On existence of periodic solutions for stable interval plants with odd, sector type nonlinearities

In several systems, the physical parameters of the system vary over time or operating points. A popular way of representing such plants with structured or parametric uncertainties is by means of interval polynomials. However, ensuring the stability of such systems is a robust control problem. Fortunately, Kharitonov's theorem enables the analysis of such interval plants and also provides tools for design of robust controllers in such cases. The present paper considers one such case, where the interval plant is connected with a timeinvariant, static, odd, sector type nonlinearity in its feedback path. This paper provides necessary conditions for the existence of self sustaining periodic oscillations in such interval plants, and indicates a possible design algorithm to avoid such periodic solutions or limit cycles. The describing function technique is used to approximate the nonlinearity and subsequently arrive at the results. Furthermore, the value set approach, along with Mikhailov conditions, are resorted to in providing graphical techniques for the derivation of the conditions and subsequent design algorithm of the controller.

Uncovering the Lagrangian from observations of trajectories

We approach the problem of automatically modeling a mechanical system from data about its dynamics, using a method motivated by variational integrators. We write the discrete Lagrangian as a quadratic polynomial with varying coefficients, and then use the discrete Euler-Lagrange equations to numerically solve for the values of these coefficients near the data points. This method correctly modeled the Lagrangian of a simple harmonic oscillator and a simple pendulum, even with significant measurement noise added to the trajectories.

Stable Mixing of Complete and Incomplete Information

An increasing number of parameter estimation tasks involve the use of at least two information sources, one complete but limited, the other abundant but incomplete. Standard algorithms such as EM (or em) used in this context are unfortunately not stable in the sense that they can lead to a dramatic loss of accuracy with the inclusion of incomplete observations. We provide a more controlled solution to this problem through differential equations that govern the evolution of locally optimal solutions (fixed points) as a function of the source weighting. This approach permits us to explicitly identify any critical (bifurcation) points leading to choices unsupported by the available complete data. The approach readily applies to any graphical model in O(n^3) time where n is the number of parameters. We use the naive Bayes model to illustrate these ideas and demonstrate the effectiveness of our approach in the context of text classification problems.

The Synthesis of Stable Force-Closure Grasps

This thesis addresses the problem of synthesizing grasps that are force-closure and stable. The synthesis of force-closure grasps constructs independent regions of contact for the fingertips, such that the motion of the grasped object is totally constrained. The synthesis of stable grasps constructs virtual springs at the contacts, such that the grasped object is stable, and has a desired stiffness matrix about its stable equilibrium. A grasp on an object is force-closure if and only if we can exert, through the set of contacts, arbitrary forces and moments on the object. So force-closure implies equilibrium exists because zero forces and moment is spanned. In the reverse direction, we prove that a non-marginal equilibrium grasp is also a force-closure grasp, if it has at least two point contacts with friction in 2D, or two soft-finger contacts or three hard-finger contacts in 3D. Next, we prove that all force-closure grasps can be made stable, by using either active or passive springs at the contacts. The thesis develops a simple relation between the stability and stiffness of the grasp and the spatial configuration of the virtual springs at the contacts. The stiffness of the grasp depends also on whether the points of contact stick, or slide without friction on straight or curved surfaces of the object. The thesis presents fast and simple algorithms for directly constructing stable fore-closure grasps based on the shape of the grasped object. The formal framework of force-closure and stable grasps provides a partial explanation to why we stably grasp objects to easily, and to why our fingers are better soft than hard.

The Synthesis of Arbitrary Stable Dynamics in Non-linear Neural Networks II: Feedback and Universality

We wish to construct a realization theory of stable neural networks and use this theory to model the variety of stable dynamics apparent in natural data. Such a theory should have numerous applications to constructing specific artificial neural networks with desired dynamical behavior. The networks used in this theory should have well understood dynamics yet be as diverse as possible to capture natural diversity. In this article, I describe a parameterized family of higher order, gradient-like neural networks which have known arbitrary equilibria with unstable manifolds of known specified dimension. Moreover, any system with hyperbolic dynamics is conjugate to one of these systems in a neighborhood of the equilibrium points. Prior work on how to synthesize attractors using dynamical systems theory, optimization, or direct parametric. fits to known stable systems, is either non-constructive, lacks generality, or has unspecified attracting equilibria. More specifically, We construct a parameterized family of gradient-like neural networks with a simple feedback rule which will generate equilibrium points with a set of unstable manifolds of specified dimension. Strict Lyapunov functions and nested periodic orbits are obtained for these systems and used as a method of synthesis to generate a large family of systems with the same local dynamics. This work is applied to show how one can interpolate finite sets of data, on nested periodic orbits.

Viscoelastic flow through a planar contraction using a semi-Lagrangian finite volume method

A semi-Lagrangian finite volume scheme for solving viscoelastic flow problems is presented. A staggered grid arrangement is used in which the dependent variables are located at different mesh points in the computational domain. The convection terms in the momentum and constitutive equations are treated using a semi-Lagrangian approach in which particles on a regular grid are traced backwards over a single time-step. The method is applied to the 4 : 1 planar contraction problem for an Oldroyd B fluid for both creeping and inertial flow conditions. The development of vortex behaviour with increasing values of We is analyzed.

