Flexural vibration patterning using an array of actuators

This paper describes a method to create unique vibration patterns by means of an array of actuators acting on the boundaries of the controlled structure. The method builds, in an iterative process, a black-box model by employing a series of probing external excitation vectors. Once a model has been identified, an optimization stage seeks the dynamic force-vector that generates the best approximation for a specified deformation pattern. Among the obtainable periodic responses are standing or travelling flexural waves of single or multi-frequencies in one or two spatial dimensions, as well as rotating, vortex-like, flexural waves in 2D. The paper describes the force-tuning process through which dozens of actuators can be modified automatically until the response, measured at hundreds of sensed locations, complies with the anticipated response. The excitation that yields the desired response is calculated using an over-determined set of least-squares equations that approximates the inverse of the identified model. The precise iterative tuning process can overcome some nonlinearity, manifested by additional harmonics in the response, by injecting forces that nullify their effect. Methods for wavelength optimization and wave identification in 1D and 2D are also discussed. The proposed tuning method showed good results in numerical simulation and in real world experiments.     

Engineered self-organization of neural networks using carbon nanotube clusters

A novel approach was developed to form engineered, electrically viable, neuronal networks, consisting of ganglion-like clusters of neurons. In the present method, the clusters are formed as the cells migrate on low affinity substrate towards high affinity, lithographically defined carbon nanotube templates on which they adhere and assemble. Subsequently, the gangliated neurons send neurites to form interconnected networks with pre-designed geometry and graph connectivity. This process is distinct from previously reported formation of clusterized neural networks in which a network of linked neurons collapses via neuronal migration along the inter-neuron links. The template preparation method is based on photo-lithography, micro-contact printing and carbon nanotube chemical vapor deposition techniques. The present work provides a new approach to form complex, engineered, interconnected neuronal network with pre-designed geometry via engineering the self-assembly process of neurons.     

2 kW, M2 < 10 radially polarized beams from aberration-compensated rod-based Nd:YAG lasers

Radially polarized light in a 2.1 kW, good quality beam was obtained from a Nd:YAG rod-based master oscillator power amplifier. Several techniques were utilized: a pure radially polarized oscillator, efficient pump chambers, external compensation of lower-order aberrations, and higher-order aberration compensation by pairing of pump chambers.     

Plasmon-soliton

Formation of a novel hybrid-vector spatial plasmon-soliton in a Kerr slab embedded between metal plates is predicted and analyzed with a modified nonlinear Schrodinger equation encompassing hybrid-vector field characteristics. Assisted by the transverse plasmonic effect, the self-trapping dimension of the plasmon-soliton was substantially compressed (compared with the dielectrically cladded slab case) when reducing the slab width. The practical limitation of the plasmon-soliton size reduction is determined by available nonlinear materials and metal loss. For the extreme reported values of nonlinear index change, we predict a soliton with a cross section of 300 nm x 30 nm (average dimension of 100 nm).     

Integral generators for the cohomology ring of moduli spaces of sheaves over Poisson surfaces

Let M be a smooth and compact moduli space of stable coherent sheaves on a projective surface S with an effective (or trivial) anti-canonical line bundle. We find generators for the cohomology ring of M, with integral coefficients. When S is simply connected and a universal sheaf E exists over S×M, then its class [E] admits a Künneth decomposition as a class in the tensor product of the topological K-rings. The generators are the Chern classes of the Künneth factors of [E] in . The general case is similar.     

Pyridine modified polyethylene copolymer compatibilizer for melt blended carbon nanotube composites: effects of chain structure and matrix viscosity

The electrical percolation threshold of different polyethylene/carbon nanotube nanocomposites was studied as a function of chain structure, matrix viscosity, and the effect of compatibilizer. The lower the viscosity of the matrix the lower is the percolation threshold, regardless of the chain architecture and degree of crystallization. To improve dispersion a series of acrylic acid copolymer are introduced into the system. The highest concentration of acid co‐monomer that maintain miscibility with the polyethylene matrix is 5 wt.%. The compatibilizer in its pristine form does not have a significant effect on dispersion and on volume resistivity. When the acidic copolymer was modified with aminomethylpyridine, in order to facilitate π–π interaction with the nanotubes, a 4‐decade reduction was recorder for the high viscosity matrices at 10 wt.% compatibilizer loading. Copyright © 2014 John Wiley & Sons, Ltd.     

Random triangle removal

Starting from a complete graph on n   vertices, repeatedly delete the edges of a uniformly chosen triangle. This stochastic process terminates once it arrives at a triangle-free graph, and the fundamental question is to estimate the final number of edges (equivalently, the time it takes the process to finish, or how many edge-disjoint triangles are packed via the random greedy algorithm). Bollobás and Erd?s (1990) conjectured that the expected final number of edges has order n^3/2$n^{3/2}$. An upper bound of o(n²)$o(n^2)$ was shown by Spencer (1995) and independently by Rödl and Thoma (1996). Several bounds were given for variants and generalizations (e.g., Alon, Kim and Spencer (1997) and Wormald (1999)), while the best known upper bound for the original question of Bollobás and Erd?s was n^7/4+o(1)$n^{7/4+o(1)}$ due to Grable (1997). No nontrivial lower bound was available.     

A bijection between permutations and floorplans, and its applications

A floorplan represents the relative relations between modules on an integrated circuit. Floorplans are commonly classified as slicing, mosaic, or general. Separable and Baxter permutations are classes of permutations that can be defined in terms of forbidden subsequences. It is known that the number of slicing floorplans equals the number of separable permutations and that the number of mosaic floorplans equals the number of Baxter permutations [B. Yao, H. Chen, C.K. Cheng, R.L. Graham, Floorplan representations: complexity and connections, ACM Trans. Design Automation Electron. Systems 8(1) (2003) 55-80]. We present a simple and efficient bijection between Baxter permutations and mosaic floorplans with applications to integrated circuits design. Moreover, this bijection has two additional merits: (1) It also maps between separable permutations and slicing floorplans; and (2) it suggests enumerations of mosaic floorplans according to various structural parameters.