Consensus-based control for a network of diffusion PDEs with boundary local interaction

In this paper the problem of driving the state of a network of identical agents, modeled by boundary-controlled heat equations, towards a common steady-state profile is addressed. Decentralized consensus protocols are proposed to address two distinct problems. The first problem is that of steering the states of all agents towards the same constant steady-state profile which corresponds to the spatial average of the agents initial condition. A linear local interaction rule addressing this requirement is given. The second problem deals with the case where the controlled boundaries of the agents dynamics are corrupted by additive persistent disturbances. To achieve synchronization between agents, while completely rejecting the effect of the boundary disturbances, a nonlinear sliding-mode based consensus protocol is proposed. Performance of the proposed local interaction rules are analyzed by applying a Lyapunov-based approach. Simulation results are presented to support the effectiveness of the proposed algorithms

On the constrained KP hierarchy

An explanation for the so-called constrained hierarhies is presented by linking them with the symmetries of the KP hierarchy. While the existence of ordinary symmetries (belonging to the hierarchy) allows one to reduce the KP hierarchy to the KdV hierarchies, the existence of additional symmetries allows to reduce KP to the constrained KP.Comment: 7pp, LaTe

Negative high-frequency differential conductivity in semiconductor superlattices

We examine the high-frequency differential conductivity response properties of semiconductor superlattices having various miniband dispersion laws. Our analysis shows that the anharmonicity of Bloch oscillations (beyond tight-binding approximation) leads to the occurrence of negative high-frequency differential conductivity at frequency multiples of the Bloch frequency. This effect can arise even in regions of positive static differential conductivity. The influence of strong electron scattering by optic phonons is analyzed. We propose an optimal superlattice miniband dispersion law to achieve high-frequency field amplification

Visualization of the 3-dimensional flow around a model with the aid of a laser knife

A method for visualizing the three-dimensional flow around models of various shapes in a wind tunnel at a Mach number of 5 is described. A laser provides a planar light flux such that any plane through the model can be selectively illuminated. The shape of shock waves and separation regions is then determined by the intensity of light scattered by soot particles in the flow

Derived Categories of Coherent Sheaves and Triangulated Categories of Singularities

In this paper we establish an equivalence between the category of graded D-branes of type B in Landau-Ginzburg models with homogeneous superpotential W and the triangulated category of singularities of the fiber of W over zero. The main result is a theorem that shows that the graded triangulated category of singularities of the cone over a projective variety is connected via a fully faithful functor to the bounded derived category of coherent sheaves on the base of the cone. This implies that the category of graded D-branes of type B in Landau-Ginzburg models with homogeneous superpotential W is connected via a fully faithful functor to the derived category of coherent sheaves on the projective variety defined by the equation W=0.Comment: 26 pp., LaTe

Combined Backstepping/Second-Order Sliding-Mode Boundary Stabilization of an Unstable Reaction-Diffusion Process

In this letter we deal with a class of open-loop unstable reaction-diffusion PDEs with boundary control and Robin-type boundary conditions. A second-order sliding mode algorithm is employed along with the backstepping method to asymptotically stabilize the controlled plant while providing at the same time the rejection of an external persistent boundary disturbance. A constructive Lyapunov analysis supports the presented synthesis, and simulation results are presented to validate the developed approach

Tunable subpicosecond electron bunch train generation using a transverse-to-longitudinal phase space exchange technique

We report on the experimental generation of a train of subpicosecond electron bunches. The bunch train generation is accomplished using a beamline capable of exchanging the coordinates between the horizontal and longitudinal degrees of freedom. An initial beam consisting of a set of horizontally-separated beamlets is converted into a train of bunches temporally separated with tunable bunch duration and separation. The experiment reported in this Letter unambiguously demonstrates the conversion process and its versatility.Comment: 4 pages, 5 figures, 1 table; accepted for publication in PR

Generation of Relativistic Electron Bunches with Arbitrary Current Distribution via Transverse-to-Longitudinal Phase Space Exchange

We propose a general method for tailoring the current distribution of relativistic electron bunches. The technique relies on a recently proposed method to exchange the longitudinal phase space emittance with one of the transverse emittances. The method consists of transversely shaping the bunch and then converting its transverse profile into a current profile via a transverse-to-longitudinal phase-space-exchange beamline. We show that it is possible to tailor the current profile to follow, in principle, any desired distributions. We demonstrate, via computer simulations, the application of the method to generate trains of microbunches with tunable spacing and linearly-ramped current profiles. We also briefly explore potential applications of the technique.Comment: 13 pages, 17 figure

Fermionic approach to the evaluation of integrals of rational symmetric functions

We use the fermionic construction of two-matrix model partition functions to evaluate integrals over rational symmetric functions. This approach is complementary to the one used in the paper ``Integrals of Rational Symmetric Functions, Two-Matrix Models and Biorthogonal Polynomials'' \cite{paper2}, where these integrals were evaluated by a direct method.Comment: 34 page