This paper introduces the Cross-frequency Amplitude Transfer Function (CATF), a model-free method for quantifying nonlinear stimulus-response interaction based on phase-locked amplitude relationship. The CATF estimates the amplitude transfer from input frequencies at stimulation signal to their harmonics/intermodulation at the response signal. We first verified the performance of CATF in simulation tests with systems containing a static nonlinear function and a linear dynamic, i.e., Hammerstein and Wiener systems. We then applied the CATF to investigate the second-order nonlinear amplitude transfer in the human proprioceptive system from the periphery to the cortex. The simulation demonstrated that the CATF is a general method which can well quantify nonlinear stimulus-response amplitude transfer for different orders of nonlinearity in Wiener or Hammerstein system configurations. Applied to the human proprioceptive system, we found a complicated nonlinear system behavior with substantial amplitude transfer from the periphery stimulation to cortical response signals in the alpha band. This complicated system behavior may be associated with the nonlinear behavior of the muscle spindle and the dynamic interaction in the thalamocortical radiation. This paper provides a new tool to identify nonlinear interaction in the nervous system. The results provide novel insight of nonlinear dynamics in the human proprioceptive system@en

Natural, artificial, and biological porous media can be seen everywhere in our daily lives. Transport phenomena in porous media, such as flow, diffusion, reaction, adsorption and deformation, are encountered in a wide variety of practical applications and scientific interests over widely disparate length scales, from molecular, to pore, core, and field scales. However, determination of transport properties in porous media remains a challenging issue. During the 12^th Annual Meeting of the International Society for Porous Media (InterPore), held online from August 31-September 4, 2020, advances on porous media science and engineering in very broad areas were presented. The meeting was attended by more than 750 participants from across the globe, and a significant milestone was achieved in the history of InterPore conferences due to its online interactive platform. Participants could access the pre-recorded talks, leave comments and questions, chat with each other, one week before the conference. Then, all the feedback related to a talk was discussed in the presence of the author during several Q&A sessions. Invited and Keynote talks were live, and were also recorded. Each Q&A session was moderated by two experts, who first reviewed the 8 contributions of their session and then summarized the questions for each talk. The author could further elaborate their work and answer the questions.

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The potential of well test technology is discussed in this paper to estimate the miscible condition and displacement fronts position during CO₂ flooding. To interpret the multiphase well test curve of CO₂ flooding process, an accurate compositional numerical model is developed in this study. The model includes fully EoS-based compositional nonlinear formulation, unstructured gridding and multi-segmented well. A systematic well test analysis of CO₂ flooding at different regimes, including immiscible, multi-contact miscible and first-contact miscible gas injection, was performed for hydrocarbon systems with different number of components. Based on the interpretation root cause analysis, proposed in this work, the specific characteristics of the well test curve of CO₂ flooding have been identified and described. These characteristics provide the guidance for the distinction among the different regime of CO₂ displacement. It was demonstrated that the most important characteristics stay invariant from the number of components involved into numerical study. Finally, a tangent line method has been proposed to detect the key point on the pressure derivative curve corresponding to a CO₂ front. This method allows to predict the displacement front position for problems of practical interest.

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Communication between neuronal populations is facilitated by synchronization of their oscillatory activity. Although nonlinearity has been observed in the sensorimotor system, its nonlinear connectivity has not been widely investigated yet. This study investigates nonlinear connectivity during the human stretch reflex based on neuronal synchronization. Healthy participants generated isotonic wrist flexion while receiving a periodic mechanical perturbation to the wrist. Using a novel cross-frequency phase coupling metric, we estimate directional nonlinear connectivity, including time delay, from the perturbation to brain and to muscle, as well as from brain to muscle. Nonlinear phase coupling is significantly stronger from the perturbation to the muscle than to the brain, with a shorter time delay. The time delay from the perturbation to the muscle is 33 ms, similar to the reported latency of the spinal stretch reflex at the wrist. Source localization of nonlinear phase coupling from the brain to the muscle suggests activity originating from the motor cortex, although its effect on the stretch reflex is weak. As such nonlinear phase coupling between the perturbation and muscle activity is dominated by the spinal reflex loop. This study provides new evidence of nonlinear neuronal synchronization in the stretch reflex at the wrist joint with respect to spinal and transcortical loops.

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