relapse. The basic reproduction number is defined, and the globally asymptotic stability of disease-free equilibrium is shown when , while if the globally asymptotic stability of endemic equilibrium is also acquired. Theoretical results are validated through performing numerical simulations, wherein we detect that TB dynamic behavior between models with discrete and distributed delays could be same and opposite, and TB is more persistent in the model with distributed delay.
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April 2023
College of Science, China University of Petroleum (East China), Qingdao, 266580 People's Republic of China.
In this paper, we analyze a stochastic SIRC model with Ornstein-Uhlenbeck process. Firstly, we give the existence and uniqueness of global solution of stochastic SIRC model and prove it. In addition, the existence of ergodic stationary distributions for stochastic SIRC system is proved by constructing a suitable series of Lyapunov functions.
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December 2022
Instituto de Matemática e Estatística - UFRGS, Av. Bento Gonçalves, 9500, Porto Alegre, RS 91509-900 Brazil.
This paper introduces a theory of Thermodynamic Formalism for Iterated Function Systems with Measures (IFSm). We study the spectral properties of the Transfer and Markov operators associated to a IFSm. We introduce variational formulations for the topological entropy of holonomic measures and the topological pressure of IFSm given by a potential.
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December 2022
V.N.Karazin Kharkiv National University, Kharkiv, 61022 Ukraine.
We study a virus dynamics model with reaction-diffusion, logistic growth terms and a general non-linear infection rate functional response. The model has a distributed delay, including the case of state-selective delay. We construct a dynamical system in a Hilbert space and prove the existence of a finite-dimensional global attractor.
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