We have performed the most comprehensive resonance-model fit of π − π − π þ states using the results of our previously published partial-wave analysis (PWA) of a large data set of diffractive-dissociation events from the reaction π − þ p → π − π − π þ þ p recoil with a 190 GeV=c pion beam. The PWA results, which were obtained in 100 bins of three-pion mass, 0.5 < m 3π < 2.5 GeV=c 2 , and simultaneously in 11 bins of the reduced four-momentum transfer squared, 0.1 < t 0 < 1.0 ðGeV=cÞ 2 , are subjected to a resonance-model fit using Breit-Wigner amplitudes to simultaneously describe a subset of 14 selected waves using 11 isovector light-meson states with J PC ¼ 0 −þ , 1 þþ , 2 þþ , 2 −þ , 4 þþ , and spin-exotic 1 −þ quantum numbers. The model contains the well-known resonances πð1800Þ, a 1 ð1260Þ, a 2 ð1320Þ, π 2 ð1670Þ, π 2 ð1880Þ, and a 4 ð2040Þ. In addition, it includes the disputed π 1 ð1600Þ, the excited states a 1 ð1640Þ, a 2 ð1700Þ, and π 2 ð2005Þ, as well as the resonancelike a 1 ð1420Þ. We measure the resonance parameters mass and width of these objects by combining the information from the PWA results obtained in the 11 t 0 bins. We extract the relative branching fractions of the ρð770Þπ and f 2 ð1270Þπ decays of a 2 ð1320Þ and a 4 ð2040Þ, where the former one is measured for the first time. In a novel approach, we extract the t 0 dependence of the intensity of the resonances and of their phases. The t 0 dependence of the intensities of most resonances differs distinctly from the t 0 dependence of the nonresonant components. For the first time, we determine the t 0 dependence of the phases of the production amplitudes and confirm that the production mechanism of the Pomeron exchange is common to all resonances. We have performed extensive systematic studies on the model dependence and correlations of the measured physical parameters.

A semi-inclusive measurement of charged hadron multiplicities in deep inelastic muon scattering off an isoscalar target was performed using data collected by the COMPASS Collaboration at CERN. The following kinematic domain is covered by the data: photon virtuality Q 2 > 1 ðGeV=cÞ 2 , invariant mass of the hadronic system W > 5 GeV=c 2 , Bjorken scaling variable in the range 0.003 < x < 0.4, fraction of the virtual photon energy carried by the hadron in the range 0.2 < z < 0.8, and square of the hadron transverse momentum with respect to the virtual photon direction in the range 0.02 ðGeV=cÞ 2 < P 2 hT < 3 ðGeV=cÞ 2 . The multiplicities are presented as a function of P 2 hT in three-dimensional bins of x, Q 2 , z and compared to previous semi-inclusive measurements. We explore the small-P 2 hT region, i.e. P 2 hT < 1 ðGeV=cÞ 2 , where hadron transverse momenta are expected to arise from nonperturbative effects, and also the domain of larger P 2 hT , where contributions from higher-order perturbative QCD are expected to dominate. The multiplicities are fitted using a single-exponential function at small P 2 hT to study the dependence of the average transverse momentum hP 2 hT i on x, Q 2 and z. The power-law behavior of the multiplicities at large P 2 hT is investigated using various functional forms. The fits describe the data reasonably well over the full measured range.

We have investigated the pattern formation in systems described by the nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation for the cases where the dimension of the pattern concentration area is less than that of independent variables space. We have obtained a system of integro-differential equations which describe the dynamics of the concentration area and the semiclassically limited distribution of a pattern in the class of trajectory concentrated functions. Also, asymptotic large-time solutions have been obtained that describe the semiclassically limited distribution of a quasi-steady-state pattern on the concentration manifold. The approach is illustrated by an example for which the analytical solution is in good agreement with the prediction of a numerical simulation.

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