arXiv subjects

Jinfeng Wang

Publications and source records attributed to Jinfeng Wang.

23 records · Page 2Linked to original sources

arXiv2021

Enhancing Population Persistence by a Protection Zone in a Reaction-Diffusion Model with Strong Allee Effect

Protecting endangered species has been an important issue in ecology. We derive a reaction-diffusion model for a population in a one-dimensional bounded habitat, where the population is subjected to a strong Allee effect in its natural domain but obeys a logistic growth in a protection zone. We establish the conditions for population persistence and extinction via the principal eigenvalue of an associated eigenvalue problem and investigate the dependence of this principal eigenvalue on the location (i.e., the starting point and the length) of the protection zone. The results are used to design the optimal protection zone under different boundary conditions, that is, to suggest the starting point and length of the protection zone with respect to different population growth rate in the protection zone, in order for the population to persist in a long term.

math.DS↗

arXiv2019

TGMFE Algorithm Combined with Some Time Second-Order Schemes for Nonlinear Fourth-Order Reaction Diffusion System

In this article, a two-grid mixed finite element (TGMFE) method with some second-order time discrete schemes is developed for numerically solving nonlinear fourth-order reaction diffusion equation. The two-grid MFE method is used to approximate spatial direction, and some second-order $θ$ schemes formulated at time $t_{k-θ}$ are considered to discretize the time direction. TGMFE method covers two main steps: a nonlinear MFE system based on the space coarse grid is solved by the iterative algorithm and a coarse solution is arrived at, then a linearized MFE system with fine grid is considered and a TGMFE solution is obtained. Here, the stability and a priori error estimates in $L^2$-norm for both nonlinear Galerkin MFE system and TGMFE scheme are derived. Finally, some convergence results are computed for both nonlinear Galerkin MFE system and TGMFE scheme to verify our theoretical analysis, which show that the convergence rate of the time second-order $θ$ scheme including Crank-Nicolson scheme and second-order backward difference scheme is close to $2$, and that with the comparison to the computing time of nonlinear Galerkin MFE method, the CPU-time by using TGMFE method can be saved.

math.NA↗

arXiv2018

Autoencoder Based Residual Deep Networks for Robust Regression Prediction and Spatiotemporal Estimation

To have a superior generalization, a deep learning neural network often involves a large size of training sample. With increase of hidden layers in order to increase learning ability, neural network has potential degradation in accuracy. Both could seriously limit applicability of deep learning in some domains particularly involving predictions of continuous variables with a small size of samples. Inspired by residual convolutional neural network in computer vision and recent findings of crucial shortcuts in the brains in neuroscience, we propose an autoencoder-based residual deep network for robust prediction. In a nested way, we leverage shortcut connections to implement residual mapping with a balanced structure for efficient propagation of error signals. The novel method is demonstrated by multiple datasets, imputation of high spatiotemporal resolution non-randomness missing values of aerosol optical depth, and spatiotemporal estimation of fine particulate matter <2.5 μm, achieving the cutting edge of accuracy and efficiency. Our approach is also a general-purpose regression learner to be applicable in diverse domains.

cs.LG↗

arXiv2016

A Two-Grid Finite Element Approximation for A Nonlinear Time-Fractional Cable Equation

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 two-grid FE method and the integer and fractional derivatives in time are discretized by second-order two-step backward difference method and second-order weighted and shifted Grünwald difference (WSGD) scheme, is presented to solve nonlinear fractional Cable equation. The studied algorithm in this paper mainly covers two steps: First, the numerical solution of nonlinear FE scheme on the coarse grid is solved, Second, based on the solution of initial iteration on the coarse grid, the linearized FE system on the fine grid is solved by using Newton iteration. Here, the stability based on fully discrete two-grid method is derived. Moreover, the a priori estimates with second-order convergence rate in time is proved in detail, which is higher than the L1-approximation result with $O(τ^{2-α}+τ^{2-β})$. Finally, the numerical results by using the two-grid method and FE method are calculated, respectively, and the CPU-time is compared to verify our theoretical results.

math.NA↗

arXiv2006

Lattice fringe signatures of epitaxy on nanotubes

Carbon nanotubes are of potential interest as heterogeneous catalysis supports, in part because they offer a high surface area hexagonal array of carbon atoms for columnar or epitaxial attachment. Fringe visibility modeling of electron microscope lattice images allows one to investigate the relationship between individual nanoparticles and such nanotube supports. We show specifically how (111) columnar or epitaxial growth of FCC metal lattices, on carbon nanotubes viewed side-on, results in well-defined patterns of (111)-fringe orientations with respect to the tube axis. In the epitaxial case, the observations also provide information on chirality of the nanotube's outermost graphene sheet.

cond-mat.mtrl-sci↗