arXiv subjects

Fei Fang

Publications and source records attributed to Fei Fang.

131 records · Page 8Linked to original sources

arXiv2017

The effect of heterogeneity on flocking behavior and systemic risk

The goal of this paper is to study organized flocking behavior and systemic risk in heterogeneous mean-field interacting diffusions. We illustrate in a number of case studies the effect of heterogeneity in the behavior of systemic risk in the system, i.e., the risk that several agents default simultaneously as a result of interconnections. We also investigate the effect of heterogeneity on the "flocking behavior" of different agents, i.e., when agents with different dynamics end up following very similar paths and follow closely the mean behavior of the system. Using Laplace asymptotics, we derive an asymptotic formula for the tail of the loss distribution as the number of agents grows to infinity. This characterizes the tail of the loss distribution and the effect of the heterogeneity of the network on the tail loss probability.

q-fin.RM↗

arXiv2014

Infinitely many non-radial sign-changing solutions for a Fractional Laplacian equation with critical nonlinearity

In this work, the following fractional Laplacian problem with pure critical nonlinearity is considered \begin{equation*} \left\{ \begin{array}{ll} (-Δ)^{s} u=|u|^{\frac{4s}{N-2s}}u, &\mbox{in}\ \mathbb{R}^N, \\ u\in \mathcal{D}^{s,2}(\mathbb{R}^N), \end{array} \right. \end{equation*} where $s\in (0,1)$, $N$ is a positive integer with $N\geq 3$, $(-Δ)^{s}$ is the fractional Laplacian operator. We will prove that this problem has infinitely many non-radial sign-changing solutions.

math.AP↗

arXiv2013

On Schrödinger equations with periodic potentials and with nonperiodic nonlinearities

We consider the Schrödinger equation $-Δu +V(x)u=f(x, u)$, where $V$ is periodic and $f$ is non-periodic, 0 is a boundary point of the continuous spectrum of $A:=-Δ+V(x)$. We use M. Willem and W. M. Zou's linking theorem and M. Schechter's method to establish an existence result for this problem in weak superlinear cases. In a sense, we enrich a recent result of M. Willem and W.M. Zou [M. Willem and W.M. Zou, On a Schrödinger Equation with Periodic Potential and Spectrum Point Zero,Indiana Univ. Math. J. 2003].

math.AP↗

arXiv2013

Nontrivial solutions for semilinear elliptic systems via Orlicz-Sobolev theory

In this paper, the semilinear elliptic systems with Dirichlet boundary value are considered \begin{align} \left\{\begin{array}{ll} -Δv=f(u) & \mathrm{in}\ Ω, -Δu=g(v) & \mathrm{in}\ Ω, u=0, \ v=0 & \mathrm{on}\ \partialΩ, \end{array} \right. \end{align} We extend the notion of subcritical growth from polynomial growth to N-function growth. Under N-function growth, nontrivial solutions are obtained via Orlicz-Sobolev spaces and variational methods. It's also noteworthy that the nonlinear term $g(v)$ does not have to satisfy the usual Ambrosetti-Rabinowitz condition. So, in a sense, we enrich recent results of D. ~G. de Figueiredo, J. ~M. do {Ó} and B. ~Ruf [D. ~G. de Figueiredo, J.M. do {Ó}, B. ~Ruf, An {O}rlicz-space approach to superlinear elliptic systems, J. Funct. Anal. 224 (2005) 471--496].

math.AP↗

arXiv2002

Field-induced Domain Reorientation and Polarization Rotation of <110> Oriented Pb(Mg1/3Nb2/3)O3-PbTiO3 Single Crystals

Polarization hysteresis loops, x-ray diffraction (XRD) and temperature dependent dielectric constant under different electric fields for <110> oriented 0.7 Pb(Mg1/3Nb2/3)O3-0.3PbTiO3 single crystals were measured. The field-induced phase transition and the process of depolarization were discussed. The results show that with the electric field increasing, the crystal form changes along via polar-axis reorientation and polarization rotation. However, the depolarization process is not just the reversal of the polarization process. It is noticed that just from the temperature dependent dielectric behavior is not enough to judge the processes of the E-field induced phase transition.

cond-mat.mtrl-sci↗