Certain Aspects Related To Computation By Modified Crack Closure Integral(MCCI)

This paper presents the proper computational approach for the estimation of strain energy release rates by modified crack closure integral (MCCI). In particular, in the estimation of consistent nodal force vectors used in the MCCI expressions for quarter-point singular elements (wherein all the nodal force vectors participate in computation of strain energy release rates by MCCI). The numerical example of a centre crack tension specimen under uniform loading is presented to illustrate the approach.

Computation of Diffuse Solar Radiation

A technique for computing the spectral and angular (both the zenith and azimuthal) distribution of the solar energy reaching the surface of earth and any other plane in the atmosphere has been developed. Here the computer code LOWTRAN is used for getting the atmospheric transmittances in conjunction with two approximate procedures: one based on the Eddington method and the other on van de Hulst's adding method, for solving the equation of radiative transfer to obtain the diffuse radiation in the cloud-free situation. The aerosol scattering phase functions are approximated by the Hyeney-Greenstein functions. When the equation of radiative transfer is solved using the adding method, the azimuthal and zenith angle dependence of the scattered radiation is evaluated, whereas when the Eddington technique is utilized only the total downward flux of scattered solar radiation is obtained. Results of the diffuse and beam components of solar radiation received on surface of earth compare very well with those computed by other methods such as the more exact calculations using spherical harmonics and when atmospheric conditions corresponding to that prevailing locally in a tropical location (as in India) are used as inputs the computed values agree closely with the measured values.

Analysis and computation of the oil film thickness between the piston ring and cylinder liner of an internal combustion engine

A study of the essential features of piston rings in the cylinder liner of an internal combustion engine reveals that the lubrication problem posed by it is basically that of a slider bearing. According to steady-flow-hydrodynamics, viz. Image the oil film thickness becomes zero at the dead centre positions as the velocity, U = 0. In practice, however, such a phenomenon cannot be supported by consideration of the wear rates of pistion rings and cylinder liners. This can be explained by including the “squeeze” action term in the

Block- and strand-multiplexing for fast computation of a class of transforms

The transforms dealt with in this paper are defined in terms of the transform kernels which are Kroneeker products of the two or more component kernels. The signal flow-graph for the computation of such a transform is obtained with the flow-graphs for the component transforms as building blocks.

Finite field computation technique for exact solution of systems of linear equations and interval linear programming problems

An error-free computational approach is employed for finding the integer solution to a system of linear equations, using finite-field arithmetic. This approach is also extended to find the optimum solution for linear inequalities such as those arising in interval linear programming probloms.

On the computation of two-dimensional compressible flow fields by the modified local stability scheme

The modified local stability scheme is applied to several two-dimensional problems—blunt body flow, regular reflection of a shock and lambda shock. The resolution of the flow features obtained by the modified local stability scheme is found to be better than that achieved by the other first order schemes and almost identical to that achieved by the second order schemes incorporating artificial viscosity. The scheme is easy for coding, consumes moderate amount of computer storage and time. The scheme can be advantageously used in place of second order schemes.

Adiabatic quantum computation with a one-dimensional projector Hamiltonian

Adiabatic quantum computation is based on the adiabatic evolution of quantum systems. We analyze a particular class of quantum adiabatic evolutions where either the initial or final Hamiltonian is a one-dimensional projector Hamiltonian on the corresponding ground state. The minimum-energy gap, which governs the time required for a successful evolution, is shown to be proportional to the overlap of the ground states of the initial and final Hamiltonians. We show that such evolutions exhibit a rapid crossover as the ground state changes abruptly near the transition point where the energy gap is minimum. Furthermore, a faster evolution can be obtained by performing a partial adiabatic evolution within a narrow interval around the transition point. These results generalize and quantify earlier works.

Computation of Thermal Stress Intensity Factors for Bimaterial Interface Cracks Using Domain Integral Method

The concept of domain integral used extensively for J integral has been applied in this work for the formulation of J(2) integral for linear elastic bimaterial body containing a crack at the interface and subjected to thermal loading. It is shown that, in the presence of thermal stresses, the J(k) domain integral over a closed path, which does not enclose singularities, is a function of temperature and body force. A method is proposed to compute the stress intensity factors for bimaterial interface crack subjected to thermal loading by combining this domain integral with the J(k) integral. The proposed method is validated by solving standard problems with known solutions.

