A heterogeneous parasitic-mutualistic model of mistletoes and birds on a periodically evolving domain.

The extension of quantum theory to time-varying space domains is often challenging, since domain evolution frequently results in non-autonomous and non-adiabatic evolution of corresponding wave function for a given quantum mechanical system. For generic domain evolution, we show that the evolution of the wave function is determined by the mixing of spatial modes or bound states, and this is the instigator for non-adiabatic wave function evolution. For some applications, it is desirable to retain adiabaticity of the wave function and with knowledge of how domain evolution causes loss of adiabaticity, we construct a control potential—comprising a harmonic term and a volume expansion/contraction term—which may be used to counteract this feature of domain evolution, thereby preserving wave function adiabaticity throughout the time evolution of the space domain. Examples of quantum mechanical systems on time-varying space domains are used to illustrate the theory, including analogues of classical examples such as the hydrogen atom and quantum harmonic oscillator on unbounded stretched space and a particle in a stretched and translated box. We also discuss how to combine our approach with numerical simulations, using the compressed hydrogen atom confined within an evolving sphere to demonstrate the method.

An extended heterogeneous car-following model with the consideration of the drivers’ different psychological headways

Theory and experiment of nonlinear vibrations and dynamic snap-through phenomena for bi-stable asymmetric laminated composite square panels under foundation excitation

This paper deals with a reaction-diffusion model on a periodically and isotropically evolving domain in order to explore the diffusive dynamics of Aedes aegypti mosquito, where we divide it into two sub-populations: the winged population and an aquatic form. The spatial-temporal risk index $ R_0(\rho) $ depending on the domain evolution rate $ \rho(t) $ as well as its analytical properties is investigated. The long-time behaviors of the periodic solutions under the condition $ R_0(\rho)>1 $ and $ R_0(\rho)\leq1 $ are explored, respectively. Moreover, we consider the specific case where $ \rho(t)\equiv1 $ to better understand the impact of the periodic evolution rate on the persistence and extinction of Aedes aegypti mosquito. Numerical simulations further verify our analytical results that the periodic domain evolution has a significant impact on the dispersal of Aedes aegypti mosquito.

The diffusive logistic equation on periodically evolving domains

Vulnerable transmission lines are weaknesses in the power system security, which are easy to induce cascading failures and blackouts. To identify the vulnerable transmission lines with the increasing complexity of the interconnected power grid, the authors propose a vulnerable transmission line identification method using the depth of the K ‐shell (Ks) decomposition under power transfer (named the DKsPS method), which fully considers the dynamic characteristics of the power transfer and transmission capability after the power grid fault. This method establishes a correlation network based on the correlation matrix of transmission lines under the N − 1 check and then identifies the vulnerable transmission lines by using the modified Ks decomposition. Numerical simulations on both the IEEE‐39 bus system and the Northeast China power grid verify the validity and accuracy of the DKsPS method.

Deep saline aquifers have strong heterogeneity under natural conditions, which affects the migration of carbon dioxide (CO2) injection into the reservoir. How to characterize the heterogeneity of rock mass is of great significance to research the CO2 migration law during CO2 storage. A method is proposed to construct different heterogeneous models from the point of view of whether the amount of data is sufficient or not, the wholly heterogeneous model with sufficient data, the deterministic multifacies heterogeneous model which is simplified by lithofacies classification, and the random multifacies heterogeneous model which is derived from known formation based on transfer probability theory are established, respectively. Numerical simulation is carried out to study the migration law of CO2 injected into the above three heterogeneous models. The results show that the migration of CO2 in heterogeneous deep saline aquifers shows a significant fingering flow phenomenon and reflect the physical process in CO2 storage; the migration law of CO2 in the deterministic multifacies heterogeneous model is similar to that in the wholly heterogeneous model and indicates that the numerical simulation of simplifying the wholly heterogeneous structure to the lithofacies classification structure is suitable for simulating the CO2 storage process. The random multifacies heterogeneous model based on the transfer probability theory accords with the development law of sedimentary formation and can be used to evaluate the CO2 migration law in unknown heterogeneous formations. On the other hand, by comparing the dry-out effect of CO2 in different heterogeneous models, it is pointed out that the multifacies characterization method will weaken the influence due to the local homogenization of the model in small-scale research; it is necessary to refine the grid and subdivide the lithofacies of the local key area elements to eliminate the research error. The research results provide feasible references and suggestions for the heterogeneous modeling of the missing data area and the simplification of large-scale heterogeneous models.

