Strong structural controllability and the multi-link inverted pendulum

This technical note investigates the controllability of the linearized dynamics of the multilink inverted pendulum as the number of links and the number and location of actuators changes. It is demonstrated that, in some instances, there exist sets of parameter values that render the system uncontrollable and so usual methods for assessing controllability are difficult to employ. To assess the controllability, a theorem on strong structural controllability for single-input systems is extended to the multiinput case.

The price of space: the convergence of value in use and value in exchange

This paper discusses concepts of value from the point of view of the user of the space and the counter view of the provider of the same. Land and property are factors of production. The value of the land flows from the use to which it is put, and that in turn, is dependent upon the demand (and supply) for the product or service that is produced/provided from that space. If there is a high demand for the product (at a fixed level of supply), the price will increase and the economic rent for the land/property will increase accordingly. This is the underlying paradigm of Ricardian rent theory where the supply of land is fixed and a single good is produced. In such a case the rent of land is wholly an economic rent. Economic theory generally distinguishes between two kinds of price, price of production or “value in use” (as determined by the labour theory of value), and market price or “value in exchange” (as determined by supply and demand). It is based on a coherent and consistent theory of value and price. Effectively the distinction is between what space is ‘worth’ to an individual and that space’s price of exchange in the market place. In a perfect market where any individual has access to the same information as all others in the market, price and worth should coincide. However in a market where access to information is not uniform, and where different uses compete for the same space, it is more likely that the two figures will diverge. This paper argues that the traditional reliance of valuers to use methods of comparison to determine “price” has led to an artificial divergence of “value in use” and “value in exchange”, but now such comparison are becoming more difficult due to the diversity of lettings in the market place, there will be a requirement to return to fundamentals and pay heed to the thought process of the user in assessing the worth of the space to be let.

Numerical convergence of the Block-Maxima approach to the generalized extreme value distribution

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems. In this setting, recent works have shown how to get a statistics of extremes in agreement with the classical Extreme Value Theory. We pursue these investigations by giving analytical expressions of Extreme Value distribution parameters for maps that have an absolutely continuous invariant measure. We compare these analytical results with numerical experiments in which we study the convergence to limiting distributions using the so called block-maxima approach, pointing out in which cases we obtain robust estimation of parameters. In regular maps for which mixing properties do not hold, we show that the fitting procedure to the classical Extreme Value Distribution fails, as expected. However, we obtain an empirical distribution that can be explained starting from a different observable function for which Nicolis et al. (Phys. Rev. Lett. 97(21): 210602, 2006) have found analytical results.

On the Convergence of Two-Stage Iterative Processes for Solving Linear Equations

This paper considers two-stage iterative processes for solving the linear system $Af = b$. The outer iteration is defined by $Mf^{k + 1} = Nf^k + b$, where $M$ is a nonsingular matrix such that $M - N = A$. At each stage $f^{k + 1} $ is computed approximately using an inner iteration process to solve $Mv = Nf^k + b$ for $v$. At the $k$th outer iteration, $p_k $ inner iterations are performed. It is shown that this procedure converges if $p_k \geqq P$ for some $P$ provided that the inner iteration is convergent and that the outer process would converge if $f^{k + 1} $ were determined exactly at every step. Convergence is also proved under more specialized conditions, and for the procedure where $p_k = p$ for all $k$, an estimate for $p$ is obtained which optimizes the convergence rate. Examples are given for systems arising from the numerical solution of elliptic partial differential equations and numerical results are presented.

A variational method to retrieve the extinction profile in liquid clouds using multiple field-of-view lidar

Liquid clouds play a profound role in the global radiation budget but it is difficult to remotely retrieve their vertical profile. Ordinary narrow field-of-view (FOV) lidars receive a strong return from such clouds but the information is limited to the first few optical depths. Wideangle multiple-FOV lidars can isolate radiation scattered multiple times before returning to the instrument, often penetrating much deeper into the cloud than the singly-scattered signal. These returns potentially contain information on the vertical profile of extinction coefficient, but are challenging to interpret due to the lack of a fast radiative transfer model for simulating them. This paper describes a variational algorithm that incorporates a fast forward model based on the time-dependent two-stream approximation, and its adjoint. Application of the algorithm to simulated data from a hypothetical airborne three-FOV lidar with a maximum footprint width of 600m suggests that this approach should be able to retrieve the extinction structure down to an optical depth of around 6, and total opticaldepth up to at least 35, depending on the maximum lidar FOV. The convergence behavior of Gauss-Newton and quasi-Newton optimization schemes are compared. We then present results from an application of the algorithm to observations of stratocumulus by the 8-FOV airborne “THOR” lidar. It is demonstrated how the averaging kernel can be used to diagnose the effective vertical resolution of the retrieved profile, and therefore the depth to which information on the vertical structure can be recovered. This work enables exploitation of returns from spaceborne lidar and radar subject to multiple scattering more rigorously than previously possible.

