Dynamics of bi-periodic structures

Many structures considered for space applications are bi-periodic in their construction. Bi-periodicity means that two types of structural subassemblies, alternating in one or more directions, make up the structure. To gain insight into the dynamics of bi-periodic space structures a variety of one and two dimensional bi-periodic structures are considered. Results indicate that bands in which natural frequencies lie for periodic structures are further subdivided as a consequence of the bi-periodicity. Analytical solutions for the modes and frequencies of finite length one dimensional bi-periodic structures are obtained for general boundary conditions. A transmission method is developed to simplify the application of boundary conditions. It is found that some modes occur at frequencies which are outside the frequency bands predicted for bi-periodic structures. Two dimensional bi-periodic crossed beam grillage and truss structures are considered in this study. For cases where a separation of variables solution is possible the two dimensional structures exhibit similar properties to the one dimensional bi-periodic structures. Analytical solutions for the one and two dimensional bi-periodic structures considered above lead to a compact solution form similar to that of periodic structures analysis.     

Numerical investigations on gas-solid flow in circulating fluidized bed risers using a new cluster-based drag model

A cluster-based drag model is proposed for the gas-solid circulating fluidized bed (CFB) riser by including the cluster information collected from image process...     

Scaling of transverse nuclear magnetic relaxation due to magnetic nanoparticle aggregation

The aggregation of superparamagnetic iron oxide (SPIO) nanoparticles decreases the transverse nuclear magnetic resonance (NMR) relaxation time of adjacent water molecules measured by a Carr-Purcell-Meiboom-Gill (CPMG) pulse-echo sequence. This effect is commonly used to measure the concentrations of a variety of small molecules. We perform extensive Monte Carlo simulations of water diffusing around SPIO nanoparticle aggregates to determine the relationship between and details of the aggregate. We find that in the motional averaging regime scales as a power law with the number N of nanoparticles in an aggregate. The specific scaling is dependent on the fractal dimension d of the aggregates. We find for aggregates with d=2.2, a value typical of diffusion limited aggregation. We also find that in two-nanoparticle systems, is strongly dependent on the orientation of the two nanoparticles relative to the external magnetic field, which implies that it may be possible to sense the orientation of a two-nanoparticle aggregate. To optimize the sensitivity of SPIO nanoparticle sensors, we propose that it is best to have aggregates with few nanoparticles, close together, measured with long pulse-echo times.     

Strictly unital A∞-algebras

Given a graded module over a commutative ring, we define a dg-Lie algebra whose Maurer–Cartan elements are the strictly unital ${\mathrm{A}}_{\infty }$-algebra structures on that module. We use this to generalize Positselski's result that a curvature term on the bar construction compensates for a lack of augmentation, from a field to arbitrary commutative base ring. We also use this to show that the reduced Hochschild cochains control the strictly unital deformation functor. We motivate these results by giving a full development of the deformation theory of a nonunital ${\mathrm{A}}_{\infty }$-algebra.     

Eco-friendly location of small hydropower

We address the problem of locating small hydropower dams in an environmentally friendly manner. We propose the use of a multi-objective optimization model to maximize total hydropower production, while limiting negative impacts on river connectivity. Critically, we consider the so called “backwater effects” that dams have on power generation at nearby upstream sites via changes in water surface profiles. We further account for the likelihood that migratory fish and other aquatic species can successfully pass hydropower dams and other artificial/natural barriers and how this is influenced by backwater effects. Although naturally represented in nonlinear form, we manage through a series of linearization steps to formulate a mixed integer linear programing model. We illustrate the utility of our proposed framework using a case study from England and Wales. Interestingly, we show that for England and Wales, a region heavily impacted by a large number of existing river barriers, that installation of small hydropower dams fitted with even moderately effective fish passes can, in fact, create a win-win situation that results in increased hydropower and improved river connectivity.     

Enantioselective synthesis of ferrocenyl nucleoside analogues with apoptosis-inducing activity

[reaction: see text] As a contribution to bioorganometallic chemistry, an enantioselective synthesis of novel carbocyclic nucleoside analogues with a ferroceno-cyclopentene backbone was developed. Diastereoselective cuprate 1,4-addition or Mukaiyama-Michael addition to a planar-chiral enoate (ethyl (E)-2-[2-methoxycarbonyl-ferrocenyl]-acrylate) allowed for the introduction of different side chains (RCH(2)). Other important steps include a Dieckmann cyclization and the attachment of the nucleobase (NB) in an iron-assisted S(N)1 reaction. Some of the target compounds were shown to exhibit significant apoptosis-inducing activity (LD(50) = 10-20 microM) against tumor cells.     

High resolution electromechanical imaging of ferroelectric materials in a liquid environment by piezoresponse force microscopy

High-resolution imaging of ferroelectric materials using piezoresponse force microscopy (PFM) is demonstrated in an aqueous environment. The elimination of both long-range electrostatic forces and capillary interactions results in a localization of the ac field to the tip-surface junction and allows the tip-surface contact area to be controlled. This approach results in spatial resolutions approaching the limit of the intrinsic domain-wall width. Imaging at frequencies corresponding to high-order cantilever resonances minimizes the viscous damping and added mass effects on cantilever dynamics and allows sensitivities comparable to ambient conditions. PFM in liquids will provide novel opportunities for high-resolution studies of ferroelectric materials, imaging of soft polymer materials, and imaging of biological systems in physiological environments on, ultimately, the molecular level.     

Reorthogonalization for the Golub–Kahan–Lanczos bidiagonal reduction

The Golub–Kahan–Lanczos (GKL) bidiagonal reduction generates, by recurrence, the matrix factorization of $X \in \mathbb{R }^{m \times n}, m \ge n$ , given by $$\begin{aligned} X = UBV^T \end{aligned}$$ where $U \in \mathbb{R }^{m \times n}$ is left orthogonal, $V \in \mathbb{R }^{n \times n}$ is orthogonal, and $B \in \mathbb{R }^{n \times n}$ is bidiagonal. When the GKL recurrence is implemented in finite precision arithmetic, the columns of $U$ and $V$ tend to lose orthogonality, making a reorthogonalization strategy necessary to preserve convergence of the singular values. The use of an approach started by Simon and Zha (SIAM J Sci Stat Comput, 21:2257–2274, 2000) that reorthogonalizes only one of the two left orthogonal matrices $U$ and $V$ is shown to be very effective by the results presented here. Supposing that $V$ is the matrix reorthogonalized, the reorthogonalized GKL algorithm proposed here is modeled as the Householder Q–R factorization of $\left( \begin{array}{c} 0_{n \times k} \\ X V_k \end{array}\right) $ where $V_k = V(:,1:k)$ . That model is used to show that if $\varepsilon _M $ is the machine unit and $$\begin{aligned} \bar{\eta }= \Vert \mathbf{tril }(I-V^T\!~V)\Vert _F, \end{aligned}$$ where $\mathbf{tril }(\cdot )$ is the strictly lower triangular part of the contents, then: (1) the GKL recurrence produces Krylov spaces generated by a nearby matrix $X + \delta X$ , $\Vert \delta X\Vert _F = \mathcal O (\varepsilon _M + \bar{\eta }) \Vert X\Vert _F$ ; (2) singular values converge in the Lanczos process at the rate expected from the GKL algorithm in exact arithmetic on a nearby matrix; (3) a new proposed algorithm for recovering leading left singular vectors produces better bounds on loss of orthogonality and residual errors.