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This paper studies the use of a generalized hierarchical basis transformation at each level of a multilevel block factorization. The factorization may be used as a preconditioner to the conjugate gradient method, or the structure it sets up may be used to define a multigrid method. The basis transformation is performed with an averaged piecewise constant interpolant and is applicable to unstructured elliptic problems. The results show greatly improved convergence rate when the transformation is applied for solving sample diffusion and elasticity problems. The cost of the method, however, grows and can get very high with the number of non-zeros per row. Published in 2002 by John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Reports the fabrication of a waveguide-coupled photonic crystal slab (essentially a free-standing two-dimensional phototonic crystal) with a strong two-dimensional bandgap at wavelengths of about 1.5 mu meters, yet which is capable of fully controlling light in all three dimensions. Confirmation of theoretical calculations on the possibility of achieving three-dimensional light control using two-dimensional bandgaps; How it raises the prospect of being able to realize other photonic crystal and optoelectronic devices.

A simple and efficient method for generating light emitting three-dimensional (3D) nanoscale pattern in silicon is presented. The method is based on differential chemical etching on and in-between patterned metal features. Effective transfer of various two-dimensional nanoscale (10–100 nm) metal patterns on bulk silicon to 3D porous silicon network is demonstrated. The capability and limitations of this method are discussed. [ABSTRACT FROM AUTHOR]

The formation of large-scale arrays of individually seeded, electrically addressable Si nanowires with controlled dimension, placement, and orientation is demonstrated. Electron beam evaporated gold nanoparticles were used for nanowire synthesis. By controlling the lithography and metal deposition conditions, nanowire arrays with narrow size distributions have been achieved. Low-energy postgrowth ion beam treatment has been utilized to control the orientation of Si nanowires. This process also leads to the attachment of nanowires on the substrate. Fabrication of planar devices with robust metal contact formation becomes feasible. The method enables efficient and economical integration of nanowires into device architectures for various applications. [ABSTRACT FROM AUTHOR]

We present a Graphics Processing Unit (GPU)-accelerated version of the real-space SPARC electronic structure code for performing Kohn–Sham density functional theory calculations within the local density and generalized gradient approximations. In particular, we develop a modular math-kernel based implementation for NVIDIA architectures wherein the computationally expensive operations are carried out on the GPUs, with the remainder of the workload retained on the central processing units (CPUs). Using representative bulk and slab examples, we show that relative to CPU-only execution, GPUs enable speedups of up to 6× and 60× in node and core hours, respectively, bringing time to solution down to less than 30 s for a metallic system with over 14 000 electrons and enabling significant reductions in computational resources required for a given wall time. [ABSTRACT FROM AUTHOR]

The spectrum of a kernel matrix significantly depends on the parameter values of the kernel function used to define the kernel matrix. This makes it challenging to design a preconditioner for a regularized kernel matrix that is robust across different parameter values. This paper proposes the adaptive factorized Nyström (AFN) preconditioner. The preconditioner is designed for the case where the rank k of the Nyström approximation is large, i.e., for kernel function parameters that lead to kernel matrices with eigenvalues that decay slowly. AFN deliberately chooses a well-conditioned submatrix to solve with and corrects a Nyström approximation with a factorized sparse approximate matrix inverse. This makes AFN efficient for kernel matrices with large numerical ranks. AFN also adaptively chooses the size of this submatrix to balance accuracy and cost. [ABSTRACT FROM AUTHOR]

GaN and related semiconductors have become an increasingly prominent material for a wide range of active and passive devices from optoelectronics to high frequency and power electronics as well as photocatalysis. Regardless of the application, anisotropic etching is required for micro and nano structuring, currently performed by reactive ion etching (RIE). Alternately, metal-assisted chemical etching (MacEtch) is an open-circuit plasma-free anisotropic etching method that has demonstrated high aspect ratio device structures devoid of plasma-induced damage found in RIE. This paper presents an in-depth study of the ensemble electrochemical mechanisms that govern the photo-enhanced MacEtch process of GaN and related heterojunctions. Through in-depth experimental investigations, modeling and simulations, the effects of local cathode and anode design, energy-band alignments, and solution chemistry on MacEtch are correlated with the underlying electronic mechanisms of carrier generation, annihilation, transport, and extraction, establishing a fundamental framework for parametrized prediction of system behavior. These findings carry profound implications for tailored design of photoelectrochemical processes employed not just for uniformly etching wide/ultrawide bandgap materials but more broadly for semiconductor-based photocatalytic reactions in general. One-pot photo-enhanced MacEtching of AlInGaN multi-heterojunction device structures including superlattices and multi-quantum wells are demonstrated. [ABSTRACT FROM AUTHOR]

