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.

Nonaxisymmetric magnetorotational instability in ideal and viscous plasmas

The excitation of magnetorotational instability (MRI) in rotating laboratory plasmas is investigated. In contrast to astrophysical plasmas, in which gravitation plays an important role, in laboratory plasmas it can be neglected and the plasma rotation is equilibrated by the pressure gradient. The analysis is restricted to the simple model of a magnetic confinement configuration with cylindrical symmetry, in which nonaxisymmetric perturbations are investigated using the local approximation. Starting from the simplest case of an ideal plasma, the corresponding dispersion relations are derived for more complicated models including the physical effects of parallel and perpendicular viscosities. The Friemann-Rotenberg approach used for ideal plasmas is generalized for the viscous model and an analytical expression for the instability boundary is obtained. It is shown that, in addition to the standard effect of radial derivative of the rotation frequency (the Velikhov effect), which can be destabilizing or stabilizing depending on the sign of this derivative in the ideal plasma, there is a destabilizing effect proportional to the fourth power of the rotation frequency, or, what is the same, to the square of the plasma pressure gradient, and to the square of the azimuthal mode number of the perturbations. It is shown that the instability boundary also depends on the product of the plasma pressure and density gradients, which has a destabilizing effect when it is negative. In the case of parallel viscosity, the MRI looks like an ideal instability independent of viscosity, while, in the case of strong perpendicular viscosity, it is a dissipative instability with the growth rate inversely proportional to the characteristic viscous decay rate. We point out, however, that the modes of the continuous range of the magnetohydrodynamics spectrum are not taken into account in this paper, and they can be more dangerous than those that are considered. (c) 2008 American Institute of Physics.

The Importance of Protein-Protein Interactions on the pH-Induced Conformational Changes of Bovine Serum Albumin: A Small-Angle X-Ray Scattering Study

The combined effects of concentration and pH on the conformational states of bovine serum albumin (BSA) are investigated by small-angle x-ray scattering. Serum albumins, at physiological conditions, are found at concentrations of similar to 35-45 mg/mL (42 mg/mL in the case of humans). In this work, BSA at three different concentrations (10, 25, and 50 mg/mL) and pH values (2.0-9.0) have been studied. Data were analyzed by means of the Global Fitting procedure, with the protein form factor calculated from human serum albumin (HSA) crystallographic structure and the interference function described, considering repulsive and attractive interaction potentials within a random phase approximation. Small-angle x-ray scattering data show that BSA maintains its native state from pH 4.0 up to 9.0 at all investigated concentrations. A pH-dependence of the absolute net protein charge is shown and the charge number per BSA is quantified to 10(2), 8(l), 13(2), 20(2), and 26(2) for pH values 4.0, 5.4, 7.0, 8.0, and 9.0, respectively. The attractive potential diminishes as BSA concentration increases. The coexistence of monomers and dimers is observed at 50 mg/mL and pH 5.4, near the BSA isoelectric point. Samples at pH 2.0 show a different behavior, because BSA overall shape changes as a function of concentration. At 10 mg/mL, BSA is partially unfolded and a strong repulsive protein-protein interaction occurs due to the high amount of exposed charge. At 25 and 50 mg/mL, BSA undergoes some refolding, which likely results in a molten-globule state. This work concludes by confirming that the protein concentration plays an important role on the pH-unfolded BSA state, due to a delicate compromise between interaction forces and crowding effects.

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.

Phase transitions and regions of stability in Reissner-Nordstrom holographic superconductors

The phase transition of Reissner-Nordstrom AdS(4) interacting with a massive charged scalar field has been further revisited. We found exactly one stable and one unstable quasinormal mode region for the scalar field. The two of them are separated by the first marginally stable solution.

Thermal Transport and Strong Mass Renormalization in NiCl(2)-4SC(NH(2))(2)

Several quantum paramagnets exhibit magnetic-field-induced quantum phase transitions to an anti-ferromagnetic state that exists for H(c1) <= H <= H(c2). For some of these compounds, there is a significant asymmetry between the low-and high-field transitions. We present specific heat and thermal conductivity measurements in NiCl(2)-4SC(NH(2))(2), together with calculations which show that the asymmetry is caused by a strong mass renormalization due to quantum fluctuations for H <= H(c1) that are absent for H >= H(c2). We argue that the enigmatic lack of asymmetry in thermal conductivity is due to a concomitant renormalization of the impurity scattering.

