Multistability and Self-Similarity in the Parameter-Space of a Vibro-Impact System

The dynamics of a dissipative vibro-impact system called impact-pair is investigated. This system is similar to Fermi-Ulam accelerator model and consists of an oscillating one-dimensional box containing a point mass moving freely between successive inelastic collisions with the rigid walls of the box. In our numerical simulations, we observed multistable regimes, for which the corresponding basins of attraction present a quite complicated structure with smooth boundary. In addition, we characterize the system in a two-dimensional parameter space by using the largest Lyapunov exponents, identifying self-similar periodic sets. Copyright (C) 2009 Silvio L.T. de Souza et al.

Remote sensing the vertical profile of cloud droplet effective radius, thermodynamic phase, and temperature

Cloud-aerosol interaction is a key issue in the climate system, affecting the water cycle, the weather, and the total energy balance including the spatial and temporal distribution of latent heat release. Information on the vertical distribution of cloud droplet microphysics and thermodynamic phase as a function of temperature or height, can be correlated with details of the aerosol field to provide insight on how these particles are affecting cloud properties and their consequences to cloud lifetime, precipitation, water cycle, and general energy balance. Unfortunately, today's experimental methods still lack the observational tools that can characterize the true evolution of the cloud microphysical, spatial and temporal structure in the cloud droplet scale, and then link these characteristics to environmental factors and properties of the cloud condensation nuclei. Here we propose and demonstrate a new experimental approach (the cloud scanner instrument) that provides the microphysical information missed in current experiments and remote sensing options. Cloud scanner measurements can be performed from aircraft, ground, or satellite by scanning the side of the clouds from the base to the top, providing us with the unique opportunity of obtaining snapshots of the cloud droplet microphysical and thermodynamic states as a function of height and brightness temperature in clouds at several development stages. The brightness temperature profile of the cloud side can be directly associated with the thermodynamic phase of the droplets to provide information on the glaciation temperature as a function of different ambient conditions, aerosol concentration, and type. An aircraft prototype of the cloud scanner was built and flew in a field campaign in Brazil. The CLAIM-3D (3-Dimensional Cloud Aerosol Interaction Mission) satellite concept proposed here combines several techniques to simultaneously measure the vertical profile of cloud microphysics, thermodynamic phase, brightness temperature, and aerosol amount and type in the neighborhood of the clouds. The wide wavelength range, and the use of multi-angle polarization measurements proposed for this mission allow us to estimate the availability and characteristics of aerosol particles acting as cloud condensation nuclei, and their effects on the cloud microphysical structure. These results can provide unprecedented details on the response of cloud droplet microphysics to natural and anthropogenic aerosols in the size scale where the interaction really happens.

Evaluation of the carbon content of aerosols from the burning of biomass in the Brazilian Amazon using thermal, optical and thermal-optical analysis methods

Aerosol samples were collected at a pasture site in the Amazon Basin as part of the project LBA-SMOCC-2002 (Large-Scale Biosphere-Atmosphere Experiment in Amazonia - Smoke Aerosols, Clouds, Rainfall and Climate: Aerosols from Biomass Burning Perturb Global and Regional Climate). Sampling was conducted during the late dry season, when the aerosol composition was dominated by biomass burning emissions, especially in the submicron fraction. A 13-stage Dekati low-pressure impactor (DLPI) was used to collect particles with nominal aerodynamic diameters (D(p)) ranging from 0.03 to 0.10 mu m. Gravimetric analyses of the DLPI substrates and filters were performed to obtain aerosol mass concentrations. The concentrations of total, apparent elemental, and organic carbon (TC, EC(a), and OC) were determined using thermal and thermal-optical analysis (TOA) methods. A light transmission method (LTM) was used to determine the concentration of equivalent black carbon (BC(e)) or the absorbing fraction at 880 nm for the size-resolved samples. During the dry period, due to the pervasive presence of fires in the region upwind of the sampling site, concentrations of fine aerosols (D(p) < 2.5 mu m: average 59.8 mu g m(-3)) were higher than coarse aerosols (D(p) > 2.5 mu m: 4.1 mu g m(-3)). Carbonaceous matter, estimated as the sum of the particulate organic matter (i.e., OC x 1.8) plus BC(e), comprised more than 90% to the total aerosol mass. Concentrations of EC(a) (estimated by thermal analysis with a correction for charring) and BC(e) (estimated by LTM) averaged 5.2 +/- 1.3 and 3.1 +/- 0.8 mu g m(-3), respectively. The determination of EC was improved by extracting water-soluble organic material from the samples, which reduced the average light absorption Angstrom exponent of particles in the size range of 0.1 to 1.0 mu m from >2.0 to approximately 1.2. The size-resolved BC(e) measured by the LTM showed a clear maximum between 0.4 and 0.6 mu m in diameter. The concentrations of OC and BC(e) varied diurnally during the dry period, and this variation is related to diurnal changes in boundary layer thickness and in fire frequency.

