An efficient reduction algorithm for computation of interconnect delay variability for statistical timing analysis in clock tree planning

In this paper, we propose a novel and efficient algorithm for modelling sub-65 nm clock interconnect-networks in the presence of process variation. We develop a method for delay analysis of interconnects considering the impact of Gaussian metal process variations. The resistance and capacitance of a distributed RC line are expressed as correlated Gaussian random variables which are then used to compute the standard deviation of delay Probability Distribution Function (PDF) at all nodes in the interconnect network. Main objective is to find delay PDF at a cheaper cost. Convergence of this approach is in probability distribution but not in mean of delay. We validate our approach against SPICE based Monte Carlo simulations while the current method entails significantly lower computational cost.

Heterogeneous nucleation of solidification of cadmium particles embedded in an aluminium matrix

A hypomonotectic alloy of Al-4.5wt%Cd has been manufactured by melt spinning and the resulting microstructure examined by transmission electron microscopy. As-melt spun hypomonotectic Al-4.5wt%Cd consists of a homogeneous distribution of faceted 5 to 120 nm diameter cadmium particles embedded in a matrix of aluminium, formed during the monotectic solidification reaction. The cadmium particles exhibit an orientation relationship with the aluminium matrix of {111}Al//{0001}Cd and lang110rangAlAl//lang11¯20> Cd, with four cadmium particle variants depending upon which of the four {111}Al planes is parallel to {0001}Cd. The cadmium particles exibit a distorted cuboctahedral shape, bounded by six curved {100}Al//{20¯23}Cd facets, six curved {111}Al/{40¯43}Cd facets and two flat {111}Al//{0001}Cd facets. The as-melt spun cadmium particle shape is metastable and the cadmium particles equilibrate during heat treatment below the cadmium melting point, becoming elongated to increase the surface area and decrease the separation of the {111}Al//{0001}Cd facets. The equilibrium cadmium particle shape and, therefore, the anisotropy of solid aluminium-solid cadmium and solid aluminium -liquid cadmium surface energies have been monitored by in situ heating in the transmission electron microscope over the temperature range between room temperature and 420 °C. The anisotropy of solid aluminium-solid cadmium surface energy is constant between room temperature and the cadmium melting point, with the {100}Al//{20¯23}Cd surface energy on average 40% greater than the {111}Al//{0001}Cd surface energy, and 10% greater than the {111}Al//{40¯43Cd surface energy. When the cadmium particles melt at temperatures above 321 °C, the {100}Al//{20¯23}Cd facets disappear and the {111}Al//{40¯43}Cd and {111}A1//{0001}Cd surface energies become equal. The {111}Al facets do not disappear when the cadmium particles melt, and the anisotropy of solid aluminium-liquid cadmium surface energy decreases gradually with increasing temperature above the cadmium melting point. The kinetics of cadmium solidification have been examined by heating and cooling experiments in a differential scanning calorimeter over a range of heating and cooling rates. Cadmium particle solidification is nucleated catalytically by the surrounding aluminium matrix on the {111}Al faceted surfaces, with an undercooling of 56 K and a contact angle of 42 °. The nucleation kinetics of cadmium particle solidification are in good agreement with the hemispherical cap model of heterogeneous nucleation.

Mathematical modelling of groundwater pollution in a small heterogeneous aquifer at Kärkölä, southern Finland

Yhteenveto: Kärkölän likaantuneen pohjavesialueen matemaattinen mallinnus

In-Network Computation in Random Wireless Networks: A PAC Approach to Constant Refresh Rates with Lower Energy Costs

We propose a method to compute a probably approximately correct (PAC) normalized histogram of observations with a refresh rate of Theta(1) time units per histogram sample on a random geometric graph with noise-free links. The delay in computation is Theta(root n) time units. We further extend our approach to a network with noisy links. While the refresh rate remains Theta(1) time units per sample, the delay increases to Theta(root n log n). The number of transmissions in both cases is Theta(n) per histogram sample. The achieved Theta(1) refresh rate for PAC histogram computation is a significant improvement over the refresh rate of Theta(1/log n) for histogram computation in noiseless networks. We achieve this by operating in the supercritical thermodynamic regime where large pathways for communication build up, but the network may have more than one component. The largest component however will have an arbitrarily large fraction of nodes in order to enable approximate computation of the histogram to the desired level of accuracy. Operation in the supercritical thermodynamic regime also reduces energy consumption. A key step in the proof of our achievability result is the construction of a connected component having bounded degree and any desired fraction of nodes. This construction may also prove useful in other communication settings on the random geometric graph.