On the strong uniqueness of some finite dimensional Dirichlet operators

We prove essential self-adjointness of a class of Dirichlet operators in ℝn using the hyperbolic equation approach. This method allows one to prove essential self-adjointness under minimal conditions on the logarithmic derivative of the density and a condition of Muckenhoupt type on the density itself.

Revisiting Asian monsoon formation and change associated with Tibetan Plateau forcing: I. Formation

Numerical experiments with different idealized land and mountain distributions are carried out to study the formation of the Asian monsoon and related coupling processes. Results demonstrate that when there is only extratropical continent located between 0 and 120°E and between 20/30°N and the North Pole, a rather weak monsoon rainband appears along the southern border of the continent, coexisting with an intense intertropical convergence zone (ITCZ). The continuous ITCZ surrounds the whole globe, prohibits the development of near-surface cross-equatorial flow, and collects water vapor from tropical oceans, resulting in very weak monsoon rainfall. When tropical lands are integrated, the ITCZ over the longitude domain where the extratropical continent exists disappears as a consequence of the development of a strong surface cross-equatorial flow from the winter hemisphere to the summer hemisphere. In addition, an intense interaction between the two hemispheres develops, tropical water vapor is transported to the subtropics by the enhanced poleward flow, and a prototype of the Asian monsoon appears. The Tibetan Plateau acts to enhance the coupling between the lower and upper tropospheric circulations and between the subtropical and tropical monsoon circulations, resulting in an intensification of the East Asian summer monsoon and a weakening of the South Asian summer monsoon. Linking the Iranian Plateau to the Tibetan Plateau substantially reduces the precipitation over Africa and increases the precipitation over the Arabian Sea and the northern Indian subcontinent, effectively contributing to the development of the South Asian summer monsoon.

Unusual isotope effect in the reaction of chlorosilylene with trimethylsilane-1-d: Absolute rate studies and quantum chemical and Rice–Ramsperger–Kassel–Marcus calculations provide strong evidence for the involvement of an intermediate complex

Time-resolved studies of chlorosilylene, ClSiH, generated by the 193 nm laser flash photolysis of 1-chloro-1- silacyclopent-3-ene, have been carried out to obtain rate constants for its bimolecular reaction with trimethylsilane-1-d, Me3SiD, in the gas phase. The reaction was studied at total pressures up to 100 Torr (with and without added SF6) over the temperature range of 295−407 K. The rate constants were found to be pressure independent and gave the following Arrhenius equation: log[(k/(cm3 molecule−1 s−1)] = (−13.22 ± 0.15) + [(13.20 ± 1.00) kJ mol−1]/(RT ln 10). When compared with previously published kinetic data for the reaction of ClSiH with Me3SiH, kinetic isotope effects, kD/kH, in the range from 7.4 (297 K) to 6.4 (407 K) were obtained. These far exceed values of 0.4−0.5 estimated for a single-step insertion process. Quantum chemical calculations (G3MP2B3 level) confirm not only the involvement of an intermediate complex, but also the existence of a low-energy internal isomerization pathway which can scramble the D and H atom labels. By means of Rice−Ramsperger−Kassel−Marcus modeling and a necessary (but small) refinement of the energy surface, we have shown that this mechanism can reproduce closely the experimental isotope effects. These findings provide the first experimental evidence for the isomerization pathway and thereby offer the most concrete evidence to date for the existence of intermediate complexes in the insertion reactions of silylenes.

Insertion of a hydroxido bridge into a diphenoxido dinuclear copper(II) complex: drastic change of the magnetic property from strong antiferromagnetic to ferromagnetic and enhancement in the catecholase activity

