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

Palaeomagnetism of the Ordovician dolerites of the Crozon Peninsula (France)

In order to obtain a Lower Palaeozoic pole for the Armorican Massif and to test the origin of the Ibero-Armorican arc, the Ordovician dolerites of the Crozon peninsula have been palaeomagnetically studied. The samples show a multicomponent magnetization which has been revealed by AF and thermal demagnetization and thoroughly investigated with rock magnetic experiments, polished section examinations and K/Ar dating. Four groups of directions have been recognized, often superimposed on each other in an individual sample. One component (D) has always the lowest blocking temperatures and coercivities and is considered to be of viscous origin, acquired recently in situ or in the laboratory during storage. Two components (A and B) are interpreted to be of secondary origin and to correspond to the observed K/Ar age distribution between 300 and 190 Myr. These ages represent the time interval between two regional thermo-tectonic events, associated with the Hercynian orogeny and the intrusion of dykes related to the early opening of the Central Atlantic Ocean and the Bay of Biscay. A fourth component (C) could be of Ordovician or younger Palaeozoic age; it is not clear whether the age of the magnetization is pre- or post-folding, but a pre-folding age would yield a direction of magnetization similar to Ordovician results from the Iberian peninsula. The latter interpretation suggests a fairly high palaeolatitude, which is in agreement with a glacio-marine postulated for sediments overlying the dolerite sills.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73214/1/j.1365-246X.1983.tb03785.x.pd

Observables and Correlators in Nonrelativistic ABJM Theory

Non-relativistic ABJM theory is defined by Galilean limit of mass-deformed N=6 Chern-Simons theory. Holographic string theory dual to the theory is not known yet. To understand features candidate gravity dual might exhibit, we examine local and nonlocal physical observables and their correlations in the non-relativistic ABJM theory. We show that gauge invariant local observables correspond to zero-norm states and that correlation functions among them are trivial. We also show that a particular class of nonlocal observables, Wilson loops, are topological in the sense that their correlation functions coincide with those of pure Chern-Simons theory. We argue that the theory is nevertheless physical and illustrate several physical observables whose correlation functions are nontrivial. We also study quantum aspects. We show that Chern-Simons level is finitely renormalized and that dilatation operator acting on spin chain is trivial at planar limit. These results all point to string scale geometry of gravity dual and to intriguing topological and tensionless nature of dual string defined on it.Comment: 1+30 pages, no figure, v2. typos fixed and references 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

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

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.

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.