Stable standard essential for prosperity. Speech in the Senate of the United States, February 4, 1878

This speech was given when the United States Senate was considering a bill to authorize the free coinage of the standard silver dollar and to restore its legal tender character. Mr. Bayard argues against the bill in this speech. He is interrupted during his speech multiple times and questioned about his points.

Seasonal trends in the stable isotopic composition of snow and meltwater runoff in a subarctic catchment at Okstindan, Norway

Seasonal variations in the stable isotopic composition of snow and meltwater were investigated in a sub-arctic, mountainous, but non-glacial, catchment at Okstindan in northern Norway based on analyses of delta(18)O and deltaD. Samples were collected during four field periods (August 1998; April 1999; June 1999 and August 1999) at three sites lying on an altitudinal transect (740-970 m a.s.l.). Snowpack data display an increase in the mean values of delta(18)O (increasing from a mean value of - 13.51 to - 11.49% between April and August), as well as a decrease in variability through the melt period. Comparison with a regional meteoric water line indicates that the slope of the delta(18)O - deltaD line for the snowpacks decreases over the same period, dropping from 7.49 to approximately 6.2. This change points to the role of evaporation in snowpack ablation and is confirmed by the vertical profile of deuterium excess. Snowpack seepage data, although limited, also suggest reduced values of deltaD, as might be associated with local evaporation during meltwater generation. In general, meltwaters were depleted in delta(18)O relative to the source snowpack at the peak of the melt (June), but later in the year (August) the difference between the two was not statistically significant. The diurnal pattern of isotopic composition indicates that the most depleted meltwaters coincide with the peak in temperature and, hence, meltwater production.

Stable isotope and modelling evidence for CO2 as a driver of glacial–interglacial vegetation shifts in southern Africa

Atmospheric CO2 concentration is hypothesized to influence vegetation distribution via tree–grass competition, with higher CO2 concentrations favouring trees. The stable carbon isotope (δ13C) signature of vegetation is influenced by the relative importance of C4 plants (including most tropical grasses) and C3 plants (including nearly all trees), and the degree of stomatal closure – a response to aridity – in C3 plants. Compound-specific δ13C analyses of leaf-wax biomarkers in sediment cores of an offshore South Atlantic transect are used here as a record of vegetation changes in subequatorial Africa. These data suggest a large increase in C3 relative to C4 plant dominance after the Last Glacial Maximum. Using a process-based biogeography model that explicitly simulates 13C discrimination, it is shown that precipitation and temperature changes cannot explain the observed shift in δ13C values. The physiological effect of increasing CO2 concentration is decisive, altering the C3/C4 balance and bringing the simulated and observed δ13C values into line. It is concluded that CO2 concentration itself was a key agent of vegetation change in tropical southern Africa during the last glacial–interglacial transition. Two additional inferences follow. First, long-term variations in terrestrial δ13Cvalues are not simply a proxy for regional rainfall, as has sometimes been assumed. Although precipitation and temperature changes have had major effects on vegetation in many regions of the world during the period between the Last Glacial Maximum and recent times, CO2 effects must also be taken into account, especially when reconstructing changes in climate between glacial and interglacial states. Second, rising CO2 concentration today is likely to be influencing tree–grass competition in a similar way, and thus contributing to the "woody thickening" observed in savannas worldwide. This second inference points to the importance of experiments to determine how vegetation composition in savannas is likely to be influenced by the continuing rise of CO2 concentration.

A Lagrangian model of air-mass photochemistry and mixing using a trajectory ensemble: the Cambridge Tropospheric Trajectory model of Chemistry And Transport (CiTTyCAT) version 4.2

A Lagrangian model of photochemistry and mixing is described (CiTTyCAT, stemming from the Cambridge Tropospheric Trajectory model of Chemistry And Transport), which is suitable for transport and chemistry studies throughout the troposphere. Over the last five years, the model has been developed in parallel at several different institutions and here those developments have been incorporated into one "community" model and documented for the first time. The key photochemical developments include a new scheme for biogenic volatile organic compounds and updated emissions schemes. The key physical development is to evolve composition following an ensemble of trajectories within neighbouring air-masses, including a simple scheme for mixing between them via an evolving "background profile", both within the boundary layer and free troposphere. The model runs along trajectories pre-calculated using winds and temperature from meteorological analyses. In addition, boundary layer height and precipitation rates, output from the analysis model, are interpolated to trajectory points and used as inputs to the mixing and wet deposition schemes. The model is most suitable in regimes when the effects of small-scale turbulent mixing are slow relative to advection by the resolved winds so that coherent air-masses form with distinct composition and strong gradients between them. Such air-masses can persist for many days while stretching, folding and thinning. Lagrangian models offer a useful framework for picking apart the processes of air-mass evolution over inter-continental distances, without being hindered by the numerical diffusion inherent to global Eulerian models. The model, including different box and trajectory modes, is described and some output for each of the modes is presented for evaluation. The model is available for download from a Subversion-controlled repository by contacting the corresponding authors.