Width of exotics from QCD sum rules : Tetraquarks or molecules?

We investigate the widths of the recently observed charmonium like resonances X(3872), Z(4430), and Z(2)(4250) using QCD sum rules. Extending previous analyses regarding these states as diquark-antiquark states or molecules of D mesons, we introduce the Breit-Wigner function in the pole term. We find that introducing the width increases the mass at the small Borel window region. Using the operator-product expansion up to dimension 8, we find that the sum rules based on interpolating current with molecular components give a stable Borel curve from which both the masses and widths of these resonances can be well obtained. Thus the QCD sum rule approach strongly favors the molecular description of these states.

Entropy production in irreversible systems described by a Fokker-Planck equation

We analyze the irreversibility and the entropy production in nonequilibrium interacting particle systems described by a Fokker-Planck equation by the use of a suitable master equation representation. The irreversible character is provided either by nonconservative forces or by the contact with heat baths at distinct temperatures. The expression for the entropy production is deduced from a general definition, which is related to the probability of a trajectory in phase space and its time reversal, that makes no reference a priori to the dissipated power. Our formalism is applied to calculate the heat conductance in a simple system consisting of two Brownian particles each one in contact to a heat reservoir. We show also the connection between the definition of entropy production rate and the Jarzynski equality.

Suppression of away-side jet fragments with respect to the reaction plane in Au plus Au collisions at root s(NN)=200 GeV

Pair correlations between large transverse momentum neutral pion triggers (p(T) = 4-7 GeV/c) and charged hadron partners (p(T) = 3-7 GeV/c) in central (0%-20%) and midcentral (20%-60%) Au + Au collisions at root s(NN) = 200 GeV are presented as a function of trigger orientation with respect to the reaction plane. The particles are at larger momentum than where jet shape modifications have been observed, and the correlations are sensitive to the energy loss of partons traveling through hot densematter. An out-of-plane trigger particle produces only 26 +/- 20% of the away-side pairs that are observed opposite of an in-plane trigger particle for midcentral (20%-60%) collisions. In contrast, near-side jet fragments are consistent with no suppression or dependence on trigger orientation with respect to the reaction plane. These observations are qualitatively consistent with a picture of little near-side parton energy loss either due to surface bias or fluctuations and increased away-side parton energy loss due to a long path through the medium. The away-side suppression as a function of reaction-plane angle is shown to be sensitive to both the energy loss mechanism and the space-time evolution of heavy-ion collisions.

Determination of the spin of new resonances in electroweak gauge boson pair production at the LHC

The appearance of spin-1 resonances associated with the electroweak symmetry breaking sector is expected in many extensions of the standard model. We analyze the CERN Large Hadron Collider potential to probe the spin of possible new charged and neutral vector resonances through the purely leptonic processes pp -> Z' -> l(+) l'(-) E(T), and pp -> W' -> l'(+/-) l(+) l(-) E(T), with l, l' = e or mu. We perform a model-independent analysis and demonstrate that the spin of the new states can be determined with 99% C. L. in a large fraction of the parameter space where these resonances can be observed with 100 fb(-1). We show that the best sensitivity to the spin is obtained by directly studying correlations between the final state leptons, without the need of reconstructing the events in their center-of-mass frames.

Quantum and pseudoclassical descriptions of nonrelativistic spinning particles in noncommutative space

We construct a nonrelativistic wave equation for spinning particles in the noncommutative space (in a sense, a theta modification of the Pauli equation). To this end, we consider the nonrelativistic limit of the theta-modified Dirac equation. To complete the consideration, we present a pseudoclassical model (a la Berezin-Marinov) for the corresponding nonrelativistic particle in the noncommutative space. To justify the latter model, we demonstrate that its quantization leads to the theta-modified Pauli equation. We extract theta-modified interaction between a nonrelativistic spin and a magnetic field from such a Pauli equation and construct a theta modification of the Heisenberg model for two coupled spins placed in an external magnetic field. In the framework of such a model, we calculate the probability transition between two orthogonal Einstein-Podolsky-Rosen states for a pair of spins in an oscillatory magnetic field and show that some of such transitions, which are forbidden in the commutative space, are possible due to the space noncommutativity. This allows us to estimate an upper bound on the noncommutativity parameter.

