Material Dependence of the Wire-Particle Casimir Interaction

We study the Casimir interaction between a metallic cylindrical wire and a metallic spherical particle by employing the scattering formalism. At large separations, we derive the asymptotic form of the interaction. In addition, we find the interaction between a metallic wire and an isotropic atom, both in the non-retarded and retarded limits. We identify the conditions under which the asymptotic Casimir interaction does not depend on the material properties of the metallic wire and the particle. Moreover, we compute the exact Casimir interaction between the particle and the wire numerically. We show that there is a complete agreement between the numerics and the asymptotic energies at large separations. For short separations, our numerical results show good agreement with the proximity force approximation

Robust Adaptive Control Barrier Functions: An Adaptive & Data-Driven Approach to Safety (Extended Version)

A new framework is developed for control of constrained nonlinear systems with structured parametric uncertainties. Forward invariance of a safe set is achieved through online parameter adaptation and data-driven model estimation. The new adaptive data-driven safety paradigm is merged with a recent adaptive control algorithm for systems nominally contracting in closed-loop. This unification is more general than other safety controllers as closed-loop contraction does not require the system be invertible or in a particular form. Additionally, the approach is less expensive than nonlinear model predictive control as it does not require a full desired trajectory, but rather only a desired terminal state. The approach is illustrated on the pitch dynamics of an aircraft with uncertain nonlinear aerodynamics.Comment: Added aCBF non-Lipschitz example and discussion on approach implementatio

Observational Constraints on Transverse Gravity: a Generalization of Unimodular Gravity

We explore the hypothesis that the set of symmetries enjoyed by the theory that describes gravity is not the full group of diffeomorphisms Diff(M), as in General Relativity, but a maximal subgroup of it, TransverseDiff(M), with its elements having a jacobian equal to unity; at the infinitesimal level, the parameter describing the coordinate change, xi^mu (x), is transverse, i.e., partial_mu(xi^mu)=0. Incidentally, this is the smaller symmetry one needs to propagate consistently a graviton, which is a great theoretical motivation for considering these theories. Also, the determinant of the metric, g, behaves as a "transverse scalar", so that these theories can be seen as a generalization of the better-known unimodular gravity. We present our results on the observational constraints on transverse gravity, in close relation with the claim of equivalence with general scalar-tensor theory. We also comment on the structure of the divergences of the quantum theory to the one-loop order.Comment: Prepared for the First Mediterranean Conference on Classical and Quantum Gravity, MCCQG, Kolymbari (Crete, Greece), 14-18 September, 2009; also, ERE2009: Gravitation in the Large, Bilbao (Spain), 7-11 September, 200

Inversion of stellar statistics equation for the Galactic Bulge

A method based on Lucy (1974, AJ 79, 745) iterative algorithm is developed to invert the equation of stellar statistics for the Galactic bulge and is then applied to the K-band star counts from the Two-Micron Galactic Survey in a number of off-plane regions (10 deg.>|b|>2 deg., |l|<15 deg.). The top end of the K-band luminosity function is derived and the morphology of the stellar density function is fitted to triaxial ellipsoids, assuming a non-variable luminosity function within the bulge. The results, which have already been outlined by Lopez-Corredoira et al.(1997, MNRAS 292, L15), are shown in this paper with a full explanation of the steps of the inversion: the luminosity function shows a sharp decrease brighter than M_K=-8.0 mag when compared with the disc population; the bulge fits triaxial ellipsoids with the major axis in the Galactic plane at an angle with the line of sight to the Galactic centre of 12 deg. in the first quadrant; the axial ratios are 1:0.54:0.33, and the distance of the Sun from the centre of the triaxial ellipsoid is 7860 pc. The major-minor axial ratio of the ellipsoids is found not to be constant. However, the interpretation of this is controversial. An eccentricity of the true density-ellipsoid gradient and a population gradient are two possible explanations. The best fit for the stellar density, for 1300 pc<t<3000 pc, are calculated for both cases, assuming an ellipsoidal distribution with constant axial ratios, and when K_z is allowed to vary. From these, the total number of bulge stars is ~ 3 10^{10} or ~ 4 10^{10}, respectively.Comment: 19 pages, 23 figures, accepted in MNRA

