3,005 research outputs found
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
Critical thermodynamics of two-dimensional N-vector cubic model in the five-loop approximation
The critical behavior of the two-dimensional N-vector cubic model is studied
within the field-theoretical renormalization-group (RG) approach. The
beta-functions and critical exponents are calculated in the five-loop
approximation, RG series obtained are resummed using Pade-Borel-Leroy and
conformal mapping techniques. It is found that for N = 2 the continuous line of
fixed points is well reproduced by the resummed RG series and an account for
the five-loop terms makes the lines of zeros of both beta-functions closer to
each another. For N > 2 the five-loop contributions are shown to shift the
cubic fixed point, given by the four-loop approximation, towards the Ising
fixed point. This confirms the idea that the existence of the cubic fixed point
in two dimensions under N > 2 is an artifact of the perturbative analysis. In
the case N = 0 the results obtained are compatible with the conclusion that the
impure critical behavior is controlled by the Ising fixed point.Comment: 18 pages, 4 figure
Photonic band-gap engineering for volume plasmon polaritons in multiscale multilayer hyperbolic metamaterials
We theoretically study the propagation of large-wavevector waves (volume
plasmon polaritons) in multilayer hyperbolic metamaterials with two levels of
structuring. We show that when the parameters of a subwavelength
metal-dielectric multilayer ("substructure") are modulated ("superstructured")
on a larger, wavelength scale, the propagation of volume plasmon polaritons in
the resulting multiscale hyperbolic metamaterials is subject to photonic band
gap phenomena. A great degree of control over such plasmons can be exerted by
varying the superstructure geometry. When this geometry is periodic, stop bands
due to Bragg reflection form within the volume plasmonic band. When a cavity
layer is introduced in an otherwise periodic superstructure, resonance peaks of
the Fabry-Perot nature are present within the stop bands. More complicated
superstructure geometries are also considered. For example, fractal Cantor-like
multiscale metamaterials are found to exhibit characteristic self-similar
spectral signatures in the volume plasmonic band. Multiscale hyperbolic
metamaterials are shown to be a promising platform for large-wavevector bulk
plasmonic waves, whether they are considered for use as a new kind of
information carrier or for far-field subwavelength imaging.Comment: 12 pages, 10 figures, now includes Appendix
Search for Spatial Structures at Scales Z~1. III. The Effect of Lensing on QSO ?
We carried out a search for peak inhomogeneities in the distribution of
matter - namely clumps and voids, within the range Z ~ 1-3. We used a new
method, based on the lensing of quasars by a combination of lenses, belonging
to the above sought inhomogeneities in the matter distribution. This work
confirms the evidence of the existence of inhomogeneities found by us earlier -
of a clump (superattractor N.1), and of a void (supervoid). Besides, the
existence of a new gigantic clump (superattractor N.2) was also discovered at Z
~ 3. These clumps could well serve as centers of the Bose-condensation in the
early Universe; in particular - as Anselm's arion condensate, which leads to
the formation of quasiperiodic structures with a period p ~ 100-200 Mpc.Comment: 22 pages, 2 figures, 6 tables. submitted to Astrophys.& Space Sc
Fermionic construction of partition functions for two-matrix models and perturbative Schur function expansions
A new representation of the 2N fold integrals appearing in various two-matrix
models that admit reductions to integrals over their eigenvalues is given in
terms of vacuum state expectation values of operator products formed from
two-component free fermions. This is used to derive the perturbation series for
these integrals under deformations induced by exponential weight factors in the
measure, expressed as double and quadruple Schur function expansions,
generalizing results obtained earlier for certain two-matrix models. Links with
the coupled two-component KP hierarchy and the two-component Toda lattice
hierarchy are also derived.Comment: Submitted to: "Random Matrices, Random Processes and Integrable
Systems", Special Issue of J. Phys. A, based on the Centre de recherches
mathematiques short program, Montreal, June 20-July 8, 200
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