Likelihood estimation for distributed parameter models for NASA Mini-MAST truss

A maximum likelihood estimation for distributed parameter models of large flexible structures was formulated. Distributed parameter models involve far fewer unknown parameters than independent modal characteristics or finite element models. The closed form solutions for the partial differential equations with corresponding boundary conditions were derived. The closed-form expressions of sensitivity functions led to highly efficient algorithms for analyzing ground or on-orbit test results. For an illustration of this approach, experimental data of the NASA Mini-MAST truss was used. The estimations of modal properties involve lateral bending modes and torsional modes. The results show that distributed parameter models are promising in the parameter estimation of large flexible structures

A model of driven and decaying magnetic turbulence in a cylinder

Using mean-field theory, we compute the evolution of the magnetic field in a cylinder with outer perfectly conducting boundaries, an imposed axial magnetic and electric field. The thus injected magnetic helicity in the system can be redistributed by magnetic helicity fluxes down the gradient of the local current helicity of the small-scale magnetic field. A weak reversal of the axial magnetic field is found to be a consequence of the magnetic helicity flux in the system. Such fluxes are known to alleviate so-called catastrophic quenching of the {\alpha}-effect in astrophysical applications. Application to the reversed field pinch in plasma confinement devices is discussed.Comment: 7 pages, 4 figures, submitted to Phys. Rev.

Riesz Transform on Locally Symmetric Spaces and Riemannian Manifolds with a Spectral Gap

In this paper we study the Riesz transform on complete and connected Riemannian manifolds $M$ with a certain spectral gap in the $L^2$ spectrum of the Laplacian. We show that on such manifolds the Riesz transform is $L^p$ bounded for all $p \in (1,\infty)$. This generalizes a result by Mandouvalos and Marias and extends a result by Auscher, Coulhon, Duong, and Hofmann to the case where zero is an isolated point of the $L^2$ spectrum of the Laplacian.Comment: 8 p

The isocohomological property, higher Dehn functions, and relatively hyperbolic groups

The property that the polynomial cohomology with coefficients of a finitely generated discrete group is canonically isomorphic to the group cohomology is called the (weak) isocohomological property for the group. In the case when a group is of type $HF^\infty$, i.e. that has a classifying space with the homotopy type of a cellular complex with finitely many cells in each dimension, we show that the isocohomological property is equivalent to the universal cover of the classifying space satisfying polynomially bounded higher Dehn functions. If a group is hyperbolic relative to a collection of subgroups, each of which is polynomially combable (respectively $HF^\infty$ and isocohomological), then we show that the group itself has these respective properties too. Combining with the results of Connes-Moscovici and Dru{\c{t}}u-Sapir we conclude that a group satisfies the Novikov conjecture if it is relatively hyperbolic to subgroups that are of property RD, of type $HF^\infty$ and isocohomological.Comment: 35 pages, no figure

Behaviour of moist and saturated sand during shock and release

Relatively little is known about the changes that occur in the shock compaction and release of granular matter with varying levels of moisture. Here, we report a series of plate impact experiments giving shock Hugoniot and release data for a well characterized sand at dry, 10% moist, and saturated water contents. The results reveal that at low moisture content the shock impedance is slightly reduced, while the release remains predominantly inelastic. Close to saturation, much more substantial changes occur: the shock impedance stiffens substantially, the Hugoniot appears to split into two branches, and the release becomes almost completely elastic. We discuss mechanisms underpinning these changes in behavior.This work was supported through the Force Protection Engineering research programme led by QinetiQ Plc. on behalf of DSTL.This is the author accepted manuscript. The final version is available from AIP via http://dx.doi.org/10.1063/1.493468

A piecewise continuous Timoshenko beam model for the dynamic analysis of tapered beam-like structures

Distributed parameter modeling offers a viable alternative to the finite element approach for modeling large flexible space structures. The introduction of the transfer matrix method into the continuum modeling process provides a very useful tool to facilitate the distributed parameter model applied to some more complex configurations. A uniform Timoshenko beam model for the estimation of the dynamic properties of beam-like structures has given comparable results. But many aeronautical and aerospace structures are comprised of non-uniform sections or sectional properties, such as aircraft wings and satellite antennas. This paper proposes a piecewise continuous Timoshenko beam model which is used for the dynamic analysis of tapered beam-like structures. A tapered beam is divided into several segments of uniform beam elements. Instead of arbitrarily assumed shape functions used in finite element analysis, the closed-form solution of the Timoshenko beam equation is used. Application of the transfer matrix method relates all the elements as a whole. By corresponding boundary conditions and compatible conditions a characteristic equation for the global tapered beam has been developed, from which natural frequencies can be derived. A computer simulation is shown in this paper, and compared with the results obtained from the finite element analysis. While piecewise continuous Timoshenko beam model decreases the number of elements significantly; comparable results to the finite element method are obtained

