KP solitons in shallow water

The main purpose of the paper is to provide a survey of our recent studies on soliton solutions of the Kadomtsev-Petviashvili (KP) equation. The classification is based on the far-field patterns of the solutions which consist of a finite number of line-solitons. Each soliton solution is then defined by a point of the totally non-negative Grassmann variety which can be parametrized by a unique derangement of the symmetric group of permutations. Our study also includes certain numerical stability problems of those soliton solutions. Numerical simulations of the initial value problems indicate that certain class of initial waves asymptotically approach to these exact solutions of the KP equation. We then discuss an application of our theory to the Mach reflection problem in shallow water. This problem describes the resonant interaction of solitary waves appearing in the reflection of an obliquely incident wave onto a vertical wall, and it predicts an extra-ordinary four-fold amplification of the wave at the wall. There are several numerical studies confirming the prediction, but all indicate disagreements with the KP theory. Contrary to those previous numerical studies, we find that the KP theory actually provides an excellent model to describe the Mach reflection phenomena when the higher order corrections are included to the quasi-two dimensional approximation. We also present laboratory experiments of the Mach reflection recently carried out by Yeh and his colleagues, and show how precisely the KP theory predicts this wave behavior.Comment: 50 pages, 25 figure

Lowest weight representations of super Schrodinger algebras in low dimensional spacetime

We investigate the lowest weight representations of the super Schrodinger algebras introduced by Duval and Horvathy. This is done by the same procedure as the semisimple Lie algebras. Namely, all singular vectors within the Verma modules are constructed explicitly then irreducibility of the associated quotient modules is studied again by the use of singular vectors. We present the classification of irreducible Verma modules for the super Schrodinger algebras in (1+1) and (2+1) dimensional spacetime with N = 1, 2 extensions.Comment: 10pages, talk given at GROUP28 conference New Castle 26-30th July 2010, reference adde

A class of solvable Lie algebras and their Casimir Invariants

A nilpotent Lie algebra n_{n,1} with an (n-1) dimensional Abelian ideal is studied. All indecomposable solvable Lie algebras with n_{n,1} as their nilradical are obtained. Their dimension is at most n+2. The generalized Casimir invariants of n_{n,1} and of its solvable extensions are calculated. For n=4 these algebras figure in the Petrov classification of Einstein spaces. For larger values of n they can be used in a more general classification of Riemannian manifolds.Comment: 16 page

Observation of Parity Violation in the Omega-minus -> Lambda + K-minus Decay

The alpha decay parameter in the process Omega-minus -> Lambda + K-minus has been measured from a sample of 4.50 million unpolarized Omega-minus decays recorded by the HyperCP (E871) experiment at Fermilab and found to be [1.78 +/- 0.19(stat) +/- 0.16(syst)]{\times}10^{-2}. This is the first unambiguous evidence for a nonzero alpha decay parameter, and hence parity violation, in the Omega-minus -> Lambda + K-minus decay.Comment: 10 pages, 7 figure

Measurement of the Alpha Asymmetry Parameter for the Omega- to Lambda K- Decay

We have measured the alpha parameter of the Omega- to Lambda K- decay using data collected with the HyperCP spectrometer during the 1997 fixed-target run at Fermilab. Analyzing a sample of 0.96 million Omega- to Lambda K^-, Lambda to p pi- decays, we obtain alpha_Omega*alpha_Lambda = [1.33+/-0.33(stat)+/-0.52(syst)] x 10^{-2}. With the accepted value of alpha_Lambda, alpha_Omega is found to be [2.07+/-0.51(stat)+/-0.81(syst)] x 10^{-2}.Comment: 5 pages, 4 figures, to be appeared as a Rapid Communication in Phys. Rev.

HyperCP: A high-rate spectrometer for the study of charged hyperon and kaon decays

The HyperCP experiment (Fermilab E871) was designed to search for rare phenomena in the decays of charged strange particles, in particular CP violation in $\Xi$ and $\Lambda$ hyperon decays with a sensitivity of $10^{-4}$. Intense charged secondary beams were produced by 800 GeV/c protons and momentum-selected by a magnetic channel. Decay products were detected in a large-acceptance, high-rate magnetic spectrometer using multiwire proportional chambers, trigger hodoscopes, a hadronic calorimeter, and a muon-detection system. Nearly identical acceptances and efficiencies for hyperons and antihyperons decaying within an evacuated volume were achieved by reversing the polarities of the channel and spectrometer magnets. A high-rate data-acquisition system enabled 231 billion events to be recorded in twelve months of data-taking.Comment: 107 pages, 45 Postscript figures, 14 tables, Elsevier LaTeX, submitted to Nucl. Instrum. Meth.

Evidence for the Decay Sigma+ -> p mu+ mu-

We report the first evidence for the decay Sigma+ -> p mu+ mu- from data taken by the HyperCP experiment(E871) at Fermilab. Based on three observed events, the branching ratio is B(Sigma+ -> p,mu+,mu-) = [8.6 +6.6,-5.4(stat) +/-5.5(syst)] x 10**-8. The narrow range of dimuon masses may indicate that the decay proceeds via a neutral intermediate state, Sigma+ -> p P0, P0 -> mu+ mu-, with a P0 mass of 214.3 +/- 0.5 MeV/c**2 and branching ratio B(Sigma+ -> p P0; P0 -> mu+ mu-) = [3.1 +2.4,-1.(stat) +/-1.5(syst)] x 10**-8.Comment: As published in PR

Feasibility of a mass vaccination campaign using a two-dose oral cholera vaccine in an urban cholera-endemic setting in Mozambique.

We conducted a study to assess the feasibility and the potential vaccine coverage of a mass vaccination campaign using a two-dose oral cholera vaccine in an urban endemic neighbourhood of Beira, Mozambique. The campaign was conducted from December 2003 to January 2004. Overall 98,152 doses were administered, and vaccine coverage of the target population was 58.6% and 53.6% for the first and second rounds, respectively. The direct cost of the campaign, which excludes the price of the vaccine, amounted to slightly over 90,000 dollars, resulting in the cost per fully vaccinated person of 2.09 dollars, which is relatively high. However, in endemic settings where outbreaks are likely to occur, integrating cholera vaccination into the routine activities of the public health system could reduce such costs

Genomewide Association Scan of Suicidal Thoughts and Behaviour in Major Depression

Background Suicidal behaviour can be conceptualised as a continuum from suicidal ideation, to suicidal attempts to completed suicide. In this study we identify genes contributing to suicidal behaviour in the depression study RADIANT. Methodology/Principal Findings A quantitative suicidality score was composed of two items from the SCAN interview. In addition, the 251 depression cases with a history of serious suicide attempts were classified to form a discrete trait. The quantitative trait was correlated with younger onset of depression and number of episodes of depression, but not with gender. A genome-wide association study of 2,023 depression cases was performed to identify genes that may contribute to suicidal behaviour. Two Munich depression studies were used as replication cohorts to test the most strongly associated SNPs. No SNP was associated at genome-wide significance level. For the quantitative trait, evidence of association was detected at GFRA1, a receptor for the neurotrophin GDRA (p = 2e-06). For the discrete trait of suicide attempt, SNPs in KIAA1244 and RGS18 attained p-values of <5e-6. None of these SNPs showed evidence for replication in the additional cohorts tested. Candidate gene analysis provided some support for a polymorphism in NTRK2, which was previously associated with suicidality. Conclusions/Significance This study provides a genome-wide assessment of possible genetic contribution to suicidal behaviour in depression but indicates a genetic architecture of multiple genes with small effects. Large cohorts will be required to dissect this further