Balance functions from Au+Au, d+Au, and p+p collisions at root s(NN)=200 GeV

Balance functions have been measured for charged-particle pairs, identified charged-pion pairs, and identified charged-kaon pairs in Au + Au, d + Au, and p + p collisions at root s(NN) = 200 GeV at the Relativistic Heavy Ion Collider using the STAR detector. These balance functions are presented in terms of relative pseudorapidity, Delta eta, relative rapidity, Delta y, relative azimuthal angle, Delta phi, and invariant relative momentum, q(inv). For charged-particle pairs, the width of the balance function in terms of Delta eta scales smoothly with the number of participating nucleons, while HIJING and UrQMD model calculations show no dependence on centrality or system size. For charged-particle and charged-pion pairs, the balance functions widths in terms of Delta eta and Delta y are narrower in central Au + Au collisions than in peripheral collisions. The width for central collisions is consistent with thermal blast-wave models where the balancing charges are highly correlated in coordinate space at breakup. This strong correlation might be explained by either delayed hadronization or limited diffusion during the reaction. Furthermore, the narrowing trend is consistent with the lower kinetic temperatures inherent to more central collisions. In contrast, the width of the balance function for charged-kaon pairs in terms of Delta y shows little centrality dependence, which may signal a different production mechanism for kaons. The widths of the balance functions for charged pions and kaons in terms of q(inv) narrow in central collisions compared to peripheral collisions, which may be driven by the change in the kinetic temperature.

The clusters Abell 222 and Abell 223: a multi-wavelength view

Context. The Abell 222 and 223 clusters are located at an average redshift z similar to 0.21 and are separated by 0.26 deg. Signatures of mergers have been previously found in these clusters, both in X-rays and at optical wavelengths, thus motivating our study. In X-rays, they are relatively bright, and Abell 223 shows a double structure. A filament has also been detected between the clusters both at optical and X-ray wavelengths. Aims. We analyse the optical properties of these two clusters based on deep imaging in two bands, derive their galaxy luminosity functions (GLFs) and correlate these properties with X-ray characteristics derived from XMM-Newton data. Methods. The optical part of our study is based on archive images obtained with the CFHT Megaprime/Megacam camera, covering a total region of about 1 deg(2), or 12.3 x 12.3 Mpc(2) at a redshift of 0.21. The X-ray analysis is based on archive XMM-Newton images. Results. The GLFs of Abell 222 in the g' and r' bands are well fit by a Schechter function; the GLF is steeper in r' than in g'. For Abell 223, the GLFs in both bands require a second component at bright magnitudes, added to a Schechter function; they are similar in both bands. The Serna & Gerbal method allows to separate well the two clusters. No obvious filamentary structures are detected at very large scales around the clusters, but a third cluster at the same redshift, Abell 209, is located at a projected distance of 19.2 Mpc. X-ray temperature and metallicity maps reveal that the temperature and metallicity of the X-ray gas are quite homogeneous in Abell 222, while they are very perturbed in Abell 223. Conclusions. The Abell 222/Abell 223 system is complex. The two clusters that form this structure present very different dynamical states. Abell 222 is a smaller, less massive and almost isothermal cluster. On the other hand, Abell 223 is more massive and has most probably been crossed by a subcluster on its way to the northeast. As a consequence, the temperature distribution is very inhomogeneous. Signs of recent interactions are also detected in the optical data where this cluster shows a ""perturbed"" GLF. In summary, the multiwavelength analyses of Abell 222 and Abell 223 are used to investigate the connection between the ICM and the cluster galaxy properties in an interacting system.

INFERENCE FOR EIGENVALUES AND EIGENVECTORS OF GAUSSIAN SYMMETRIC MATRICES

This article presents maximum likelihood estimators (MLEs) and log-likelihood ratio (LLR) tests for the eigenvalues and eigenvectors of Gaussian random symmetric matrices of arbitrary dimension, where the observations are independent repeated samples from one or two populations. These inference problems are relevant in the analysis of diffusion tensor imaging data and polarized cosmic background radiation data, where the observations are, respectively, 3 x 3 and 2 x 2 symmetric positive definite matrices. The parameter sets involved in the inference problems for eigenvalues and eigenvectors are subsets of Euclidean space that are either affine subspaces, embedded submanifolds that are invariant under orthogonal transformations or polyhedral convex cones. We show that for a class of sets that includes the ones considered in this paper, the MLEs of the mean parameter do not depend on the covariance parameters if and only if the covariance structure is orthogonally invariant. Closed-form expressions for the MLEs and the associated LLRs are derived for this covariance structure.

