Evaluation of a load cell model for dynamic calibration of the rotor systems research aircraft

The Rotor Systems Research Aircraft uses load cells to isolate the rotor/transmission system from the fuselage. An analytical model of the relationship between applied rotor loads and the resulting load cell measurements is derived by applying a force-and-moment balance to the isolated rotor/transmission system. The model is then used to estimate the applied loads from measured load cell data, as obtained from a ground-based shake test. Using nominal design values for the parameters, the estimation errors, for the case of lateral forcing, were shown to be on the order of the sensor measurement noise in all but the roll axis. An unmodeled external load appears to be the source of the error in this axis

Cuts and flows of cell complexes

We study the vector spaces and integer lattices of cuts and flows associated with an arbitrary finite CW complex, and their relationships to group invariants including the critical group of a complex. Our results extend to higher dimension the theory of cuts and flows in graphs, most notably the work of Bacher, de la Harpe and Nagnibeda. We construct explicit bases for the cut and flow spaces, interpret their coefficients topologically, and give sufficient conditions for them to be integral bases of the cut and flow lattices. Second, we determine the precise relationships between the discriminant groups of the cut and flow lattices and the higher critical and cocritical groups with error terms corresponding to torsion (co)homology. As an application, we generalize a result of Kotani and Sunada to give bounds for the complexity, girth, and connectivity of a complex in terms of Hermite's constant.Comment: 30 pages. Final version, to appear in Journal of Algebraic Combinatoric

Newton-Hooke spacetimes, Hpp-waves and the cosmological constant

We show explicitly how the Newton-Hooke groups act as symmetries of the equations of motion of non-relativistic cosmological models with a cosmological constant. We give the action on the associated non-relativistic spacetimes and show how these may be obtained from a null reduction of 5-dimensional homogeneous pp-wave Lorentzian spacetimes. This allows us to realize the Newton-Hooke groups and their Bargmann type central extensions as subgroups of the isometry groups of the pp-wave spacetimes. The extended Schrodinger type conformal group is identified and its action on the equations of motion given. The non-relativistic conformal symmetries also have applications to time-dependent harmonic oscillators. Finally we comment on a possible application to Gao's generalization of the matrix model.Comment: 21 page

`Stringy' Newton-Cartan Gravity

We construct a "stringy" version of Newton-Cartan gravity in which the concept of a Galilean observer plays a central role. We present both the geodesic equations of motion for a fundamental string and the bulk equations of motion in terms of a gravitational potential which is a symmetric tensor with respect to the longitudinal directions of the string. The extension to include a non-zero cosmological constant is given. We stress the symmetries and (partial) gaugings underlying our construction. Our results provide a convenient starting point to investigate applications of the AdS/CFT correspondence based on the non-relativistic "stringy" Galilei algebra.Comment: 44 page

Connections and dynamical trajectories in generalised Newton-Cartan gravity I. An intrinsic view

The "metric" structure of nonrelativistic spacetimes consists of a one-form (the absolute clock) whose kernel is endowed with a positive-definite metric. Contrarily to the relativistic case, the metric structure and the torsion do not determine a unique Galilean (i.e. compatible) connection. This subtlety is intimately related to the fact that the timelike part of the torsion is proportional to the exterior derivative of the absolute clock. When the latter is not closed, torsionfreeness and metric-compatibility are thus mutually exclusive. We will explore generalisations of Galilean connections along the two corresponding alternative roads in a series of papers. In the present one, we focus on compatible connections and investigate the equivalence problem (i.e. the search for the necessary data allowing to uniquely determine connections) in the torsionfree and torsional cases. More precisely, we characterise the affine structure of the spaces of such connections and display the associated model vector spaces. In contrast with the relativistic case, the metric structure does not single out a privileged origin for the space of metric-compatible connections. In our construction, the role of the Levi-Civita connection is played by a whole class of privileged origins, the so-called torsional Newton-Cartan (TNC) geometries recently investigated in the literature. Finally, we discuss a generalisation of Newtonian connections to the torsional case.Comment: 79 pages, 7 figures; v2: added material on affine structure of connection space, former Section 4 postponed to 3rd paper of the serie

