Betatron modulation of microwave instability in small isochronous ring

A novel coupling of the transverse betatron motion to the longitudinal microwave instability is studied. Besides the radial coherent dipole mode space charge field, simulation and theoretical studies in this paper show that the longitudinal coherent dipole mode space charge field due to centroid wiggles also plays an important role in the isochronous regime, it induces betatron oscillation frequencies in temporal evolutions of spectra of longitudinal charge densities, radial centroid offsets and coherent energy deviations of local centroids.Comment: 13 page

Modelling and prediction of foam structure

The primary objective of this thesis is to explore the relationship between the surface and underlying structure of dry foams. This relationship is important for both research and industry because the surface film size distribution is typically the only information available in opaque foams when referring to the underlying bubble size distribution. This study is carried out by simulating foams with free surfaces. Firstly, the method of simulating 3D dry foams with free surfaces is presented. The simulation method is verified for foams with uniform bubble sizes by comparing their simulation results to experimental values reported in literature. The validity of the method and its ability to accurately model the structure of both surface and internal bubbles is demonstrated by the excellent agreement between the experimental study and the simulation results. Secondly, the simulation results are shown for the relationship between the surface film size distribution and the surface bubble size distribution. The results show that, for a given surface bubble size, there is a distribution of possible surface film sizes. However, for the range of polydispersity used in this thesis, the distribution of the ratio of film size to the size of bubble to which it is attached is found to be independent of the underlying bubble size distribution. A functional form of this relationship is obtained by nonlinear regression. Based on the functions obtained, the surface film size distributions can be computed using the underlying surface bubble size distribution. This is the inverse of what is acquired and therefore a numerical procedure for obtaining the surface bubble size distributions using the corresponding surface film size distribution is developed. This method is demonstrated to accurately reproduce the results from the full structural foam simulations

An Efficient Dynamic Programming Algorithm for the Generalized LCS Problem with Multiple Substring Exclusion Constrains

In this paper, we consider a generalized longest common subsequence problem with multiple substring exclusion constrains. For the two input sequences $X$ and $Y$ of lengths $n$ and $m$, and a set of $d$ constrains $P=\{P_1,...,P_d\}$ of total length $r$, the problem is to find a common subsequence $Z$ of $X$ and $Y$ excluding each of constrain string in $P$ as a substring and the length of $Z$ is maximized. The problem was declared to be NP-hard\cite{1}, but we finally found that this is not true. A new dynamic programming solution for this problem is presented in this paper. The correctness of the new algorithm is proved. The time complexity of our algorithm is $O(nmr)$.Comment: arXiv admin note: substantial text overlap with arXiv:1301.718

A note on the largest number of red nodes in red-black trees

In this paper, we are interested in the number of red nodes in red-black trees. We first present an $O(n^2\log n)$ time dynamic programming solution for computing $r(n)$, the largest number of red internal nodes in a red-black tree on $n$ keys. Then the algorithm is improved to some $O(\log n)$ time recursive and nonrecursive algorithms. Based on these improved algorithms we finally find a closed-form solution of $r(n)$

Complete Solutions for a Combinatorial Puzzle in Linear Time

In this paper we study a single player game consisting of $n$ black checkers and $m$ white checkers, called shifting the checkers. We have proved that the minimum number of steps needed to play the game for general $n$ and $m$ is $nm + n + m$. We have also presented an optimal algorithm to generate an optimal move sequence of the game consisting of $n$ black checkers and $m$ white checkers, and finally, we present an explicit solution for the general game