A diphenoxido-bridged dinuclear copper(II) complex, [Cu2L2(ClO4)(2)] (1), has been synthesized using a tridentate reduced Schiff base ligand, 2-[[2-(diethylamino)-ethylamino]methyl]phenol (HL). The addition of triethylamine to the methanolic solution of this complex produced a novel triple bridged (double phenoxido and single hydroxido) dinuclear copper(II) complex, [Cu2L2(OH)]ClO4 (2). Both complexes 1 and 2 were characterized by X-ray structural analyses, variable-temperature magnetic susceptibility measurements, and spectroscopic methods. In 1, the two phenoxido bridges are equatorial-equatorial and the species shows strong antiferromagnetic coupling with J = -615.6(6.1) cm(-1). The inclusion of the equatorial-equatorial hydroxido bridge in 2 changes the Cu center dot center dot center dot Cu distance from 3.018 angstrom (avg.) to 2.798 angstrom (avg.), the positions of the phenoxido bridges to axial-equatorial, and the magnetic coupling to ferromagnetic with J = 50.1(1.4) cm(-1). Using 3,5-di-tert-butylcatechol as the substrate, the catecholase activity of the complexes has been studied in a methanol solution; compound 2 shows higher catecholase activity (k(cat) = 233.4 h(-1)) than compound 1 (k(cat) = 93.6 h(-1)). Both complexes generate identical species in solution, and they are interconvertible simply by changing the pH of their solutions. The higher catecholase activity of 2 seems to be due to the presence of the OH group, which increases the pH of its solution.

Systematic winter sea-surface temperature biases in the northern Arabian Sea in HiGEM and the CMIP3 models

Analysis of 20th century simulations of the High resolution Global Environment Model (HiGEM) and the Third Coupled Model Intercomparison Project (CMIP3) models shows that most have a cold sea-surface temperature (SST) bias in the northern Arabian Sea during boreal winter. The association between Arabian Sea SST and the South Asian monsoon has been widely studied in observations and models, with winter cold biases known to be detrimental to rainfall simulation during the subsequent monsoon in coupled general circulation models (GCMs). However, the causes of these SST biases are not well understood. Indeed this is one of the first papers to address causes of the cold biases. The models show anomalously strong north-easterly winter monsoon winds and cold air temperatures in north-west India, Pakistan and beyond. This leads to the anomalous advection of cold, dry air over the Arabian Sea. The cold land region is also associated with an anomalously strong meridional surface temperature gradient during winter, contributing to the enhanced low-level convergence and excessive precipitation over the western equatorial Indian Ocean seen in many models.

Accommodation and vergence response gains to different near cues characterize specific esotropias

Aim. To describe preliminary findings of how the profile of the use of blur, disparity and proximal cues varies between non-strabismic groups and those with different types of esotropia. Design. Case control study Methodology. A remote haploscopic photorefractor measured simultaneous convergence and accommodation to a range of targets containing all combinations of binocular disparity, blur and proximal (looming) cues. 13 constant esotropes, 16 fully accommodative esotropes, and 8 convergence excess esotropes were compared with age and refractive error matched controls, and 27 young adult emmetropic controls. All wore full refractive correction if not emmetropic. Response AC/A and CA/C ratios were also assessed. Results. Cue use differed between the groups. Even esotropes with constant suppression and no binocular vision (BV) responded to disparity in cues. The constant esotropes with weak BV showed trends for more stable responses and better vergence and accommodation than those without any BV. The accommodative esotropes made less use of disparity cues to drive accommodation (p=0.04) and more use of blur to drive vergence (p=0.008) than controls. All esotropic groups failed to show the strong bias for better responses to disparity cues found in the controls, with convergence excess esotropes favoring blur cues. AC/A and CA/C ratios existed in an inverse relationship in the different groups. Accommodative lag of >1.0D at 33cm was common (46%) in the pooled esotropia groups compared with 11% in typical children (p=0.05). Conclusion. Esotropic children use near cues differently from matched non-esotropic children in ways characteristic to their deviations. Relatively higher weighting for blur cues was found in accommodative esotropia compared to matched controls.

Convergence accommodation trumps accommodative convergence

Purpose. This symposium contribution presents research that shows that disparity cues within a near stimulus drive not only vergence but also most of the accommodation. Be-cause blur is a weaker cue, accommodative convergence is therefore only of minor significance for most individuals. Methods. The Infant Vision Laboratory at the University of Reading uses a Power Ref II photorefractor to collect simultaneous accommodation and convergence data from participants fixating targets moving in depth. By manipulating target characteristics, we have been able to test how blur, disparity and proximal cues each contribute to driving responses. Results. Results from a series of studies over the past 12 years have contributed to a coherent body of evidence suggesting that disparity cues override blur and proximity cues in most individuals. Some strabismic patients do use blur as a more strongly weighted cue, and this strategy could contribute to their symptoms, clinical characteristics and response to treatment. Conclusion. Although convergence accommodation is extremely difficult to measure clinically, clinicians should be aware of its importance in binocular vision and strabismus. Although CA/C relationships typically seem more important than AC/A, bo th only partly explain the interplay between convergence and accommodation.