ON ISOMORPHIC CLASSIFICATIONS OF SPACES OF COMPACT OPERATORS

We prove an extension of the classical isomorphic classification of Banach spaces of continuous functions on ordinals. As a consequence, we give complete isomorphic classifications of some Banach spaces K(X,Y(n)), eta >= omega, of compact operators from X to Y(eta), the space of all continuous Y-valued functions defined in the interval of ordinals [1, eta] and equipped with the supremum norm. In particular, under the Continuum Hypothesis, we extend a recent result of C. Samuel by classifying, up to isomorphism, the spaces K(X(xi), c(0)(Gamma)(eta)), where omega <= xi < omega(1,) eta >= omega, Gamma is a countable set, X contains no complemented copy of l(1), X* has the Mazur property and the density character of X** is less than or equal to N(1).

ON THE THREE-DIMENSIONAL BLASCHKE-LEBESGUE PROBLEM

The width of a closed convex subset of n-dimensional Euclidean space is the distance between two parallel supporting hyperplanes. The Blaschke-Lebesgue problem consists of minimizing the volume in the class of convex sets of fixed constant width and is still open in dimension n >= 3. In this paper we describe a necessary condition that the minimizer of the Blaschke-Lebesgue must satisfy in dimension n = 3: we prove that the smooth components of the boundary of the minimizer have their smaller principal curvature constant and therefore are either spherical caps or pieces of tubes (canal surfaces).

Can we make a Bohmian electron reach the speed of light, at least for one instant?

In Bohmian mechanics, a version of quantum mechanics that ascribes world lines to electrons, we can meaningfully ask about an electron's instantaneous speed relative to a given inertial frame. Interestingly, according to the relativistic version of Bohmian mechanics using the Dirac equation, a massive particle's speed is less than or equal to the speed of light, but not necessarily less. That is, there are situations in which the particle actually reaches the speed of light-a very nonclassical behavior. That leads us to the question of whether such situations can be arranged experimentally. We prove a theorem, Theorem 5, implying that for generic initial wave functions the probability that the particle ever reaches the speed of light, even if at only one point in time, is zero. We conclude that the answer to the question is no. Since a trajectory reaches the speed of light whenever the quantum probability current (psi) over bar gamma(mu)psi is a lightlike 4-vector, our analysis concerns the current vector field of a generic wave function and may thus be of interest also independently of Bohmian mechanics. The fact that the current is never spacelike has been used to argue against the possibility of faster-than-light tunneling through a barrier, a somewhat similar question. Theorem 5, as well as a more general version provided by Theorem 6, are also interesting in their own right. They concern a certain property of a function psi : R(4) -> C(4) that is crucial to the question of reaching the speed of light, namely being transverse to a certain submanifold of C(4) along a given compact subset of space-time. While it follows from the known transversality theorem of differential topology that this property is generic among smooth functions psi : R(4) -> C(4), Theorem 5 asserts that it is also generic among smooth solutions of the Dirac equation. (C) 2010 American Institute of Physics. [doi:10.1063/1.3520529]

COUNTABLE GROUPS OF ISOMETRIES ON BANACH SPACES

A group G is representable in a Banach space X if G is isomorphic to the group of isometrics on X in some equivalent norm. We prove that a countable group G is representable in a separable real Banach space X in several general cases, including when G similar or equal to {-1,1} x H, H finite and dim X >= vertical bar H vertical bar or when G contains a normal subgroup with two elements and X is of the form c(0)(Y) or l(p)(Y), 1 <= p < +infinity. This is a consequence of a result inspired by methods of S. Bellenot (1986) and stating that under rather general conditions on a separable real Banach space X and a countable bounded group G of isomorphisms on X containing -Id, there exists an equivalent norm on X for which G is equal to the group of isometrics on X. We also extend methods of K. Jarosz (1988) to prove that any complex Banach space of dimension at least 2 may be renormed with an equivalent complex norm to admit only trivial real isometries, and that any complexification of a Banach space may be renormed with an equivalent complex norm to admit only trivial and conjugation real isometrics. It follows that every real Banach space of dimension at least 4 and with a complex structure may be renormed to admit exactly two complex structures up to isometry, and that every real Cartesian square may be renormed to admit a unique complex structure up to isometry.