Relativity principles in 1+1 dimensions and differential aging reversal

We study the behavior of clocks in 1+1 spacetime assuming the relativity principle, the principle of constancy of the speed of light and the clock hypothesis. These requirements are satisfied by a class of Finslerian theories parametrized by a real coefficient $\beta$, special relativity being recovered for $\beta=0$. The effect of differential aging is studied for the different values of $\beta$. Below the critical values $|\beta| =1/c$ the differential aging has the usual direction - after a round trip the accelerated observer returns younger than the twin at rest in the inertial frame - while above the critical values the differential aging changes sign. The non-relativistic case is treated by introducing a formal analogy with thermodynamics.Comment: 12 pages, no figures. Previous title "Parity violating terms in clocks' behavior and differential aging reversal". v2: shortened introduction, some sections removed, pointed out the relation with Finsler metrics. Submitted to Found. Phys. Let

Conformal Properties of Chern-Simons Vortices in External Fields

The construction and the symmetries of Chern-Simons vortices in harmonic and uniform magnetic force backgrounds found by Ezawa, Hotta and Iwazaki, and by Jackiw and Pi are generalized using the non-relativistic Kaluza-Klein-type framework presented in our previous paper. All Schrodinger-symmetric backgrounds are determined.Comment: 10 pages,CPT-94/p.3028, te

Effect of Supplementary Cementitious Materials on the Compressive Strength and Durability of Short-Term Cured Concrete

This research focuses on studying the effect different supplementary cementitious materials (silica fume, fly ash, slag, and their combinations) on strength and durability of concrete cured for a short period of time—14 days. This work primarily deals with the characteristics of these materials, including strength, durability, and resistance to wet and dry and freeze and thaw environments. Over 16 mixes were made and compared to the control mix. Each of these mixes was either differing in the percentages of the additives or was combinations of two or more additives. All specimens were moist cured for 14 days before testing or subjected to environmental exposure. The freeze–thaw and wet–dry specimens were also compared to the control mix. Results show that at 14 days of curing, the use of supplementary cementitious materials reduced both strength and freeze–thaw durability of concrete. The combination of 10% silica fume, 25% slag, and 15% fly ash produced high strength and high resistance to freeze–thaw and wet–dry exposures as compared to other mixes. This study showed that it is imperative to cure the concrete for an extended period of time, especially those with fly ash and slag, to obtain good strength and durability. Literature review on the use of different supplementary cementitious materials in concrete to enhance strength and durability was also reported

Non-commuting coordinates, exotic particles, & anomalous anyons in the Hall effect

Our previous ``exotic'' particle, together with the more recent anomalous anyon model (which has arbitrary gyromagnetic factor $g$) are reviewed. The non-relativistic limit of the anyon generalizes the exotic particle which has $g=0$ to any $g$.When put into planar electric and magnetic fields, the Hall effect becomes mandatory for all $g\neq2$, when the field takes some critical value.Comment: A new reference added. Talk given by P. Horvathy at the International Workshop "Nonlinear Physics: Theory and Experiment. III. July'04, Gallipoli (Lecce, Italy). To be published in Theor. Math. Phys. Latex 9 pages, no figure

Dynamics of semiclassical Bloch wave - packets

The semiclassical approximation for electron wave-packets in crystals leads to equations which can be derived from a Lagrangian or, under suitable regularity conditions, in a Hamiltonian framework. In the plane, these issues are studied %in presence of external fields using the method of the coadjoint orbit applied to the ``enlarged'' Galilei group.Comment: 15 pages, Talk given at Nonlinear Physics. Theory and Experiment. IV,Gallipoli (Lecce), Italy - June 22 - July 1, 200