Fully heterogeneous three-dimensional SAGD simulation models are computationally expensive to evaluate, necessitating the need for simpler models that can capture the overall physics of the process while reducing computation time. This paper sheds some insights into the effect of permeability heterogeneity on SAGD performance, and presents both a physics-based upscaling technique that considers the unique geometry of the steam-plume during the SAGD process, as well as a statistical upscaling scheme based on variable selection and multivariate non-linear regression. Full physics, two-dimensional SAGD simulations were performed using several stochastic shale models representing different proportions. Subsequently, the vertical variability in the models was averaged using a flow-based upscaling technique to obtain an effective anisotropic ratio. The performance of the upscaled models was assessed using full physics numerical simulation. It was observed that the upscaled anisotropic models gave different results compared to the fully heterogeneous models. The discrepancy between the heterogeneous and anisotropic models is largely due to upscaling. Two approaches were formulated to address this. The first approach iteratively adjusts the anisotropic permeability of the 2D model until a match to the 3D heterogeneous model was achieved. Then a non-linear regression model between the heterogeneous model parameters and the history-matched anisotropic permeability was formulated. In the second approach, an upscaling method considering the flux due to convergent flow towards a line sink was developed. A key result presented in this paper is that heterogeneity plays a significant role in SAGD performance. Factors such as shale correlation length and proportion affect both the initial steam rise and the lateral spread of the chamber. Traditional upscaling techniques assuming power averages or flow-based assuming uniform flow over a plane are inadequate for approximating heterogeneous models. Statistical schemes such as the one presented in this paper perform much better in capturing the recovery characteristics of the SAGD process in heterogeneous media. Considerations such as optimum well pair spacing and optimal steam-oil ratio for maximizing bitumen recovery require quick evaluation of multiple scenarios and that may be possible using the approach presented in the paper.

The switching mechanism and the thermal process of a gallium arsenide (GaAs) photoconductive semiconductor switch (PCSS) with an opposed-contact is investigated by numerical simulation of the two-dimensional (2D) structure using temperature-dependent physical parameters of the carriers in GaAs. Triggered by a low-energy laser pulse, the PCSS switches on due to the formation and evolution of multiple powerful avalanche domains. The 2D evolving characteristics of the avalanche domains on the two sides of photogenerated plasma during the switching transient are comparatively analysed. It is found that the ionizing centre of each domain moves with the drift of accumulated electrons inside the domain. Meanwhile, the evolution of avalanche domains causes an obvious thermal effect along the drift path of ionizing centres during the switch-on stage of PCSS. Then, the temperature keeps increasing at the edge of the anode and cathode although the switching current starts dropping after the conduction of PCSS, and finally peaks at ∼491 K and ∼541 K, respectively. The simulation results indicate that the 2D filamentary current flows along the drift path of ionizing centres inside the avalanche domains, which finally leads to filamentary erosion after continuous operation of the PCSS. On the basis of numerical simulation, an experiment with opposed-contact GaAs PCSS with 2.5 mm gap at the bias field of ∼90 kV cm−1 is performed. The thermal erosion is found to initially accumulate at the edge of the electrodes and then spreads along the current channel into the GaAs substrate, which is in accordance with the simulation results and analysis.

A Monte-Carlo computer simulation technique was employed to study the details of the small intestinal transit flow in the gastrointestinal (GI) tract. A heterogeneous tube model was constructed using a numerical computer simulation technique. The model was built from first principles and included several heterogeneous characteristics of the GI tract structure. We used a random, dendritic-type internal structure representing the villi of the GI tract. The small intestinal transit flow was simulated using two diffusion models, namely, the blind ant and the myopic ant models, which are different models to account the elapse of time, and which are both based on statistical properties of random walks. For each one of the models we utilize two types of biased random walk, placing different emphasis in the motion towards the output of the tube. We monitored the flow of the drug in terms of Monte-Carlo time steps (MCS) through the tube walls and dendritic villi present. The frequency of the transit times was dependent on the structure of the dendritic villi and on the type of biased random walk. The small intestinal flow profile of literature data for a large number of drugs was well characterized by the heterogeneous model using, as parameters, a certain number of villi per unit length of the tube and specific characteristics for both types of the biased random walk. A correspondence between the MCS and real time units was achieved. The transit process of the oral dosage forms in the GI tract can be reproduced with the heterogeneous model developed. This model can be used to study GI absorption phenomena.

