On scattering of solitons for the Klein-Gordon equation coupled to a particle

We establish the long time soliton asymptotics for the translation invariant nonlinear system consisting of the Klein-Gordon equation coupled to a charged relativistic particle. The coupled system has a six dimensional invariant manifold of the soliton solutions. We show that in the large time approximation any finite energy solution, with the initial state close to the solitary manifold, is a sum of a soliton and a dispersive wave which is a solution of the free Klein-Gordon equation. It is assumed that the charge density satisfies the Wiener condition which is a version of the ``Fermi Golden Rule''. The proof is based on an extension of the general strategy introduced by Soffer and Weinstein, Buslaev and Perelman, and others: symplectic projection in Hilbert space onto the solitary manifold, modulation equations for the parameters of the projection, and decay of the transversal component.Comment: 47 pages, 2 figure

Further constraints on electron acceleration in solar noise storms

We reexamine the energetics of nonthermal electron acceleration in solar noise storms. A new result is obtained for the minimum nonthermal electron number density required to produce a Langmuir wave population of sufficient intensity to power the noise storm emission. We combine this constraint with the stochastic electron acceleration formalism developed by Subramanian & Becker (2005) to derive a rigorous estimate for the efficiency of the overall noise storm emission process, beginning with nonthermal electron acceleration and culminating in the observed radiation. We also calculate separate efficiencies for the electron acceleration -- Langmuir wave generation stage and the Langmuir wave -- noise storm production stage. In addition, we obtain a new theoretical estimate for the energy density of the Langmuir waves in noise storm continuum sources.Comment: Accepted for publication in Solar Physic

Asymptotic Expansions for Stationary Distributions of Perturbed Semi-Markov Processes

New algorithms for computing of asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes are presented. The algorithms are based on special techniques of sequential phase space reduction, which can be applied to processes with asymptotically coupled and uncoupled finite phase spaces.Comment: 83 page

The universal Glivenko-Cantelli property

Let F be a separable uniformly bounded family of measurable functions on a standard measurable space, and let N_{[]}(F,\epsilon,\mu) be the smallest number of \epsilon-brackets in L^1(\mu) needed to cover F. The following are equivalent: 1. F is a universal Glivenko-Cantelli class. 2. N_{[]}(F,\epsilon,\mu)0 and every probability measure \mu. 3. F is totally bounded in L^1(\mu) for every probability measure \mu. 4. F does not contain a Boolean \sigma-independent sequence. It follows that universal Glivenko-Cantelli classes are uniformity classes for general sequences of almost surely convergent random measures.Comment: 26 page

Intrinsic Decoherence Dynamics in Smooth Hamiltonian Systems: Quantum-classical Correspondence

A direct classical analog of the quantum dynamics of intrinsic decoherence in Hamiltonian systems, characterized by the time dependence of the linear entropy of the reduced density operator, is introduced. The similarities and differences between the classical and quantum decoherence dynamics of an initial quantum state are exposed using both analytical and computational results. In particular, the classicality of early-time intrinsic decoherence dynamics is explored analytically using a second-order perturbative treatment, and an interesting connection between decoherence rates and the stability nature of classical trajectories is revealed in a simple approximate classical theory of intrinsic decoherence dynamics. The results offer new insights into decoherence, dynamics of quantum entanglement, and quantum chaos.Comment: 12 pages, 7 figures, to appear in Physical Review

Josephson dynamics for coupled polariton modes under the atom-field interaction in the cavity

We consider a new approach to the problem of Bose-Einstein condensation (BEC) of polaritons for atom-field interaction under the strong coupling regime in the cavity. We investigate the dynamics of two macroscopically populated polariton modes corresponding to the upper and lower branch energy states coupled via Kerr-like nonlinearity of atomic medium. We found out the dispersion relations for new type of collective excitations in the system under consideration. Various temporal regimes like linear (nonlinear) Josephson transition and/or Rabi oscillations, macroscopic quantum self-trapping (MQST) dynamics for population imbalance of polariton modes are predicted. We also examine the switching properties for time-averaged population imbalance depending on initial conditions, effective nonlinear parameter of atomic medium and kinetic energy of low-branch polaritons.Comment: 10 pages, 6 postscript figures, uses svjour.cl

