Metastable behavior of vortex matter in the electronic transport processes of homogenous superconductors

We study numerically the effect of vortex pinning on the hysteresis voltage-temperature (V-T) loop of vortex matter. It is found that different types of the V-T loops result from different densities of vortex pinning center. An anticlockwise V-T loop is observed for the vortex system with dense pinning centers, whereas a clockwise V-T loop is brought about for vortices with dilute pinning centers. It is shown that the size of the V-T loop becomes smaller for lower experimental speed, higher magnetic field, or weak pinning strength. Our numerical observation is in good agreement with experiments

Voltage-temperature charge verification testing of 34 ampere-hour nickel-cadmium cells

This testing was designed to evaluate various voltage-temperature (V-T) charge curves for use in low-Earth-orbit (LEO) applications of nickel-cadmium battery cells. The trends established relating V-T level to utilizable capacity were unexpected. The trends toward lower capacity at higher V-T levels was predominant in this testing. This effect was a function of the V-T level, the temperature, and the cell history. This effect was attributed to changes occurring in the positive plate. The results imply that for some applications, the use of even lower V-T levels may be warranted. The need to limit overcharge, especially in the early phases of missions, is underlined by this test program

A Note on Weighted Rooted Trees

Let $T$ be a tree rooted at $r$. Two vertices of $T$ are related if one is a descendant of the other; otherwise, they are unrelated. Two subsets $A$ and $B$ of $V(T)$ are unrelated if, for any $a\in A$ and $b\in B$, $a$ and $b$ are unrelated. Let $\omega$ be a nonnegative weight function defined on $V(T)$ with $\sum_{v\in V(T)}\omega(v)=1$. In this note, we prove that either there is an $(r, u)$-path $P$ with $\sum_{v\in V(P)}\omega(v)\ge \frac13$ for some $u\in V(T)$, or there exist unrelated sets $A, B\subseteq V(T)$ such that $\sum_{a\in A }\omega(a)\ge \frac13$ and $\sum_{b\in B }\omega(b)\ge \frac13$. The bound $\frac13$ is tight. This answers a question posed in a very recent paper of Bonamy, Bousquet and Thomass\'e

Infinitely many periodic solutions for second order Hamiltonian systems

In this paper, we study the existence of infinitely many periodic solutions for second order Hamiltonian systems $\ddot{u}+\nabla_u V(t,u)=0$, where $V(t, u)$ is either asymptotically quadratic or superquadratic as $|u|\to \infty$.Comment: to appear in JDE(doi:10.1016/j.jde.2011.05.021

Wellposedness of the discontinuous ODE associated with two-phase flows

We consider the initial value problem \dot x (t) = v(t,x(t)) \;\mbox{ for } t\in (a,b), \;\; x(t_0)=x_0 which determines the pathlines of a two-phase flow, i.e.\ $v=v(t,x)$ is a given velocity field of the type $$v(t,x)= \begin{cases} v^+(t,x) &\text{ if } x \in \Omega^+(t)\\ v^-(t,x) &\text{ if } x \in \Omega^-(t) \end{cases}$$ with $\Omega^\pm (t)$ denoting the bulk phases of the two-phase fluid system under consideration. The bulk phases are separated by a moving and deforming interface $\Sigma (t)$. Since we allow for flows with phase change, these pathlines are allowed to cross or touch the interface. Imposing a kind of transversality condition at $\Sigma (t)$, which is intimately related to the mass balance in such systems, we show existence and uniqueness of absolutely continuous solutions of the above ODE in case the one-sided velocity fields $v^\pm:\overline{{\rm gr}(\Omega^\pm)}\to \mathbb{R}^n$ are continuous in $(t,x)$ and locally Lipschitz continuous in $x$. Note that this is a necessary prerequisite for the existence of well-defined co-moving control volumes for two-phase flows, a basic concept for mathematical modeling of two-phase continua