Interior Medial Axis Transform computation of 3D objects bound by free-form surfaces

This paper presents an algorithm for generating the Interior Medial Axis Transform (iMAT) of 3D objects with free-form boundaries. The algorithm proposed uses the exact representation of the part and generates an approximate rational spline description of the iMAT. The algorithm generates the iMAT by a tracing technique that marches along the object's boundary. The level of approximation is controlled by the choice of the step size in the tracing procedure. Criteria based on distance and local curvature of boundary entities are used to identify the junction points and the search for these junction points is done in an efficient way. The algorithm works for multiply-connected objects as well. Results of the implementation are provided. (C) 2010 Elsevier Ltd. All rights reserved.

Computation of restoration of ligand response in the random kinetics of a prostate cancer cell signaling pathway

Mutation and/or dysfunction of signaling proteins in the mitogen activated protein kinase (MAPK) signal transduction pathway are frequently observed in various kinds of human cancer. Consistent with this fact, in the present study, we experimentally observe that the epidermal growth factor (EGF) induced activation profile of MAP kinase signaling is not straightforward dose-dependent in the PC3 prostate cancer cells. To find out what parameters and reactions in the pathway are involved in this departure from the normal dose-dependency, a model-based pathway analysis is performed. The pathway is mathematically modeled with 28 rate equations yielding those many ordinary differential equations (ODE) with kinetic rate constants that have been reported to take random values in the existing literature. This has led to us treating the ODE model of the pathways kinetics as a random differential equations (RDE) system in which the parameters are random variables. We show that our RDE model captures the uncertainty in the kinetic rate constants as seen in the behavior of the experimental data and more importantly, upon simulation, exhibits the abnormal EGF dose-dependency of the activation profile of MAP kinase signaling in PC3 prostate cancer cells. The most likely set of values of the kinetic rate constants obtained from fitting the RDE model into the experimental data is then used in a direct transcription based dynamic optimization method for computing the changes needed in these kinetic rate constant values for the restoration of the normal EGF dose response. The last computation identifies the parameters, i.e., the kinetic rate constants in the RDE model, that are the most sensitive to the change in the EGF dose response behavior in the PC3 prostate cancer cells. The reactions in which these most sensitive parameters participate emerge as candidate drug targets on the signaling pathway. (C) 2011 Elsevier Ireland Ltd. All rights reserved.

Instability and dewetting of ultrathin solid viscoelastic films on homogeneous and heterogeneous substrates

Instability and dewetting engendered by the van der Waals force in soft thin (<100 nm) linear viscoelastic solid (e. g., elastomeric gel) films on uniform and patterned surfaces are explored. Linear stability analysis shows that, although the elasticity of the film controls the onset of instability and the corresponding critical wavelength, the dominant length-scale remains invariant with the elastic modulus of the film. The unstable modes are found to be long-wave, for which a nonlinear long-wave analysis and simulations are performed to uncover the dynamics and morphology of dewetting. The stored elastic energy slows down the temporal growth of instability significantly. The simulations also show that a thermodynamically stable film with zero-frequency elasticity can be made unstable in the presence of physico-chemical defects on the substrate and can follow an entirely different pathway with far fewer holes as compared to the viscous films. Further, the elastic restoring force can retard the growth of a depression adjacent to the hole-rim and thus suppress the formation of satellite holes bordering the primary holes. These findings are in contrast to the dewetting of viscoelastic liquid films where nonzero frequency elasticity accelerates the film rupture and promotes the secondary instabilities. Thus, the zero-frequency elasticity can play a major role in imposing a better-defined long-range order to the dewetted structures by arresting the secondary instabilities. (C) 2011 American Institute of Physics. doi: 10.1063/1.3554748]

Heterogeneous nucleation of pb particles embedded in a Zn matrix

Zinc-10 and 20 wt pct Pb alloys have been rapidly solidified by melt spinning to obtain a very fine scale dispersion of nanometer-sized Pb particles embedded in Zn matrix. The microstructure and crystallography of the Pb particles have been studied using transmission electron microscopy (TEM). Each embedded Pb particle is a single crystal, with a truncated hexagonal biprism shape with the 6/mmm Zn matrix point group symmetry surrounded by and { 0001 á },\text { \text10[`\text1] \text0 },\text and { \text10[`\text1] \text1 }0001 1010 and 1011 facets. The Pb particles solidify with a well-defined orientation relationship with the Zn matrix of ( 0001 )Zn ||(111)Pb\text and\text [ \text11[`\text2] \text0 ]Zn| ||[ 1[`1] 0 ]Pb 0001Zn(111)Pb and 1120Zn110Pb . The melting and solidification behavior of the Pb particle have been studied using differential scanning calorimetry (DSC). The Pb particles solidify with an undercooling of approximately 30 K, by heterogeneous nucleation on the {0001} facets of the surrounding Zn matrix, with an apparent contact angle of 23 deg.