Acute Bacterial Meningitis in Adults – A Review of 493 Episodes

To characterize acute bacterial meningitis in adults, we reviewed the charts of all persons 16 years of age or older in whom acute bacterial meningitis was diagnosed at Massachusetts General Hospital from 1962 through 1988. We included patients who were admitted after initial treatment at other hospitals. During the 27-year period, 445 adults were treated for 493 episodes of acute bacterial meningitis, of which 197 (40 percent) were nosocomial. Gram-negative bacilli (other than Haemophilus influenzae) caused 33 percent of the nosocomial episodes but only 3 percent of the community-acquired episodes. In the 296 episodes of community-acquired meningitis, the most common pathogens were Streptococcus pneumoniae (37 percent), Neisseria meningitidis (13 percent), and Listeria monocytogenes (10 percent); these organisms accounted for only 8 percent of the nosocomial episodes. Only 19 of the 493 episodes of meningitis (4 percent) were due to H. influenzae. Nine percent of all patients had recurrent meningitis; many had a cerebrospinal fluid leak. Seizures occurred in 23 percent of patients with community-acquired meningitis, and 28 percent had focal central nervous system findings. Risk factors for death among those with single episodes of community-acquired meningitis included older age ( ≥ 60 years), obtunded mental state on admission, and seizures within the first 24 hours. Among those with single episodes, the in-hospital mortality rate was 25 percent for community-acquired and 35 percent for nosocomial meningitis. The overall case fatality rate was 25 percent and did not vary significantly over the 27 years. In our large urban hospital, a major proportion of cases of acute bacterial meningitis in adults were nosocomial. Recurrent episodes of meningitis were frequent. The overall mortality rate remained high., Few studies of bacterial meningitis have focused on the clinical and pathologic features of the illness in adults1–5. Most large series have included both children and adults, with children accounting for 45 to 87 percent of cases6–16. Results have rarely been reported according to age group in these studies. To characterize acute bacterial meningitis in adults, we reviewed our experience at Massachusetts General Hospital over a 27-year period, from 1962 through 1988

Study of KS KL Coupled Decays and KL -Be Interactions with the CMD-2 Detector at VEPP-2M Collider

The integrated luminosity about 4000 inverse nanobarn of around phi meson mass ( 5 millions of phi mesons) has been collected with the CMD-2 detector at the VEPP-2M collider. A latest analysis of the KS KL coupled decays based on 30 % of available data is presented in this paper. The KS KL pairs from phi meson decays were reconstructed in the drift chamber when both kaons decayed into two charged particles. From a sample of 1423 coupled decays a selection of candidates to the CP violating KL into pi+ pi- decay was performed. CP violating decays were not identified because of the domination of events with a KL regenerating at the Be beam pipe into KS and a background from KL semileptonic decays. The regeneration cross section of 110 MeV/c KL mesons was found to be 53 +- 17 mb in agreement with theoretical expectations. The angular distribution of KS mesons after regeneration and the total cross section of KL for Be have been measured.Comment: 14 pages, 8 figure

High Speed Solution of Spacecraft Trajectory Problems Using Taylor Series Integration

Taylor series integration is implemented in a spacecraft trajectory analysis code-the Spacecraft N-body Analysis Program (SNAP) - and compared with the code s existing eighth-order Runge-Kutta Fehlberg time integration scheme. Nine trajectory problems, including near Earth, lunar, Mars and Europa missions, are analyzed. Head-to-head comparison at five different error tolerances shows that, on average, Taylor series is faster than Runge-Kutta Fehlberg by a factor of 15.8. Results further show that Taylor series has superior convergence properties. Taylor series integration proves that it can provide rapid, highly accurate solutions to spacecraft trajectory problems