New Precision Electroweak Tests in Supergravity Models

We update the analysis of the precision electroweak tests in terms of 4 epsilon parameters, $\epsilon_{1,2,3,b}$, to obtain more accurate experimental values of them by taking into account the new LEP data released at the 28th ICHEP (1996, Poland). We also compute $\epsilon_1$ and $\epsilon_b$ in the context of the no-scale $SU(5)\times U(1)$ supergravity model to obtain the updated constraints by imposing the correlated constraints in terms of the experimental ellipses in the $\epsilon_1-\epsilon_b$ plane and also by imposing the new bound on the lightest chargino mass, $m_{\chi^\pm_1}\gtrsim 79$ $GeV$. Upon imposing these new experimental results, we find that the situations in the no-scale model are much more favorable than those in the standard model, and if $m_t\gtrsim 170$ $GeV$, then the allowed regions at the 95% C.~L. in the no-scale model are $\tan\beta\gtrsim 4$ and $m_{\chi^\pm_1}\lesssim 120 (82)$ $GeV$ for $\mu>0 (\mu<0)$, which are in fact much more stringent than in our previous analysis. Therefore, assuming that $m_t\gtrsim 170$ $GeV$, if the lightest chargino mass bound were to be pushed up only by a few GeV, the sign on the Higgs mixing term $\mu$ in the no-scale model could well be determined from the $\epsilon_1-\epsilon_b$ constraint to be positive at the 95% C.~L. At any rate, better accuracy in the measured $m_t$ from the Tevatron in the near future combined with the LEP data is most likely to provide a decisive test of the no-scale $SU(5)\times U(1)$ supergravity model.Comment: 15 pages, REVTEX, 1 figure (not included but available as a ps file from [email protected]

Threading the spindle: a geometric study of chiral liquid crystal polymer microparticles

Polymeric particles are strong candidates for designing artificial materials capable of emulating the complex twisting-based functionality observed in biological systems. In this letter, we provide the first detailed investigation of the swelling behavior of bipolar polymer liquid crystalline microparticles. Deswelling from the spherical bipolar configuration causes the microparticle to contract anisotropically and twist in the process, resulting in a twisted spindle shaped structure. We propose a model to describe the observed spiral patterns and twisting behavior

Two-fluid dynamics for a Bose-Einstein condensate out of local equilibrium with the non-condensate

We extend our recent work on the two-fluid hydrodynamics of a Bose-condensed gas by including collisions involving both condensate and non-condensate atoms. These collisions are essential for establishing a state of local thermodynamic equilibrium between the condensate and non-condensate. Our theory is more general than the usual Landau two-fluid theory, to which it reduces in the appropriate limit, in that it allows one to describe situations in which a state of complete local equilibrium between the two components has not been reached. The exchange of atoms between the condensate and non-condensate is associated with a new relaxational mode of the gas.Comment: 4 pages, revtex, 1 postscript figure, Fig.1 has been correcte

An event study to provide validation of TING and CMIT geomagnetic middle-latitude electron densities at the F2 peak

[1] The coupled thermosphere-ionosphere magnetosphere (CMIT) model and the Thermosphere Ionosphere Nested Grid (TING) model have been run to simulate the 15 May 1997 interplanetary coronal mass ejection\u27s (ICME) effects on the Earth\u27s ionosphere and thermosphere. Comparisons were made between these model runs, the IRI-2007 model, and geomagnetic middle-latitude ionosonde data (NmF2) from the World Data Center to determine how well the models simulated the event and to understand the causes of model-data disagreement. The following conclusions were drawn from this study: (1) skill scores were more often negative than positive on average; (2) the best and the worst skill scores occurred on the recovery day; (3) the line plots comparing models to data look better than the skill scores might suggest; (4) skill scores are significantly affected by timing issues and large, short-duration variability; (5) skill scores give an indication of the relative ability of one model relative to another, rather than an absolute statement of model accuracy; (6) the models capture negative storm effects better than they capture positive storm effects; (7) the TING model captured many short duration features seen in the data at high middle latitude stations that result from changes in the size of the auroral oval; (8) CMIT overestimates the energy driving changes in NmF2, whereas TING provides approximately the correct energy input as a result of the saturation effects on potential that are included in TING; and (9) both TING and CMIT electron densities decreased too rapidly after sunset

A review of mathematical functions for the analysis of growth in poultry

Poultry industries face various decisions in the production cycle that affect the profitability of an operation. Predictions of growth when the birds are ready for sale are important factors that contribute to the economy of poultry operations. Mathematical functions called ‘growth functions’ have been used to relate body weight (W) to age or cumulative feed intake. These can also be used as response functions to predict daily energy and protein dietary requirements for maintenance and growth (France et al., 1989). When describing growth versus age in poultry, a fixed point of inflexion can be a limitation with equations such as the Gompertz and logistic. Inflexion points vary depending on age, sex, breed and type of animal, so equations such as the Richards and López are generally recommended. For describing retention rate against daily intake, which generally does not exhibit an inflexion point, the monomolecular would appear the function of choice