Unnatural parity exchange in π+p → (ϱ, ω)Δ++

The magnitudes and relative phases of the unnatural parity exchange amplitudes in π⁺p → (?^o, ω)Δ⁺⁺ are determined at 7.1 GeV/c using a model dependent amplitude analysis technique.     

Macroscopic behaviour of a charged Boltzmann gas

We consider a classical charged gas (with self-consistent Coulomb interaction) described by a solvable linearized Boltzmann equation with thermalization on uniformly distributed scatterers. It is shown that if one scales the time t, the reciprocal space coordinate k and the Debye length l as λ²t, (1/λ)k, λl, respectively, in the λ → ∞ limit the charge density is equal to the solution of the corresponding diffusion-conduction (macroscopic) equation.     

Non-Lipschitzian control algorithms for extended mechanical systems

We derive the properties of a general control algorithm [Braiman et al., Phys. Rev. Lett. 90, 094301 (2003)] for quantities describing global features of nonlinear extended mechanical systems. The control algorithm is based on the concepts of non-Lipschitzian dynamics and global targeting. We show that (i) certain average quantities of the controlled system can be driven-exactly or approximately-towards desired targets which become linearly stable attractors for the system's dynamics; (ii) the basins of attraction of these targets are reached in very short times; and (iii) while within reasonably broad ranges the time-scales of the control and of the intrinsic dynamics may be quite different, this disparity does not affect significantly the overall efficiency of the proposed scheme, up to natural fluctuations.     

Half-range solutions of indefinite Sturm-Liouville problems

For diffusion equations of indefinite Sturm-Liouville type, we develop two equivalent methods of constructing explicit representations for the solutions. The first method is based on an eigenfunction expansion whereas the second uses a Wiener-Hopf-type integral equation and factorization. Some illustrative examples are worked out.     

Half-range completeness for the Fokker-Planck equation

Half-range completeness theorems are proved for eigenfunctions associated to the one-dimensional Fokker-Planck equation in a semi-infinite medium. Existence and uniqueness results for perfectly absorbing, partially absorbing, and purely specularly reflecting boundary conditions are deduced for the stationary and time-dependent problems. Similar results are obtained for a slab geometry.     

A minimax problem for semilinear nonlocal competitive systems

A two-sided game for the control of a stationary semilinear competitive system with autonomous sources is considered, where the controls are the kernels of the nonlocal interaction terms. The saddle point (the optimal solution of the game) is characterized as the unique solution of the associated optimality system, which is solved by an iterative scheme.This research has been partially sponsored by DARPA under Contract No. 1868-A037-A1 with Martin Marietta Energy Systems, Inc., under Contract No. DE-AC05-84OR21400 with U.S. Department of Energy. S. Lenhart's work was also partially supported by an NSF grant.     

Optimal control of swinging alliances in a parabolic competition model

A system of parabolic partial differential equations describes the interaction of three populations, modeling a dynamic competition/cooperation scenario. More precisely, two populations are always competing with each other, but the third population can switch the mode of alliance with the other two populations between cooperation and competition. The control is a function measuring the strength and nature of the alliance and the goal is to maximize the population with the swinging alliance while keeping the other two populations close to each other and minimizing the cost of the alliance action. Various scenarios are illustrated with numerical results.