Bocheng Bao Dr Bocheng Bao from the Changzhou University in China, talks to us about the work behind the paper ‘Chaotic bursting in memristive diode bridge coupled Sallen-Key low-pass filter’, page 1104. The appearance of real memristors is gradually generating far-reaching influences in the field of circuit fundamental theory, but they are not expected to be commercially available in the near future. To solve this problem, numerous emulators behaving like memristors have been presented for the development of memristor-based application circuits. Nevertheless, most of the emulators, using masses of ready-made discrete components, imitate the theoretical characteristics. Only the circuits implemented with operational amplifiers and analogue multipliers, as well as those composed of diode-bridge with RC or LC filters, have been utilised for hardware experiments of memristor-based chaotic circuits. Since a simple low-order memristive chaotic circuit using minimal discrete components can serve as a teaching paradigm in mathematical and experimental demonstrations of dynamical phenomena, it is a research topic of significant value to seek such memristive chaotic circuits and thereby reveal these phenomena. I have more than 20 years' experience of working in industry and have served as a senior engineer and general manager in several enterprises. In 2008, I returned to college and took the nascent concept of memristor and memristive chaotic circuits as the main content of my PhD thesis. I joined the School of Information Science and Engineering, Changzhou University, China, in 2011, and currently I am working on theoretical analyses, numerical simulations and hardware experiments of memristor-based application circuits and switching DC-DC converters. Due to the similar characteristics between memristor and neuron synapse, memristors can be applied to the artificial neural network (ANNs). A special bursting phenomenon has been discovered in some memristor-based chaotic circuits recently, which indicates that the communication activity in biological neurons and endocrine cells can be modeled using a memristor-based chaotic circuit. It is quite important to seek new memristor-based chaotic circuits with special dynamics, which is effective in helping us understand the dynamical properties of ANNs. By parallel coupling a memristive diode bridge with an inductor into a second-order Sallen-Key low-pass filter (LPF), we have created a novel third-order memristive chaotic oscillator with simple circuit realisation. From this, a point-cycle chaotic bursting phenomenon is numerically simulated and experimentally captured. It is highly interesting that the striking chaotic bursting phenomenon can also be discovered in a third-order simple memristive chaotic oscillator, which will provide great convenience for future research on the mechanism of chaotic bursting. The Sallen-Key LPF-based chaotic circuit, to the knowledge of the authors, has not previously been reported in any literature. The previously reported memristor-based chaotic circuits are at least third-order non-autonomous or fourth-order autonomous, leading to greater complexity of electrical connection topologies or algebraic system structures. However, the proposed novel memristive chaotic oscillator is only third-order and its circuit realisation is extremely simple. Due to its simple circuit realisation, this oscillator could be used for future construction and investigation of memristor-based ANNs. Our research group is now working on theoretical analysis, numerical simulations and hardware experiments of memristor-based application circuits including chaotic oscillating circuits and artificial neural networks. In the past few years, we have constructed some novel memristor-based application circuits and revealed several specific dynamic phenomena of coexisting self-excited/hidden multiple attractors, coexisting self-excited/hidden infinitely many attractors, and periodic/chaotic bursting therein. Memristor-based chaotic circuits, particularly memristor-based ANNs, belong to a completely new research field within circuit fundamental theory and engineering applications. We think this field will be an extremely important topic for researchers over the next ten years and many new achievements will be reported. We sincerely look forward to seeing how our lifestyles will be completely changed owing to the widespread applications of memristor-based ANNs in the near future!

Dynamic phenomena in long chain interconnections of Chua's chaotic circuits are studied. We show via numerical simulations that a large variety of behavior is typically encountered in such systems. Most interesting observations include transmission delay of chaotic "waves", disorganized propagation, synchronized states, and "chaotic interference". Results of first laboratory tests are also included.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Capture of stochastic P-bifurcation in a delayed mechanical centrifugal governor

Peak current and valley current controlled switching DC-DC converters show symmetrical dynamic phenomenon within a wide circuit parameter range. The unified discrete iterative map model of peak current and valley current controlled buck, boost, and buck-boost converters is established, and the unified piecewise smooth iterative map and their corresponding characteristic equations are also derived. The forward and inverse bifurcation diagrams and Lyapunov exponent spectrums with duty ratio as parameter are obtained by numerical simulation. The research results indicate that the bifurcation diagrams and Lyapunov exponent of peak and valley current-mode controlled switching converters show symmetrical dynamic phenomenon corresponding to a symmetrical point or a symmetrical axis. The numerical simulation results are verified by the time-domain simulation, which further indicates that with the duty ratio varying, the peak and valley current-mode controlled switching converter reveals a symmetrical dynamic phenomenon, or a symmetrical dynamic phenomenon accompanying an asymmetrical dynamic phenomenon, or an asymmetrical dynamic phenomenon.

In this paper, a deterministic Lymphatic Filariasis (LF) model with preventive measures in human and treatment barriers is developed and analysed to assess the impact of treatment barriers on the transmission dynamics of LF in endemic areas. Qualitative analysis and numerical simulation are presented in terms of the reproduction number of the model in the absence and presence of treatment barriers. It is established that the treatment intervention has shown improvement in the reduction of LF infection in the population. Furthermore, in the absence of treatment barriers the model guaranteed disease extinction behaviour, while in the presence of treatment barriers the model shows disease persistence behaviour when . This means that in the presence of treatment barriers there is coexistence of the stable disease-free state and the stable persistent state of the disease when . The persistence behaviour may be due to plentiful infected individuals who accumulate in the community due to treatment barriers while the disease has no natural recovery. The numerical simulations are performed to complement the analytical results.