The significance of grain morphology and moisture content on the response of silica sand to ballistic penetration

The dynamic response of sand is of interest for a wide range of applications, from civil engineering to asteroid impact, in addition to defense and industrial processes. Granular dynamics are controlled by a complex network of intergrain force chains; yet, our understanding of how grain morphology, moisture, rate, and loading geometry affect the response to rapid compaction remains limited. Here, we show how just 1% moisture can significantly reduce penetration resistance in silica sand, while smoother-grained material—with a similar bulk density, grain size, and mineralogy—exhibits markedly improved stopping power. Cylindrical targets are impacted by spherical steel projectiles, with Digital Speckle Radiography employed to determine both the penetration depth and the sand bed displacement at a series of incremental time steps after impact. The results provide substantial insight into how slight adjustments to grain-grain contact points can affect the bulk dynamic response of brittle granular materials.</jats:p

Applying transfer matrix method to the estimation of the modal characteristics of the NASA Mini-Mass Truss

It is beneficial to use a distributed parameter model for large space structures because the approach minimizes the number of model parameters. Holzer's transfer matrix method provides a useful means to simplify and standardize the procedure for solving the system of partial differential equations. Any large space structures can be broken down into sub-structures with simple elastic and dynamical properties. For each single element, such as beam, tether, or rigid body, we can derive the corresponding transfer matrix. Combining these elements' matrices enables the solution of the global system equations. The characteristics equation can then be formed by satisfying the appropriate boundary conditions. Then natural frequencies and mode shapes can be determined by searching the roots of the characteristic equation at frequencies within the range of interest. This paper applies this methodology, and the maximum likelihood estimation method, to refine the modal characteristics of the NASA Mini-Mast Truss by successively matching the theoretical response to the test data of the truss. The method is being applied to more complex configurations

Laboratory Plasma Dynamos, Astrophysical Dynamos, and Magnetic Helicity Evolution

The term ``dynamo'' means different things to the laboratory fusion plasma and astrophysical plasma communities. To alleviate the resulting confusion and to facilitate interdisciplinary progress, we pinpoint conceptual differences and similarities between laboratory plasma dynamos and astrophysical dynamos. We can divide dynamos into three types: 1. magnetically dominated helical dynamos which sustain a large scale magnetic field against resistive decay and drive the magnetic geometry toward the lowest energy state, 2. flow-driven helical dynamos which amplify or sustain large scale magnetic fields in an otherwise turbulent flow, and 3. flow-driven nonhelical dynamos which amplify fields on scales at or below the driving turbulence. We discuss how all three types occur in astrophysics whereas plasma confinement device dynamos are of the first type. Type 3 dynamos requires no magnetic or kinetic helicity of any kind. Focusing on type 1 and 2 dynamos, we show how different limits of a unified set of equations for magnetic helicity evolution reveal both types. We explicitly describe a steady-state example of a type 1 dynamo, and three examples of type 2 dynamos: (i) closed volume and time dependent; (ii) steady-state with open boundaries; (iii) time dependent with open boundaries.Comment: accepted by MNRA

Magnetic instability in a sheared azimuthal flow

We study the magneto-rotational instability of an incompressible flow which rotates with angular velocity Omega(r)=a+b/r^2 where r is the radius and $a$ and b are constants. We find that an applied magnetic field destabilises the flow, in agreement with the results of Rudiger & Zhang 2001. We extend the investigation in the region of parameter space which is Rayleigh stable. We also study the instability at values of magnetic Prandtl number which are much larger and smaller than Rudiger & Zhang. Large magnetic Prandtl numbers are motivated by their possible relevance in the central region of galaxies (Kulsrud & Anderson 1992). In this regime we find that increasing the magnetic Prandtl number greatly enhances the instability; the stability boundary drops below the Rayleigh line and tends toward the solid body rotation line. Very small magnetic Prandtl numbers are motivated by the current MHD dynamo experiments performed using liquid sodium and gallium. Our finding in this regime confirms Rudiger & Zhang's conjecture that the linear magneto-rotational instability and the nonlinear hydrodynamical instability (Richard & Zahn 1999) take place at Reynolds numbers of the same order of magnitude.Comment: 4 pages, 4 figure