PARTIAL STABILITY FOR A CLASS OF NONLINEAR SYSTEMS

This paper studies a nonlinear, discrete-time matrix system arising in the stability analysis of Kalman filters. These systems present an internal coupling between the state components that gives rise to complex dynamic behavior. The problem of partial stability, which requires that a specific component of the state of the system converge exponentially, is studied and solved. The convergent state component is strongly linked with the behavior of Kalman filters, since it can be used to provide bounds for the error covariance matrix under uncertainties in the noise measurements. We exploit the special features of the system-mainly the connections with linear systems-to obtain an algebraic test for partial stability. Finally, motivated by applications in which polynomial divergence of the estimates is acceptable, we study and solve a partial semistability problem.

Emission and dry deposition of accumulation mode particles in the Amazon Basin

Size-resolved vertical aerosol number fluxes of particles in the diameter range 0.25-2.5 mu m were measured with the eddy covariance method from a 53 m high tower over the Amazon rain forest, 60 km NNW of Manaus, Brazil. This study focuses on data measured during the relatively clean wet season, but a shorter measurement period from the more polluted dry season is used as a comparison. Size-resolved net particle fluxes of the five lowest size bins, representing 0.25-0.45 mu m in diameter, were in general dominated by deposition in more or less all wind sectors in the wet season. This is an indication that the source of primary biogenic aerosol particles may be small in this particle size range. Transfer velocities within this particle size range were observed to increase linearly with increasing friction velocity and increasing particle diameter. In the diameter range 0.5-2.5 mu m, vertical particle fluxes were highly dependent on wind direction. In wind sectors where anthropogenic influence was low, net upward fluxes were observed. However, in wind sectors associated with higher anthropogenic influence, deposition fluxes dominated. The net upward fluxes were interpreted as a result of primary biogenic aerosol emission, but deposition of anthropogenic particles seems to have masked this emission in wind sectors with higher anthropogenic influence. The net emission fluxes were at maximum in the afternoon when the mixed layer is well developed, and were best correlated with horizontal wind speed according to the equation log(10)F = 0.48.U + 2.21 where F is the net emission number flux of 0.5-2.5 mu m particles [m(-2) s(-1)] and U is the horizontal wind speed [ms(-1)] at the top of the tower.

A comparison of dry and wet season aerosol number fluxes over the Amazon rain forest

Vertical number fluxes of aerosol particles and vertical fluxes of CO(2) were measured with the eddy covariance method at the top of a 53 m high tower in the Amazon rain forest as part of the LBA (The Large Scale Biosphere Atmosphere Experiment in Amazonia) experiment. The observed aerosol number fluxes included particles with sizes down to 10 nm in diameter. The measurements were carried out during the wet and dry season in 2008. In this study focus is on the dry season aerosol fluxes, with significant influence from biomass burning, and these are compared with aerosol fluxes measured during the wet season. Net particle deposition fluxes dominated in daytime in both seasons and the deposition flux was considerably larger in the dry season due to the much higher dry season particle concentration. The particle transfer velocity increased linearly with increasing friction velocity in both seasons. The difference in transfer velocity between the two seasons was small, indicating that the seasonal change in aerosol number size distribution is not enough for causing any significant change in deposition velocity. In general, particle transfer velocities in this study are low compared to studies over boreal forests. The reasons are probably the high percentage of accumulation mode particles and the low percentage of nucleation mode particles in the Amazon boundary layer, both in the dry and wet season, and low wind speeds in the tropics compared to the midlatitudes. In the dry season, nocturnal particle fluxes behaved very similar to the nocturnal CO(2) fluxes. Throughout the night, the measured particle flux at the top of the tower was close to zero, but early in the morning there was an upward particle flux peak that is not likely a result of entrainment or local pollution. It is possible that these morning upward particle fluxes are associated with emission of primary biogenic particles from the rain forest. Emitted particles may be stored within the canopy during stable conditions at nighttime, similarly to CO(2), and being released from the canopy when conditions become more turbulent in the morning.

Aerosol number fluxes over the Amazon rain forest during the wet season

Number fluxes of particles with diameter larger than 10 nm were measured with the eddy covariance method over the Amazon rain forest during the wet season as part of the LBA (The Large Scale Biosphere Atmosphere Experiment in Amazonia) campaign 2008. The primary goal was to investigate whether sources or sinks dominate the aerosol number flux in the tropical rain forest-atmosphere system. During the measurement campaign, from 12 March to 18 May, 60% of the particle fluxes pointed downward, which is a similar fraction to what has been observed over boreal forests. The net deposition flux prevailed even in the absolute cleanest atmospheric conditions during the campaign and therefore cannot be explained only by deposition of anthropogenic particles. The particle transfer velocity v(t) increased with increasing friction velocity and the relation is described by the equation v(t) = 2.4x10(-3)xu(*) where u(*) is the friction velocity. Upward particle fluxes often appeared in the morning hours and seem to a large extent to be an effect of entrainment fluxes into a growing mixed layer rather than primary aerosol emission. In general, the number source of primary aerosol particles within the footprint area of the measurements was small, possibly because the measured particle number fluxes reflect mostly particles less than approximately 200 nm. This is an indication that the contribution of primary biogenic aerosol particles to the aerosol population in the Amazon boundary layer may be low in terms of number concentrations. However, the possibility of horizontal variations in primary aerosol emission over the Amazon rain forest cannot be ruled out.

Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices

The properties of the localized states of a two-component Bose-Einstein condensate confined in a nonlinear periodic potential (nonlinear optical lattice) are investigated. We discuss the existence of different types of solitons and study their stability by means of analytical and numerical approaches. The symmetry properties of the localized states with respect to nonlinear optical lattices are also investigated. We show that nonlinear optical lattices allow the existence of bright soliton modes with equal symmetry in both components and bright localized modes of mixed symmetry type, as well as dark-bright bound states and bright modes on periodic backgrounds. In spite of the quasi-one-dimensional nature of the problem, the fundamental symmetric localized modes undergo a delocalizing transition when the strength of the nonlinear optical lattice is varied. This transition is associated with the existence of an unstable solution, which exhibits a shrinking (decaying) behavior for slightly overcritical (undercritical) variations in the number of atoms.

Diffusion anomaly and dynamic transitions in the Bell-Lavis water model

In this paper we investigate the dynamic properties of the minimal Bell-Lavis (BL) water model and their relation to the thermodynamic anomalies. The BL model is defined on a triangular lattice in which water molecules are represented by particles with three symmetric bonding arms interacting through van der Waals and hydrogen bonds. We have studied the model diffusivity in different regions of the phase diagram through Monte Carlo simulations. Our results show that the model displays a region of anomalous diffusion which lies inside the region of anomalous density, englobed by the line of temperatures of maximum density. Further, we have found that the diffusivity undergoes a dynamic transition which may be classified as fragile-to-strong transition at the critical line only at low pressures. At higher densities, no dynamic transition is seen on crossing the critical line. Thus evidence from this study is that relation of dynamic transitions to criticality may be discarded. (C) 2010 American Institute of Physics. [doi:10.1063/1.3479001]

Stability, causality, and quasinormal modes of cosmic strings and cylinders

In this work we consider the evolution of a massive scalar field in cylindrically symmetric space-times. Quasinormal modes have been calculated for static and rotating cosmic cylinders. We found unstable modes in some cases. Rotating as well as static cosmic strings, i.e., without regular interior solutions, do not display quasinormal oscillation modes. We conclude that rotating cosmic cylinder space-times that present closed timelike curves are unstable against scalar perturbations.

Perturbative finiteness of three-dimensional supersymmetric QED to all orders

Within the superfield formalism, we study the ultraviolet properties of the three-dimensional super-symmetric quantum electrodynamics. The theory is shown to be finite at all loop orders in a particular gauge.

Passage of radiation through wormholes of arbitrary shape

We study quasinormal modes and scattering properties via calculation of the S matrix for scalar and electromagnetic fields propagating in the background of spherically symmetric and axially symmetric traversable Lorentzian wormholes of a generic shape. Such wormholes are described by the general Morris-Thorne ansatz. The properties of quasinormal ringing and scattering are shown to be determined by the behavior of the wormhole's shape function b(r) and shift factor Phi(r) near the throat. In particular, wormholes with the shape function b(r), such that b(dr) approximate to 1, have very long-lived quasinormal modes in the spectrum. We have proved that the axially symmetric traversable Lorentzian wormholes, unlike black holes and other compact rotating objects, do not allow for superradiance. As a by-product we have shown that the 6th order WKB formula used for scattering problems of black or wormholes gives quite high accuracy and thus can be used for quite accurate calculations of the Hawking radiation processes around various black holes.

Electromagnetic absorption cross section of Reissner-Nordstroumlm black holes revisited

The absorption cross section of Reissner-Nordstroumlm black holes for the electromagnetic field is computed numerically for arbitrary frequencies, taking into account the coupling of the electromagnetic and gravitational perturbations. We also compute the conversion coefficients of electromagnetic to gravitational waves by scattering from a Reissner-Nordstroumlm black hole.