Observation of charge-dependent azimuthal correlations and possible local strong parity violation in heavy-ion collisions

Parity (P)-odd domains, corresponding to nontrivial topological solutions of the QCD vacuum, might be created during relativistic heavy-ion collisions. These domains are predicted to lead to charge separation of quarks along the orbital momentum of the system created in noncentral collisions. To study this effect, we investigate a three-particle mixed-harmonics azimuthal correlator which is a P-even observable, but directly sensitive to the charge-separation effect. We report measurements of this observable using the STAR detector in Au + Au and Cu + Cu collisions at root s(NN) = 200 and 62 GeV. The results are presented as a function of collision centrality, particle separation in rapidity, and particle transverse momentum. A signal consistent with several of the theoretical expectations is detected in all four data sets. We compare our results to the predictions of existing event generators and discuss in detail possible contributions from other effects that are not related to P violation.

Azimuthal Charged-Particle Correlations and Possible Local Strong Parity Violation

Parity-odd domains, corresponding to nontrivial topological solutions of the QCD vacuum, might be created during relativistic heavy-ion collisions. These domains are predicted to lead to charge separation of quarks along the system's orbital momentum axis. We investigate a three-particle azimuthal correlator which is a P even observable, but directly sensitive to the charge separation effect. We report measurements of charged hadrons near center-of-mass rapidity with this observable in Au+Au and Cu+Cu collisions at s(NN)=200 GeV using the STAR detector. A signal consistent with several expectations from the theory is detected. We discuss possible contributions from other effects that are not related to parity violation.

Gravitational stability of simply rotating Myers-Perry black holes: Tensorial perturbations

We study the stability of D >= 7 asymptotically flat black holes rotating in a single two-plane against tensor-type gravitational perturbations. The extensive search of quasinormal modes for these black holes did not indicate any presence of growing modes, implying the stability of simply rotating Myers-Perry black holes against tensor-type perturbations.

Stability of higher dimensional Reissner-Nordstrom-anti-de Sitter black holes

We investigate stability of the D-dimensional Reissner-Nordstrom-anti-de Sitter metrics as solutions of the Einstein-Maxwell equations. We have shown that asymptotically anti-de Sitter (AdS) black holes are dynamically stable for all values of charge and anti-de Sitter radius in D=5,6...11 dimensional space-times. This does not contradict dynamical instability of RNAdS black holes found by Gubser in N=8 gauged supergravity, because the latter instability comes from the tachyon mode of the scalar field, coupled to the system. Asymptotically AdS black holes are known to be thermodynamically unstable for some region of parameters, yet, as we have shown here, they are stable against gravitational perturbations.

(In)stability of D-dimensional black holes in Gauss-Bonnet theory

We make an extensive study of evolution of gravitational perturbations of D-dimensional black holes in Gauss-Bonnet theory. There is an instability at higher multipoles l and large Gauss-Bonnet coupling alpha for D = 5, 6, which is stabilized at higher D. Although a small negative gap of the effective potential for the scalar type of gravitational perturbations exists for higher D and whatever alpha, it does not lead to any instability.

Exotic phases induced by strong spin-orbit coupling in ordered double perovskites

