Related papers: Solving the Cable Equation Using a Compact Differe…
In this article, a nonlinear fractional Cable equation is solved by a two-grid algorithm combined with finite element (FE) method. A temporal second-order fully discrete two-grid FE scheme, in which the spatial direction is approximated by…
In this paper, we introduce a novel category of central compact schemes inspired by existing cell-node and cell-centered compact finite difference schemes, that offer a superior spectral resolution for solving the dispersive wave equation.…
This research introduces an extended application of neural networks for solving nonlinear partial differential equations (PDEs). A neural network, combined with a pseudo-arclength continuation, is proposed to construct bifurcation diagrams…
(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…
Neurons are thought of as the building blocks of excitable brain tissue. However, at the single neuron level, the neuronal membrane, the dendritic arbor and the axonal projections can also be considered an extended active medium. Active…
Power cables have complex geometries in order to reduce their ac resistance. Although there are many different cable designs, most have in common that their inner conductors' cross-section is divided into several electrically insulated…
Partial differential equations (PDEs) are typically used as models of physical processes but are also of great interest in PDE-based image processing. However, when it comes to their use in imaging, conventional numerical methods for…
Cable theory has been developed over the last decades, usually assuming that the extracellular space around membranes is a perfect resistor. However, extracellular media may display more complex electrical properties due to various…
This paper shows how partial differential problems can be solved thanks to cellular computing and an adaptation of the Least Squares Finite Elements Method. As cellular computing can be implemented on distributed parallel architectures,…
Sophisticated machine learning struggles to transition onto battery-operated devices due to the high-power consumption of neural networks. Researchers have turned to neuromorphic engineering, inspired by biological neural networks, for more…
Cable subsystems characterized by long, slender, and flexible structural elements are featured in numerous engineering systems. In each of them, interaction between an individual cable and the surrounding fluid is inevitable. Such a…
A complete single-neuron model must correctly reproduce the firing of spikes and bursts. We present a study of a simplified model of deep pyramidal cells of the cortex with active dendrites. We hypothesized that we can model the soma and…
The branching methods developed are effective methods to solve some semi linear PDEs and are shown numerically to be able to solve some full non linear PDEs. These methods are however restricted to some small coefficients in the PDE and…
Drift-diffusion models that account for the motion of both electronic and ionic charges are important tools for explaining the hysteretic behaviour and guiding the development of metal halide perovskite solar cells. Furnishing numerical…
We present a receiver-side framework for identifying amplitude distortions in frequency-selective OFDM channels. The core novelty is the use of the DCT Neuron, a compact adaptive processor based on the discrete cosine transform (DCT), to…
Interface problems depict many fundamental physical phenomena and widely apply in the engineering. However, it is challenging to develop efficient fully decoupled numerical methods for solving degenerate interface problems in which the…
Semidefinite programming (SDP) is widely acknowledged as one of the most effective methods for deriving the tightest lower bounds of the optimal power flow (OPF) problems. In this paper, an enhanced semidefinite relaxation model that…
The circuits comprising superconducting optoelectronic synapses, dendrites, and neurons are described by numerically cumbersome and formally opaque coupled differential equations. Reference 1 showed that a phenomenological model of…
Finite difference schemes are here solved by means of a linear matrix equation. The theoretical study of the related algebraic system is exposed, and enables us to minimize the error due to a finite difference approximation.
Measuring functional connectivity from fMRI is important in understanding processing in cortical networks. However, because brain's connection pattern is complex, currently used methods are prone to produce false connections. We introduce…