Efficient computation of volume fractions for multi-material cell complexes in a grid by slicing

The paper presents a novel slicing based method for computation of volume fractions in multi-material solids given as a B-rep whose faces are triangulated and shared by either one or two materials. Such objects occur naturally in geoscience applications and the said computation is necessary for property estimation problems and iterative forward modeling. Each facet in the model is cut by the planes delineating the given grid structure or grid cells. The method, instead of classifying the points or cells with respect to the solid, exploits the convexity of triangles and the simple axis-oriented disposition of the cutting surfaces to construct a novel intermediate space enumeration representation called slice-representation, from which both the cell containment test and the volume-fraction computation are done easily. Cartesian and cylindrical grids with uniform and non-uniform spacings have been dealt with in this paper. After slicing, each triangle contributes polygonal facets, with potential elliptical edges, to the grid cells through which it passes. The volume fractions of different materials in a grid cell that is in interaction with the material interfaces are obtained by accumulating the volume contributions computed from each facet in the grid cell. The method is fast, accurate, robust and memory efficient. Examples illustrating the method and performance are included in the paper.

Time and Energy Complexity of Distributed Computation of a Class of Functions in Wireless Sensor Networks

We consider a scenario in which a wireless sensor network is formed by randomly deploying n sensors to measure some spatial function over a field, with the objective of computing a function of the measurements and communicating it to an operator station. We restrict ourselves to the class of type-threshold functions (as defined in the work of Giridhar and Kumar, 2005), of which max, min, and indicator functions are important examples: our discussions are couched in terms of the max function. We view the problem as one of message-passing distributed computation over a geometric random graph. The network is assumed to be synchronous, and the sensors synchronously measure values and then collaborate to compute and deliver the function computed with these values to the operator station. Computation algorithms differ in (1) the communication topology assumed and (2) the messages that the nodes need to exchange in order to carry out the computation. The focus of our paper is to establish (in probability) scaling laws for the time and energy complexity of the distributed function computation over random wireless networks, under the assumption of centralized contention-free scheduling of packet transmissions. First, without any constraint on the computation algorithm, we establish scaling laws for the computation time and energy expenditure for one-time maximum computation. We show that for an optimal algorithm, the computation time and energy expenditure scale, respectively, as Theta(radicn/log n) and Theta(n) asymptotically as the number of sensors n rarr infin. Second, we analyze the performance of three specific computation algorithms that may be used in specific practical situations, namely, the tree algorithm, multihop transmission, and the Ripple algorithm (a type of gossip algorithm), and obtain scaling laws for the computation time and energy expenditure as n rarr infin. In particular, we show that the computation time for these algorithms scales as Theta(radicn/lo- g n), Theta(n), and Theta(radicn log n), respectively, whereas the energy expended scales as , Theta(n), Theta(radicn/log n), and Theta(radicn log n), respectively. Finally, simulation results are provided to show that our analysis indeed captures the correct scaling. The simulations also yield estimates of the constant multipliers in the scaling laws. Our analyses throughout assume a centralized optimal scheduler, and hence, our results can be viewed as providing bounds for the performance with practical distributed schedulers.

Geometric quantum computation using fictitious spin-1/2 subspaces of strongly dipolar coupled nuclear spins

Geometric phases have been used in NMR to implement controlled phase shift gates for quantum-information processing, only in weakly coupled systems in which the individual spins can be identified as qubits. In this work, we implement controlled phase shift gates in strongly coupled systems by using nonadiabatic geometric phases, obtained by evolving the magnetization of fictitious spin-1/2 subspaces, over a closed loop on the Bloch sphere. The dynamical phase accumulated during the evolution of the subspaces is refocused by a spin echo pulse sequence and by setting the delay of transition selective pulses such that the evolution under the homonuclear coupling makes a complete 2 pi rotation. A detailed theoretical explanation of nonadiabatic geometric phases in NMR is given by using single transition operators. Controlled phase shift gates, two qubit Deutsch-Jozsa algorithm, and parity algorithm in a qubit-qutrit system have been implemented in various strongly dipolar coupled systems obtained by orienting the molecules in liquid crystal media.

Computation-Based Reliability Analysis in Real Time Applications

Reliability analysis for computing systems in aerospace applications must account for actual computations the system performs in the use environment. This paper introduces a theoretical nonhomogeneous Markov model for such applications.

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.

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.