We construct and analyze a microscopic model for insulating rocksalt ordered double perovskites, with the chemical formula A(2)BB'O(6), where the B' atom has a 4d(1) or 5d(1) electronic configuration and forms a face-centered-cubic lattice. The combination of the triply degenerate t(2g) orbital and strong spin-orbit coupling forms local quadruplets with an effective spin moment j=3/2. Moreover, due to strongly orbital-dependent exchange, the effective spins have substantial biquadratic and bicubic interactions (fourth and sixth order in the spins, respectively). This leads, at the mean-field level, to three main phases: an unusual antiferromagnet with dominant octupolar order, a ferromagnetic phase with magnetization along the [110] direction, and a nonmagnetic but quadrupolar ordered phase, which is stabilized by thermal fluctuations and intermediate temperatures. All these phases have a two-sublattice structure described by the ordering wave vector Q=2 pi(001). We consider quantum fluctuations and argue that in the regime of dominant antiferromagnetic exchange, a nonmagnetic valence-bond solid or quantum-spin-liquid state may be favored instead. Candidate quantum-spin-liquid states and their basic properties are described. We also address the effect of single-site anisotropy driven by lattice distortions. Existing and possible future experiments are discussed in light of these results.

The role of electron localization in the atomic structure of transition-metal 13-atom clusters: the example of Co(13), Rh(13), and Hf(13)

The crystalline structure of transition-metals (TM) has been widely known for several decades, however, our knowledge on the atomic structure of TM clusters is still far from satisfactory, which compromises an atomistic understanding of the reactivity of TM clusters. For example, almost all density functional theory (DFT) calculations for TM clusters have been based on local (local density approximation-LDA) and semilocal (generalized gradient approximation-GGA) exchange-correlation functionals, however, it is well known that plain DFT fails to correct the self-interaction error, which affects the properties of several systems. To improve our basic understanding of the atomic and electronic properties of TM clusters, we report a DFT study within two nonlocal functionals, namely, the hybrid HSE (Heyd, Scuseria, and Ernzerhof) and GGA + U functionals, of the structural and electronic properties of the Co(13), Rh(13), and Hf(13) clusters. For Co(13) and Rh(13), we found that improved exchange-correlation functionals decrease the stability of open structures such as the hexagonal bilayer (HBL) and double simple-cubic (DSC) compared with the compact icosahedron (ICO) structure, however, DFT-GGA, DFT-GGA + U, and DFT-HSE yield very similar results for Hf(13). Thus, our results suggest that the DSC structure obtained by several plain DFT calculations for Rh(13) can be improved by the use of improved functionals. Using the sd hybridization analysis, we found that a strong hybridization favors compact structures, and hence, a correct description of the sd hybridization is crucial for the relative energy stability. For example, the sd hybridization decreases for HBL and DSC and increases for ICO in the case of Co(13) and Rh(13), while for Hf(13), the sd hybridization decreases for all configurations, and hence, it does not affect the relative stability among open and compact configurations.

GLOBAL WELL-POSEDNESS AND NON-LINEAR STABILITY OF PERIODIC TRAVELING WAVES FOR A SCHRODINGER-BENJAMIN-ONO SYSTEM

The objective of this paper is two-fold: firstly, we develop a local and global (in time) well-posedness theory for a system describing the motion of two fluids with different densities under capillary-gravity waves in a deep water flow (namely, a Schrodinger-Benjamin-Ono system) for low-regularity initial data in both periodic and continuous cases; secondly, a family of new periodic traveling waves for the Schrodinger-Benjamin-Ono system is given: by fixing a minimal period we obtain, via the implicit function theorem, a smooth branch of periodic solutions bifurcating a Jacobian elliptic function called dnoidal, and, moreover, we prove that all these periodic traveling waves are nonlinearly stable by perturbations with the same wavelength.

POSITIVITY PROPERTIES OF THE FOURIER TRANSFORM AND THE STABILITY OF PERIODIC TRAVELLING-WAVE SOLUTIONS

In this paper we establish a method to obtain the stability of periodic travelling-wave solutions for equations of Korteweg-de Vries-type u(t) + u(p)u(x) - Mu(x) = 0, with M being a general pseudodifferential operator and where p >= 1 is an integer. Our approach uses the theory of totally positive operators, the Poisson summation theorem, and the theory of Jacobi elliptic functions. In particular we obtain the stability of a family of periodic travelling waves solutions for the Benjamin Ono equation. The present technique gives a new way to obtain the existence and stability of cnoidal and dnoidal waves solutions associated with the Korteweg-de Vries and modified Korteweg-de Vries equations, respectively. The theory has prospects for the study of periodic travelling-wave solutions of other partial differential equations.