Heterogeneous permanganate oxidation of 1,5-dienes: a novel synthesis of 5-substituted butanolides

In the presence of a catalytic amount of water, 1,5-dienes undergo novel and unusual oxidation with potassium permanganate�copper sulfate in dichloromethane to give substituted butanolides in good yields under very mild conditions.

Decoupled three-dimensional finite element computation of thermoelastic damping using Zener's approximation

We consider three dimensional finite element computations of thermoelastic damping ratios of arbitrary bodies using Zener's approach. In our small-damping formulation, unlike existing fully coupled formulations, the calculation is split into three smaller parts. Of these, the first sub-calculation involves routine undamped modal analysis using ANSYS. The second sub-calculation takes the mode shape, and solves on the same mesh a periodic heat conduction problem. Finally, the damping coefficient is a volume integral, evaluated elementwise. In the only other decoupled three dimensional computation of thermoelastic damping reported in the literature, the heat conduction problem is solved much less efficiently, using a modal expansion. We provide numerical examples using some beam-like geometries, for which Zener's and similar formulas are valid. Among these we examine tapered beams, including the limiting case of a sharp tip. The latter's higher-mode damping ratios dramatically exceed those of a comparable uniform beam.

On Computation of Minimum Distance of Linear Block Codes Above 1/2 Rate Coding

The minimum distance of linear block codes is one of the important parameter that indicates the error performance of the code. When the code rate is less than 1/2, efficient algorithms are available for finding minimum distance using the concept of information sets. When the code rate is greater than 1/2, only one information set is available and efficiency suffers. In this paper, we investigate and propose a novel algorithm to find the minimum distance of linear block codes with the code rate greater than 1/2. We propose to reverse the roles of information set and parity set to get virtually another information set to improve the efficiency. This method is 67.7 times faster than the minimum distance algorithm implemented in MAGMA Computational Algebra System for a (80, 45) linear block code.

Heterogeneous permanganate oxidations: Synthesis of medium ring keto-lactones via substituent directed oxidative cyclisation

Homoallyl alcohols 4a-b and 5a-b undergo smooth oxidative cyclisation to give the corresponding ring enlarged keto-lactones under heterogeneous permanganate oxidation conditions.

High-Throughput Study of the Cu(CH3COO)(2)center dot H2O-5-Nitroisophthalic Acid Heterocyclic Ligand System: Synthesis, Structure, Magnetic, and Heterogeneous Catalytic Studies of Three Copper Nitroisophthalates

A high-throughput screening was employed to identify new compounds in Cu(CH3COO)(2)center dot H2O-NIPA-heterocyclic ligand systems. Of the compounds identified, three compounds, Cu-3{(NO2)-C6H3-(COO)(2)}(3)(C3N6H6)] (1), Cu-2(mu(3)-OH)(H2O){(NO2)-C6H3-(COO)(2)}(CN4H)]center dot-(H2O) (II), and Cu-2(mu(3)-OH)(H2O){(NO2)-C6H3-(COO)(2}-)(CN5H2)]center dot 2(H2O) (III), have been isolated as good quality single crystals by employing conventional hydrothermal methods. Three other compounds, Cu-2{(NO2)-C6H3-(COO)(2)}-(CN4H)(H2O) (IIa), Cu-2{(NO2)-C6H3-(COO)(2)}(CN5H2) (IIIa), and Cu-2{(NO2)-C6H3-(COO)(2)}{(CN5H2)(2)}2H(2)O (IIIb), were identified by a combination of elemental analysis, thermogravimetric analysis (TGA), and IR spectroscopic studies, although their structures are yet to be determined. The single crystalline compounds were also characterized by elemental analysis, TGA, IR, UV vis, magnetic, and catalytic studies. The structures of the compounds have paddle wheel (I) and infinite Cu 0(H) Cu chains (II and HI) connected with NLPA and heterocyclic ligands forming two-(II) and three-dimensional (I and III) structures. The bound and lattice water molecules in 11 and 111 could be reversibly removed/inserted without affecting the structure. In the case of II, the removal of water gives rise to a structural transition, but the dehydrated phase reverts back to the original phase on prolonged exposure to atmospheric conditions. Magnetic studies indicate an overall antiferromagnetism in all of the compounds. Lewis acid catalytic studies indicate that compounds II and HI are active for cyanosilylation of imines.

Distributed computation of fixed points of infinity-nonexpansive maps

The distributed implementation of an algorithm for computing fixed points of an infinity-nonexpansive map is shown to converge to the set of fixed points under very general conditions.