Gravitational wave recoil in Robinson-Trautman spacetimes

We consider the gravitational recoil due to nonreflection-symmetric gravitational wave emission in the context of axisymmetric Robinson-Trautman spacetimes. We show that regular initial data evolve generically into a final configuration corresponding to a Schwarzschild black hole moving with constant speed. For the case of (reflection-)symmetric initial configurations, the mass of the remnant black hole and the total energy radiated away are completely determined by the initial data, allowing us to obtain analytical expressions for some recent numerical results that have appeared in the literature. Moreover, by using the Galerkin spectral method to analyze the nonlinear regime of the Robinson-Trautman equations, we show that the recoil velocity can be estimated with good accuracy from some asymmetry measures (namely the first odd moments) of the initial data. The extension for the nonaxisymmetric case and the implications of our results for realistic situations involving head-on collision of two black holes are also discussed.

Quasinormal modes of brane-localized standard model fields in Gauss-Bonnet theory

We study the massless scalar, Dirac, and electromagnetic fields propagating on a 4D-brane, which is embedded in higher-dimensional Gauss-Bonnet space-time. We calculate, in the time domain, the fundamental quasinormal modes of a spherically symmetric black hole for such fields. Using WKB approximation we study quasinormal modes in the large multipole limit. We observe also a universal behavior, independent on a field and value of the Gauss-Bonnet parameter, at an asymptotically late time.

Intersubband-induced spin-orbit interaction in quantum wells

Recently, we have found an additional spin-orbit (SO) interaction in quantum wells with two subbands [Bernardes , Phys. Rev. Lett. 99, 076603 (2007)]. This new SO term is nonzero even in symmetric geometries, as it arises from the intersubband coupling between confined states of distinct parities, and its strength is comparable to that of the ordinary Rashba. Starting from the 8x8 Kane model, here we present a detailed derivation of this new SO Hamiltonian and the corresponding SO coupling. In addition, within the self-consistent Hartree approximation, we calculate the strength of this new SO coupling for realistic symmetric modulation-doped wells with two subbands. We consider gated structures with either a constant areal electron density or a constant chemical potential. In the parameter range studied, both models give similar results. By considering the effects of an external applied bias, which breaks the structural inversion symmetry of the wells, we also calculate the strength of the resulting induced Rashba couplings within each subband. Interestingly, we find that for double wells the Rashba couplings for the first and second subbands interchange signs abruptly across the zero bias, while the intersubband SO coupling exhibits a resonant behavior near this symmetric configuration. For completeness we also determine the strength of the Dresselhaus couplings and find them essentially constant as function of the applied bias.

Isotropic and anisotropic spin-spin interactions and a quantum phase transition in a dinuclear Cu(II) compound

We report electron-paramagnetic resonance (EPR) studies at similar to 9.5 GHz (X band) and similar to 34 GHz (Q band) of powder and single-crystal samples of the compound Cu(2)[TzTs](4) [N-thiazol-2-yl-toluenesulfonamidatecopper(II)], C(40)H(36)Cu(2)N(8)O(8)S(8), having copper(II) ions in dinuclear units. Our data allow determining an antiferromagnetic interaction J(0)=(-113 +/- 1) cm(-1) (H(ex)=-J(0)S(1)center dot S(2)) between Cu(II) ions in the dinuclear unit and the anisotropic contributions to the spin-spin coupling matrix D (H(ani)=S(1)center dot D center dot S(2)), a traceless symmetric matrix with principal values D/4=(0.198 +/- 0.003) cm(-1) and E/4=(0.001 +/- 0.003) cm(-1) arising from magnetic dipole-dipole and anisotropic exchange couplings within the units. In addition, the single-crystal EPR measurements allow detecting and estimating very weak exchange couplings between neighbor dinuclear units, with an estimated magnitude parallel to J(')parallel to=(0.060 +/- 0.015) cm(-1). The interactions between a dinuclear unit and the ""environment"" of similar units in the structure of the compound produce a spin dynamics that averages out the intradinuclear dipolar interactions. This coupling with the environment leads to decoherence, a quantum phase transition that collapses the dipolar interaction when the isotropic exchange coupling with neighbor dinuclear units equals the magnitude of the intradinuclear dipolar coupling. Our EPR experiments provide a new procedure to follow the classical exchange-narrowing process as a shift and collapse of the line structure (not only as a change of the resonance width), which is described with general (but otherwise simple) theories of magnetic resonance. Using complementary procedures, our EPR measurements in powder and single-crystal samples allow measuring simultaneously three types of interactions differing by more than three orders of magnitude (between 113 cm(-1) and 0.060 cm(-1)).

Experimentally Witnessing the Quantumness of Correlations

The quantification of quantum correlations (other than entanglement) usually entails labored numerical optimization procedures also demanding quantum state tomographic methods. Thus it is interesting to have a laboratory friendly witness for the nature of correlations. In this Letter we report a direct experimental implementation of such a witness in a room temperature nuclear magnetic resonance system. In our experiment the nature of correlations is revealed by performing only few local magnetization measurements. We also compared the witness results with those for the symmetric quantum discord and we obtained a fairly good agreement.