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Reaction networks, or equivalently Petri nets, are a general framework for describing processes in which entities of various kinds interact and turn into other entities. In chemistry, where the reactions are assigned ‘rate constants’, any reaction network gives rise to a nonlinear dynamical system called its ‘rate equation’. Here we generalize these ideas to ‘open’ reaction networks, which allow entities to flow in and out at certain designated inputs and outputs. We treat open reaction networks as morphisms in a category. Composing two such morphisms connects the outputs of the first to the inputs of the second. We construct a functor sending any open reaction network to its corresponding ‘open dynamical system’. This provides a compositional framework for studying the dynamics of reaction networks. We then turn to statics: that is, steady state solutions of open dynamical systems. We construct a ‘black-boxing’ functor that sends any open dynamical system to the relation that it imposes between input and output variables in steady states. This extends our earlier work on black-boxing for Markov processes.

Time and frequency response of an avalanche quantum dot infrared photodetector (A-QDIP) operating at long infrared (IR) wavelengths is calculated and the effect of its structure on the dynamic behavior is studied. For this purpose, the rate equations of different regions are numerically solved considering the boundary conditions. Results show that detector with long multiplication region has a slower time response. Also frequency analysis predicts a 3-dB bandwidth above 100 GHz for a device with multiplication length of 200 nm. Gain bandwidth product (GBP) is calculated and a value of about 1000 GHz is obtained. Effect of charge layer doping on dynamic response of detector is also studied and results show that increase in doping improves the GBP while the bandwidth is reduced. We also study the effect of quantum dots of absorption region on frequency response of device and results show that longer electron relaxation time into quantum dot decreases the bandwidth of detector.

Passively Q-switched fiber laser (PQFL) has great potential applications in remote sensing, ranging, and optical communications. However, the PQFLs were seldom studied in view of both theory and experiment. This paper is dedicated to make up for this shortcoming. On the one hand, by describing the coupling rate equations of the PQFL system, the Q-switched pulse output with a modulation frequency of 17.61 kHz and a modulation period of 56.8 μs was obtained at 140 mW pump power. On the other hand, an erbium-doped PQFL whose performance is tunable by controlling the pump power and polarization state was constructed by using a single-walled carbon nanotube (SWCNT) as the saturable absorber (SA). The Q-switched pulse with a repetition rate of 17.61 kHz and a signal-to-noise ratio of 50.2 dB was output at a pump power of 140 mW. The theoretical simulation results were in good agreement with the experimental results. It was also verified from such two aspects that the repetition rate of the output pulse of PQFL was approximately proportional to the pump power. This research promotes the theory and design of PQFL.

Dissipative soliton crystals (the so-called soliton combs) form in Kerr microresonators as a result of the competition between the group-velocity dispersion and the Kerr nonlinearity on one hand, and the balance of cavity loss by an external pump on the other hand. In some physical contexts, the loss can fluctuate within the microresonator cavity, inducing a saturable-absorption process which impacts the dynamics of the optical field. In this study, dissipative soliton crystals are investigated in a Kerr optical microresonator with spatially fluctuating loss. The underlying mathematical model consists of a modified Lugiato–Lefever equation with a space-dependent loss, coupled to a rate equation for the fluctuating loss. Adopting an ansatz that describes the optical-field envelope as a complex function of real amplitude and real phase with a characteristic modulation frequency, the mathematical model is reduced to a set of first-order nonlinear ordinary differential equations which are solved numerically. Simulations suggest that when the homogeneous cavity loss is small enough, the impact of loss fluctuation on the soliton-comb profile is rather moderate. The effect of loss fluctuations becomes noticeable when the homogeneous loss is sizable, with the recovery time of the induced saturable-absorption process being reasonably long to promote a slow saturable absorption. An analysis of the influence of the detuning on the amplitude and phase of the dissipative soliton crystal, as well as on the spatial variation of the loss for a fixed value of the characteristic frequency, is taken into consideration in the study.

Recent theoretical studies on network robustness have focused primarily on attacks by random selection and global vision, but numerous real-life networks suffer from proximity-based breakdown. Here we introduce the multi-hop generalized core percolation on complex networks, where nodes with degree less than $k$ and their neighbors within $L$-hop distance are removed progressively from the network. The resulting subgraph is referred to as $G(k,L)$-core, extending the recently proposed $Gk$-core and classical core of a network. We develop analytical frameworks based upon generating function formalism and rate equation method, showing for instance continuous phase transition for $G(2,1)$-core and discontinuous phase transition for $G(k,L)$-core with any other combination of $k$ and $L$. We test our theoretical results on synthetic homogeneous and heterogeneous networks, as well as on a selection of large-scale real-world networks. This unravels, e.g., a unique crossover phenomenon rooted in heterogeneous networks, which raises a caution that endeavor to promote network-level robustness could backfire when multi-hop tracing is involved.

Due to its mechanical properties and ease of use, vinyl ester resin is enjoying increasing consideration. This resin normally is produced by reaction between epoxy resin and unsaturated carboxylic acid. In the present study, bis-phenol A based epoxy resin and methacrylic acid was used to produce vinyl ester resin. The reaction was conducted under both stoichiometric and non-stoichiometric conditions in the presence of triphenylphosphine as catalyst. The stoichiometric and non-stoichiometric experiments were conducted at 95, 100, 105 and 110°C and at 90 and 95°C respectively. The first order rate equation and mechanism based rate equation were examined. Parameters are evaluated by least square method. A comparison of mechanism based rate equation and experimental data show an excellent agreement. Finally, Arrhenius equation and activation energy were presented.

2µm solid laser running at room temperature can be widely applied in many fields like optical communication, medical cure, air pollution monitoring, and is also an ideal pumping source for mid-infrared optical parameter oscillator, further more, it's safe for human eyes. To achieve above objectives, higher peak power and shorter pulse duration laser is desirable. Q switched pulse laser is an effective approach to meet the above requirements. For the development and optimization of laser system, it is a practical choice to use laser modeling to predict the influence of various parameters for laser performance. For given parameters, rate equation for Q switched Tm:Ho laser pumped by diode was obtained and used to predict the change of population densities in various manifolds. When pump pulse energy is 14J and pulse width is 40µs, output signal pulse energy and width are 1.19mJ and about 600ns, respectively. The model can be used to find the potential laser systems that meet application requirements.