Towards an analytic solution for pulsed CEST

Analytic solution for low-frequency rf sheaths in pulsed discharges.

The equations governing the evolution of rf-driven sheaths are solved analytically in the regime where the rf frequency is small compared to both the ionic plasma frequency and the ion transit time in the sheaths. Poincaré's map of first return is used to gain geometric insight into the dynamics of the circuit-sheath system. The requirements of minimizing wall bombardment while maximizing the e...

An Analytic Flow Solution for YSO Jets

We present an analytic solution for a jet flow from a young stellar object (YSO). This solution allows us to compute the speed, density, and magnetic field strength of the flow, but it is only true if YSO jet flows are powered by toroidal magnetic fields. We illustrate how the balance between centrifugal force and magnetic pressure provides the converging/diverging nozzle shape required to acce...

An Improved Empirical Solution for Describing Chemical Exchange Saturation Transfer (CEST) MRI

Introduction Both numerical simulation and analytical solution have been developed to describe CEST MRI phenomenon, which have aided our ability to quantify and optimize CEST imaging 1,2. In fact, a concise empirical solution has been proposed which decomposes CEST contrast as a product of the “ideal” contrast, saturation coefficient and spillover factor 3. However, the empirical solution is on...

Towards an Integrated Solution for Multimedia Communications

An analytic Riccati solution for two-target discrete-time control

This paper analytically solves the Riccati equation of discrete optimal control with two targets and one tool. This is accomplished by reducing the problem to a nonlinear univariate dynamic equation; this can be solved by a suitable transformation of variable. Beyond its direct application to two-target economic problems, the present approach may provide insight toward the eventual solution of ...