Mechanisms underlying temperature extremes in Iberia: a Lagrangian perspective

The mechanisms underlying the occurrence of temperature extremes in Iberia are analysed considering a Lagrangian perspective of the atmospheric flow, using 6-hourly ERA-Interim reanalysis data for the years 1979–2012. Daily 2-m minimum temperatures below the 1st percentile and 2-m maximum temperatures above the 99th percentile at each grid point over Iberia are selected separately for winter and summer. Four categories of extremes are analysed using 10-d backward trajectories initialized at the extreme temperature grid points close to the surface: winter cold (WCE) and warm extremes (WWE), and summer cold (SCE) and warm extremes (SWE). Air masses leading to temperature extremes are first transported from the North Atlantic towards Europe for all categories. While there is a clear relation to large-scale circulation patterns in winter, the Iberian thermal low is important in summer. Along the trajectories, air mass characteristics are significantly modified through adiabatic warming (air parcel descent), upper-air radiative cooling and near-surface warming (surface heat fluxes and radiation). High residence times over continental areas, such as over northern-central Europe for WCE and, to a lesser extent, over Iberia for SWE, significantly enhance these air mass modifications. Near-surface diabatic warming is particularly striking for SWE. WCE and SWE are responsible for the most extreme conditions in a given year. For WWE and SCE, strong temperature advection associated with important meridional air mass transports are the main driving mechanisms, accompanied by comparatively minor changes in the air mass properties. These results permit a better understanding of mechanisms leading to temperature extremes in Iberia.

Late Quaternary environmental change in the interior South American tropics: new insight from leaf wax stable isotopes

Stable isotope analysis of leaf waxes in a sediment core from Laguna La Gaiba, a shallow lake located at the Bolivian margin of the Pantanal wetlands, provides new perspective on vegetation and climate change in the lowland interior tropics of South America over the past 40,000 years. The carbon isotopic compositions (δ13C) of long-chain n-alkanes reveal large shifts between C3-and C4-dominated vegetation communities since the last glacial period, consistent with landscape reconstructions generated with pollen data from the same sediment core. Leaf wax δ13C values during the last glacial period reflect an open landscape composed of C4grasses and C3herbs from 41–20ka. A peak in C4abundance during the Last Glacial Maximum (LGM, ∼21ka) suggests drier or more seasonal conditions relative to the earlier glacial period, while the development of a C3-dominated forest community after 20 ka points to increased humidity during the last deglaciation. Within the Holocene, large changes in the abundance of C4 vegetation indicate a transition from drier or more seasonal conditions during the early/mid-Holocene to wetter conditions in the late Holocene coincident with increasing austral summer insolation. Strong negative correlations between leaf wax δ13C and δD values over the entire record indicate that the majority of variability in leaf wax δD at this site can be explained by variability in the magnitude of biosynthetic fractionation by different vegetation types rather than changes in meteoric water δD signatures. However, positive δD deviations from the observed δ13C–δD trends are consistent with more enriched source water and drier or more seasonal conditions during the early/mid-Holocene and LGM. Overall, our record adds to evidence of varying influence of glacial boundary conditions and orbital forcing on South American Summer Monsoon precipitation in different regions of the South American tropics. Moreover, the relationships between leaf wax stable isotopes and pollen data observed at this site underscore the complementary nature of pollen and leaf wax δ13C data for reconstructing past vegetation changes and the potentially large effects of such changes on leaf wax δD signatures.

Protecting clean critical points by local disorder correlations

We show that a broad class of quantum critical points can be stable against locally correlated disorder even if they are unstable against uncorrelated disorder. Although this result seemingly contradicts the Harris criterion, it follows naturally from the absence of a random-mass term in the associated order parameter field theory. We illustrate the general concept with explicit calculations for quantum spin-chain models. Instead of the infinite-randomness physics induced by uncorrelated disorder, we find that weak locally correlated disorder is irrelevant. For larger disorder, we find a line of critical points with unusual properties such as an increase of the entanglement entropy with the disorder strength. We also propose experimental realizations in the context of quantum magnetism and cold-atom physics. Copyright (C) EPLA, 2011

Augmented Lagrangian methods under the constant positive linear dependence constraint qualification

Two Augmented Lagrangian algorithms for solving KKT systems are introduced. The algorithms differ in the way in which penalty parameters are updated. Possibly infeasible accumulation points are characterized. It is proved that feasible limit points that satisfy the Constant Positive Linear Dependence constraint qualification are KKT solutions. Boundedness of the penalty parameters is proved under suitable assumptions. Numerical experiments are presented.

Construction of Hamiltonian-Minimal Lagrangian submanifolds in Complex Euclidean Space

We describe several families of Lagrangian submanifolds in complex Euclidean space which are H-minimal, i.e. critical points of the volume functional restricted to Hamiltonian variations. We make use of various constructions involving planar, spherical and hyperbolic curves, as well as Legendrian submanifolds of the odd-dimensional unit sphere.