Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

The energy compaction and multiresolution properties of wavelets have made the image fusion successful in combining important features such as edges and textures from source images without introducing any artifacts for context enhancement and situational awareness. The wavelet transform is visualized as a convolution of wavelet filter coefficients with the image under consideration and is computationally intensive. The advent of lifting-based wavelets has reduced the computations but at the cost of visual quality and performance of the fused image. To retain the visual quality and performance of the fused image with reduced computations, a discrete cosine harmonic wavelet (DCHWT)-based image fusion is proposed. The performance of DCHWT is compared with both convolution and lifting-based image fusion approaches. It is found that the performance of DCHWT is similar to convolution-based wavelets and superior/similar to lifting-based wavelets. Also, the computational complexity (in terms of additions and multiplications) of the proposed method scores over convolution-based wavelets and is competitive to lifting-based wavelets.

Multifocus and multispectral image fusion based on pixel significance using discrete cosine harmonic wavelet transform

A review on state of health estimations and remaining useful life prognostics of lithium-ion batteries

Multifocus and multispectral image fusion based on pixel significance using discrete cosine harmonic

The Department of Mechanical Engineering (https:// www.mccormick.northwestern.edu/mechanical/graduate) prepares graduates for careers in industry, research, and academia. Students specialize in Design/Manufacturing/Tribology, Dynamics, Control, Robotics, Neural Engineering, Simulation Driven Engineering, Solid Mechanics, Fluid Dynamics, Nanotechnology/MEMS, Bioengineering and Biomechanics, Energy and Sustainability, Engineering Design and Innovation, Product Development, Engineering Management and other disciplines.

What is Mechanical Engineering

The wavelet-Galerkin approach towards the solution of one-dimensional Fisher's equation using complex harmonic wavelets is presented in this paper. The linear and nonlinear connection coefficients were explicitly derived. The wavelet-solution is compared with analogous analytical result.

Mutiscale Analysis of the Fisher Equation

A practical approach to the search for (quasi-) discrete breathers (DBs) in a triangular $\ensuremath{\beta}$-FPUT lattice (after Fermi, Pasta, Ulam, and Tsingou) is proposed. DBs are obtained by superimposing localizing functions on delocalized nonlinear vibrational modes (DNVMs) having frequencies above the phonon spectrum of the lattice. Zero-dimensional and one-dimensional DBs are obtained. The former ones are localized in both spatial dimensions, and the latter ones are only in one dimension. Among the one-dimensional DBs, two families are considered: the first is based on the DNVMs of a triangular lattice, and the second is based on the DNVMs of a chain. We speculate that our systematic approach on the triangular $\ensuremath{\beta}$-FPUT lattice reveals all possible types of spatially localized oscillations with frequencies bifurcating from the upper edge of the phonon band as all DNVMs with frequencies above the phonon band are analyzed.

/pdf/discrete-breathers-in-a-triangular-b-fermi-pasta-ulam-30ui2ja3tb.pdf

Discrete breathers in a triangular β-Fermi-Pasta-Ulam-Tsingou lattice.

Magnetic resonance imaging (MRI) plays an important role in disease diagnosis. The noise that appears in MRI images is commonly governed by a Rician distribution. The bendlets system is a second-order shearlet transform with bent elements. Thus, the bendlets system is a powerful tool with which to represent images with curve contours, such as the brain MRI images, sparsely. By means of the characteristic of bendlets, an adaptive denoising method for microsection images with Rician noise is proposed. In this method, the curve contour and texture can be identified as low-frequency components, which is not the case with other methods, such as the wavelet, shearlet, and so on. It is well known that the Rician noise belongs to a high-frequency channel, so it can be easily removed without blurring the clarity of the contour. Compared with other algorithms, such as the shearlet transform, block matching 3D, bilateral filtering, and Wiener filtering, the values of Peak Signal to Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) obtained by the proposed method are better than those of other methods.

/pdf/bendlet-transform-based-adaptive-denoising-method-for-2jzecye3.pdf

Bendlet Transform Based Adaptive Denoising Method for Microsection Images

An iterative model of the generalized Cauchy process for predicting the remaining useful life of lithium-ion batteries

The discrete harmonic wavelet transform has been reviewed and applied towards given functions. The absolute error of reconstruction of the functions has been computed.

/pdf/on-the-discrete-harmonic-wavelet-transform-hbw6lxxdka.pdf

Aleksey Kudreyko

Papers

Mutiscale Analysis of the Fisher Equation

Discrete breathers in a triangular β-Fermi-Pasta-Ulam-Tsingou lattice.

Bendlet Transform Based Adaptive Denoising Method for Microsection Images

An iterative model of the generalized Cauchy process for predicting the remaining useful life of lithium-ion batteries

On the Discrete Harmonic Wavelet Transform