Two Nonlinear Positivity-Preserving Finite Volume Schemes for Three-Dimensional Heat Conduction Equations on General Polyhedral Meshes

In this article we present two types of nonlinear positivity-preserving finite volume (PPFV) schemes for a class of three-dimensional heat conduction equations on general polyhedral meshes. First, we present a new parameter selection strategy on the one-sided flux and establish a nonlinear PPFV scheme based on a two-point flux with higher efficiency. By comparing with the scheme proposed in [H. Xie, X. Xu, C. Zhai, H. Yong, Commun. Comput. Phys. 24 (2018) 1375–1408], our scheme avoids the assumption that the values of auxiliary unknowns are nonnegative, which makes our interpolation formulae suitable to be constructed by existing approaches with high accuracy and well robustness (e.g., the finite element method), thus enhancing the adaptability to distorted meshes with large deformations. Then we derive a linear multi-point flux involving combination coefficients and, via the Patankar trick, obtain another nonlinear PPFV scheme that is concise and easy to implement. The selection strategy of combination coefficients is also provided to improve the convergence behavior of the Picard procedure. Furthermore, the existence and positivity-preserving properties of these two nonlinear PPFV solutions are proved. Numerical experiments with the discontinuous diffusion scalar as well as discontinuous and anisotropic diffusion tensors are given to confirm our theoretical findings and demonstrate that our schemes both can achieve ideal-order accuracy even on severely distorted meshes.     

Impact of Power Transformer Oil-Temperature on the Measurement Uncertainty of All-Acoustic Non-Iterative Partial Discharge Location

In this paper, the influence of the variation in transformer oil temperature on the accuracy of the all-acoustic non-iterative method for partial discharge location in a power transformer is researched. The research can improve power transformers’ testing and monitoring, particularly given the large transformer oil temperature variations during real-time monitoring. The research is based on quantifying the contribution of oil temperature to the standard combined measurement uncertainty of the non-iterative algorithm by using analytical, statistical, and Monte Carlo methods. The contribution can be quantified and controlled. The contribution varied significantly with different mutual placements of partial discharge and acoustic sensors. The correlation between the contribution and the mean distance between partial discharge and acoustic sensors was observed. Based on these findings, the procedure to quantify and control the contribution in practice was proposed. The procedure considers the specificity of the method’s mathematical model (the assumption that the oil temperature is constant), the non-iterative algorithm’s nonlinearity, and the large variations in transformer oil temperature. Existing studies did not consider the significant effect of the oil temperature on the combined measurement uncertainty of partial discharge location influenced by those phenomena. The research is limited to partial discharge located in the transformer oil.     

An optimal control problem with nonlocal conditions for the weakly nonlinear hyperbolic equation

Some problems in physics and engineering may be effectively described in terms of nonlocal problems for differential equations. These nonlocal conditions show that some data on the boundary cannot be measured, and therefore some averaged data of the problem are given. In the present paper, necessary conditions of optimality in the optimal control problem are derived for hyperbolic equations with nonlocal boundary conditions. Copyright © 2012 John Wiley & Sons, Ltd.     

Nonlinear sensory cortex response to simultaneous tactile stimuli in writer's cramp.

Writer's cramp is a task-specific dystonia that leads to involuntary hand postures during writing. Abnormalities of sensory processing may play a pathophysiological role in this disorder. Electrophysiology studies in a monkey model of focal dystonia have revealed de-differentiation of sensory maps and the existence of single cells in hand regions of area 3b with enlarged receptive fields that extend to the surfaces of more than one digit. These changes may lead to abnormal processing of simultaneous sensory inputs. To study abnormal processing of simultaneous sensory information in adult humans with writer's cramp, we used functional magnetic resonance imaging to compare the response in primary sensory cortex with simultaneous tactile stimulation of the index and middle finger, with the response to stimulation of each finger alone. We tested five patients with writer's cramp and seven unaffected (normal) subjects. In the normal subjects, a linear combination of the activation patterns for individual finger stimulation predicts the pattern of activity for combined stimulation with 12% error. In writer's cramp patients, the linear combination predicted the combined stimulation pattern with 30% error. Results indicate a nonlinear interaction between the sensory cortical response to individual finger stimulation in writer's cramp. This altered interaction may contribute to the motor abnormalities.     

Minimization of EOG artefacts from corrupted eeg signals using a neural network approach

In this paper, we propose a neural network (NN) approach to the enhancement of EEG signals in the presence of EOG artefacts. We recast the EEG enhancement problem into the optimization framework by developing an appropriate cost function. The cost function is nothing but the energy in the enhanced EEG signal obtained through a nonlinear filter formulation, unlike the conventionally-used linear filter formulation. The minimization property of feedback-type neural networks is exploited to solve this problem. An analysis has been performed to characterize the stationary points of the suggested energy function. The hardware set-up of the developed neural network has also been derived. The optimum nonlinear filter coefficients obtained from this minimization algorithm are used to estimate the EOG artefact which is then subtracted from the corrupted EEG signal, sample by sample, to get the artefact minimized signal. The time plots as the LP spectrum show that the proposed method is very effective. Thus the power and efficacy of the NN approach have been exploited for the purpose of minimizing EOG artefacts from corrupted EEG signals.     

一类工业固定床反应器热点温度的非线性自适应控制

以工业邻二甲苯氧化非绝热管式固定床反应器为研究对象，通过正交配置集中化建立了一个降阶非线性动态模型。直接以降低模型作为开环状态观测器及新型的非线性自适应控制算法设计控制器，设计了该类固定床反应器热点温度的非线性自适应控制系统。仿真结果表明，该热点温度控制系统具有良好的跟踪性能、抗干扰性能和鲁棒性能。     

A Biophysical Model of the Inner Hair Cell: The Contribution of Potassium Currents to Peripheral Auditory Compression

The term peripheral auditory compression refers to the fact that the whole range of audible sound pressure levels is mapped into a narrower range of auditory nerve responses. Peripheral compression is the by-product of independent compressive processes occurring at the level of the basilar membrane, the inner hair cell (IHC), and the auditory nerve synapse. Here, an electrical-circuit equivalent of an IHC is used to look into the compression contributed by the IHC. The model includes a mechanically driven transducer potassium (K⁺) conductance and two time- and voltage-dependent basolateral K⁺ conductances: one with fast and one with slow kinetics. Special attention is paid to faithfully implement the activation kinetics of these basolateral conductances. Optimum model parameters are provided to account for previously reported in vitro observations that demonstrate the compression associated with the gating of the transducer and of the basolateral channels. Without having to readjust its parameters, the model also accounts for the in vivo nonlinear IHC transfer characteristics. Model simulations are then used to investigate the relative contribution of the transducer and basolateral K⁺ currents to the nonlinear IHC input/output functions in vivo. The simulations suggest that the voltage-dependent activation of the basolateral currents compresses the DC potential for stereocilia displacements above approximately 5 nm. The degree of compression exceeds 2-to-1 and is similar for all stimulation frequencies. The AC potential is compressed in a similar way, but only for frequencies below 800 Hz. The simulations further suggest that the nonlinear gating of the transducer current is responsible for the expansive growth of the DC potential with increasing sound level (slope of 2 dB/dB) at low sound pressure levels.Both authors contributed equally to this work.