Generalized Legendre transformations and symmetries of the WDVV equations

The Witten-Dijkgraaf-Verlinde-Verlinde (or WDVV) equations, as one would expect from an integrable system, has many symmetries, both continuous and discrete. One class - the so-called Legendre transformations - were introduced by Dubrovin. They are a discrete set of symmetries between the stronger concept of a Frobenius manifold, and are generated by certain flat vector fields. In this paper this construction is generalized to the case where the vector field (called here the Legendre field) is non-flat but satisfies a certain set of defining equations. One application of this more general theory is to generate the induced symmetry between almost-dual Frobenius manifolds whose underlying Frobenius manifolds are related by a Legendre transformation. This also provides a map between rational and trigonometric solutions of the WDVV equations.Comment: 23 page

Full-Scale Tests of a Wood-Frame Structure under Extreme Wind Loads

Tornadoes can produce some of the strongest winds on earth; these highly localized storms can cause massive damage. Assessments of tornado wind speeds are done using post-event observations of damage via the Enhanced Fujita Scale. A very commonly observed failure occurs at the roof-to-wall connection where the roof breaks up or flies away, typically leaving the walls in place. However, once the roof is gone the walls are more vulnerable to the wind. If a wall subsequently fails, it increases the risk of injury or death for occupants. Significant research has been done for failures of roof-to-wall connections and roof failure wind loads. In contrast, little work has been done pertaining to how the walls perform when there is no roof in place. In the current study, experiments were performed on a full-scale, two storey residential structure with no roof. The objectives of the study were (i) to determine the wind loads and wind speeds required to cause exterior wall failure after the roof-to-wall connections had already failed, and (ii) to develop low-cost recommendations for strengthening wood-frame houses and, thereby, reducing risk to occupants during severe storms such as tornadoes. It was found that the capacity of the walls of the test house significantly exceeded Canadian (Ontario) design loads when clad in brick veneer. The interior wall placement and connections between the exterior and interior walls are shown to have a significant effect on overall capacity. For vinyl-clad houses, increasing the stiffness of the corners of the walls will also increase capacity – which appears to be the primary structural benefit of brick cladding

Direct measurement of diurnal polar motion by ring laser gyroscopes

We report the first direct measurements of the very small effect of forced diurnal polar motion, successfully observed on three of our large ring lasers, which now measure the instantaneous direction of Earth's rotation axis to a precision of 1 part in 10^8 when averaged over a time interval of several hours. Ring laser gyroscopes provide a new viable technique for directly and continuously measuring the position of the instantaneous rotation axis of the Earth and the amplitudes of the Oppolzer modes. In contrast, the space geodetic techniques (VLBI, SLR, GPS, etc.) contain no information about the position of the instantaneous axis of rotation of the Earth, but are sensitive to the complete transformation matrix between the Earth-fixed and inertial reference frame. Further improvements of gyroscopes will provide a powerful new tool for studying the Earth's interior.Comment: 5 pages, 4 figures, agu2001.cl

A 1.82 m^2 ring laser gyroscope for nano-rotational motion sensing

We present a fully active-controlled He-Ne ring laser gyroscope, operating in square cavity 1.35 m in side. The apparatus is designed to provide a very low mechanical and thermal drift of the ring cavity geometry and is conceived to be operative in two different orientations of the laser plane, in order to detect rotations around the vertical or the horizontal direction. Since June 2010 the system is active inside the Virgo interferometer central area with the aim of performing high sensitivity measurements of environmental rotational noise. So far, continuous not attempted operation of the gyroscope has been longer than 30 days. The main characteristics of the laser, the active remote-controlled stabilization systems and the data acquisition techniques are presented. An off-line data processing, supported by a simple model of the sensor, is shown to improve the effective long term stability. A rotational sensitivity at the level of ten nanoradiants per squareroot of Hz below 1 Hz, very close to the required specification for the improvement of the Virgo suspension control system, is demonstrated for the configuration where the laser plane is horizontal

Entanglement requirements for implementing bipartite unitary operations

We prove, using a new method based on map-state duality, lower bounds on entanglement resources needed to deterministically implement a bipartite unitary using separable (SEP) operations, which include LOCC (local operations and classical communication) as a particular case. It is known that the Schmidt rank of an entangled pure state resource cannot be less than the Schmidt rank of the unitary. We prove that if these ranks are equal the resource must be uniformly (maximally) entangled: equal nonzero Schmidt coefficients. Higher rank resources can have less entanglement: we have found numerical examples of Schmidt rank 2 unitaries which can be deterministically implemented, by either SEP or LOCC, using an entangled resource of two qutrits with less than one ebit of entanglement.Comment: 7 pages Revte

Gravitomagnetism, clocks and geometry

New techniques to evaluate the clock effect using light are described. These are based on the flatness of the cylindrical surface containing the world lines of the rays constrained to move on circular trajectories about a spinning mass. The effect of the angular momentum of the source is manifested in the fact that inertial observers must be replaced by local non rotating observers. Starting from this an exact formula for circular trajectories is found. Numerical estimates for the Earth environment show that light would be a better probe than actual clocks to evidence the angular momentum influence. The advantages of light in connection with some principle experiments are shortly reviewed.Comment: TCI Latex, 12 pages, 2 figures. To appear in European Journal of Physic

On-Road Motor Vehicle Emissions from Around the World

In 1993, on-road emissions in Continental Europe showed a pronounced South/North declining gradient for CO, HC and NO fuel specific emissions (gm/kg). Emissions in Hamburg and Rotterdam were comparable to emissions measured in 1993 in the U.S.A. with the same on-road instrument. Contrasts between emissions in the USA, the UK and Sweden demonstrated the importance both of modern catalysts and of good maintenance. The same contrast in 1998 shows the same picture but lower emissions at all three locations. In the decade from 1993-2003, U.S. emissions have declined markedly, apparently mainly as a result of lower emitting, better maintained, new vehicles. Results from Asia and South America will also be presented together with an analysis which suggests a correlation between average on-road vehicle emissions and the inverse of reported per-capita income. This latter relationship holds only up to a point. Beyond that point of increasing poverty, measured on-road emissions reach a plateau. Results from Mexico City in 1991 and 1994 show a dramatic decline in emissions, mainly caused by the imposition of modern control measures to the taxi cabs which, while only a small fraction of the registered fleet, contribute a large fraction of the vehicle miles traveled. Further improvement in Mexico City on-road emissions was observed by studies in 2000 [1] and 2003 [2]