Shooting flexible electronics

The trends of the future electronic devices should be miniaturized,flexible,stable,portable,light,and highly integrated.Although flexible electronic products(i.e.,flexible display products^[1-3],batteries^[4,5],cell phones[6])have been commercially available recently,which represents the starting of a new era in electronics,these progresses are still in their infancy and more efforts are required to boom their multifunction and speed up their marketization from lab.Considering their low-cost and mass-productive synthesis technologies,rich species,high performances,and especially,the excellent flexibility and stability,organic materials(insulating,conductive and semiconducting)have triggered the tide of the development of"plastic electronics",especially in transistors,an indispensable logic device in these logic-control based devices(i.e.,intelligent electronics).     

Fully Piecewise Linear Vector Optimization Problems

Journal of Optimization Theory and Applications - We distinguish two kinds of piecewise linear functions and provide an interesting representation for a piecewise linear function between two normed...     

A smooth homotopy method for incomplete markets

Mathematical Programming - In the general equilibrium with incomplete asset markets (GEI) model, the excess demand functions are typically not continuous at the prices for which the assets have...     

Explicit breather solution of the nonlinear Schrödinger equation

Theoretical and Mathematical Physics - We present a one-line closed-form expression for the three-parameter breather of the nonlinear Schrödinger equation. This provides an analytic proof of...     

Parametric modeling of steady-state gradient coil vibration: Resonance dynamics under variations in cylinder geometry

Gradient coil (GC) vibration is the root cause of many problems in MRI adversely affecting scanner performance, image quality, and acoustic noise levels. A critical issue is that GC vibration will be significantly increased close to any GC mechanical resonances. It is well known that altering the dimensions of a GC fundamentally affects the mechanical resonances excited by the GC windings. The precise nature of the effects (i.e., how the resonances are affected) is however not well understood. The purpose of the present paper is to study how the mechanical resonances excited by closed whole-body Z-gradient coils are affected by variations in cylinder geometry. A mathematical Z-gradient coil vibration model recently developed and validated by the authors is used to theoretically study the resonance dynamics under variation(s) in cylinder: (i) length, (ii) mean radius, and (iii) radial thickness. The forced-vibration response to Lorentz-force excitation is in each case analyzed in terms of the frequency response of the GC cylinder's displacement. In cases (i) and (ii), the qualitative dynamics are simple: reducing the cylinder length and/or mean radius causes all mechanical resonances to shift to higher frequencies. In case (iii), the qualitative dynamics are much more complicated with different resonances shifting in different directions and additional dependencies on the cylinder length. The more detailed dynamics are intricate owing to the fact that resonances shift at comparatively different rates and this leads to several novel and theoretically interesting predicted effects. Knowledge of these effects advance our understanding of the basic mechanics of GC vibration and offer practically useful insights into how such vibration may be passively reduced.     

Distribution dependent stochastic differential equations

Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications, distribution dependent stochastic differential equations (DDSDEs) have been intensively investigated. In this paper, we summarize some recent progresses in the study of DDSDEs, which include the correspondence of weak solutions and nonlinear Fokker-Planck equations, the well-posedness, regularity estimates, exponential ergodicity, long time large deviations, and comparison theorems.     

Global existence and time decay of the non-cutoff Boltzmann equation with hard potential

This paper is concerned with the Cauchy problem on the Boltzmann equation without angular cutoff assumption for hard potential in the whole space. When the initial data is a small perturbation of a global Maxwellian, the global existence of solution to this problem is proved in unweighted Sobolev spaces $H^N\left({\mathbb{R}}_{x,v}^6\right)$ with $N\ge 2$. But if we want to obtain the optimal temporal decay estimates, we need to add the velocity weight function, in this case the global existence and the optimal temporal decay estimate of the Boltzmann equation are all established. Meanwhile, we further gain a more accurate energy estimate, which can guarantee the validity of the assumption in Chen et al. (0000).