In an iterative approach for solving linear systems with dense, ill-conditioned, symmetric positive definite (SPD) kernel matrices, both fast matrix-vector products and fast preconditioning operations are required. Fast (linear-scaling) matrix-vector products are available by expressing the kernel matrix in an H² representation or an equivalent fast multipole method representation.This paper is concerned with preconditioning such matrices using the hierarchically semi separable(HSS) matrix representation. Previously, an algorithm was presented to construct an HSS approx-imation to an SPD kernel matrix that is guaranteed to be SPD. However, this algorithm has qua-dratic cost and was only designed for recursive binary partitionings of the points defining the kernelmatrix. This paper presents a general algorithm for constructing an SPD HSS approximation. Importantly, the algorithm uses the scr H² representation of the SPD matrix to reduce its computational complexity from quadratic to quasi linear. Numerical experiments illustrate how this SPD HSS approximation performs as a pre conditioner for solving linear systems arising from a range of kernel functions. [ABSTRACT FROM AUTHOR]

Dense kernel matrices represented in H2 matrix format typically require less storage and have faster matrix-vector multiplications than when these matrices are represented in the standard dense format. In this article, we present H2Pack, a high-performance, shared-memory library for constructing and operating with H2 matrix representations for kernel matrices defined by non-oscillatory, translationally invariant kernel functions. Using a hybrid analytic-algebraic compression method called the proxy point method, H2Pack can efficiently construct an H2 matrix representation with linear computational complexity. Storage and matrix-vector multiplication also have linear complexity. H2Pack also introduces the concept of "partially admissible blocks" for H2 matrices to make H2 matrix-vector multiplication mathematically identical to the fast multipole method (FMM) if analytic expansions are used. We optimize H2Pack from both the algorithm and software perspectives. Compared to existing FMM libraries, H2Pack generally has much faster H2 matrix-vector multiplications, since the proxy point method is more effective at producing block low-rank approximations than the analytic methods used in FMM. As a tradeoff, H2 matrix construction in H2Pack is typically more expensive than the setup cost in FMM libraries. Thus, H2Pack is ideal for applications that need a large number of matrix-vector multiplications for a given configuration of data points. [ABSTRACT FROM AUTHOR]

Parallel implementations of linear iterative solvers generally alternate between phases of data exchange and phases of local computation. Increasingly large problem sizes and more het- erogeneous compute architectures make load balancing and the design of low latency network inter- connects that are able to satisfy the communication requirements of linear solvers very challenging tasks. In particular, global communication patterns such as inner products become increasingly limiting at scale. We explore the use of asynchronous communication based on one-sided Message Passing Interface primitives in the context of domain decomposition solvers. In particular, a scalable asynchronous two-level Schwarz method is presented. We discuss practical issues encountered in the development of a scalable solver and show experimental results obtained on a state-of-the-art supercomputer system that illustrate the benefits of asynchronous solvers in load balanced as well as load imbalanced scenarios. Using the novel method, we can observe speedups of up to four times over its classical synchronous equivalent. [ABSTRACT FROM AUTHOR]

With increased reliance on cyber infrastructure, large scale power networks face new challenges owing to computational scalability. In this paper, we focus on developing an asynchronous decentralized solution framework for the unit commitment problem for large scale power networks. We exploit the inherent asynchrony in a region based decomposition arising out of imbalance in regional subproblems to boost computational efficiency. A two-phase algorithm is proposed that relies on the convex relaxation and privacy preserving valid inequalities in order to deliver algorithmic improvements. Our algorithm employs a novel interleaved binary mechanism that locally switches from the convex subproblem to its binary counterpart based on consistent local convergent behavior. We develop a high-performance computing oriented software framework that uses message passing interface to drive our benchmark studies. Our simulations performed on the IEEE 3012 bus case are benchmarked against the centralized and a state-of-the-art synchronous decentralized method. The results demonstrate that the asynchronous method improves computational efficiency by a significant amount and provides a competitive solution quality rivaling the benchmark methods. [ABSTRACT FROM AUTHOR]

The rapid growth of point-of-care tests demands for biosensors with high sensitivity and small size. This paper demonstrates an optofluidic metasurface that combines silicon-on-insulator (SOI) nanophotonics and nanofluidics to realize a high-performance, lateral flow-through biosensor. The metasurface is made of a periodic array of silicon nanoposts on an SOI substrate, and functionalized with specific receptor molecules. Bonding of a polydimethylsiloxane slab directly onto the surface results in an ultracompact biosensor, where analyte solutions are restricted to flow only in the space between the nanoposts. No flow exists above the nanoposts. This sensor design overcomes the issue with diffusion-limited detection of many other biosensors. The lateral flow-through feature, in conjunction with high-Q resonance modes associated with optical bound states of the metasurface, offers an improved sensitivity to subtle molecule-bonding induced changes in refractive index. The device exhibits a resonance mode around 1550 nm wavelength and provides an index sensitivity of 720 nm/RIU. Biosensing is conducted to detect the epidermal growth factor receptor 2 ( ErbB2 ), a protein biomarker for early-stage breast cancer screening, by monitoring resonance wavelength shifts in response to specific analyte-ligand binding events at the metasurface. The limit of detection of the device is 0.7 ng mL −1 for ErbB2 . [ABSTRACT FROM AUTHOR]

• Hierarchical matrix representations are extended for infinite periodic summations. • The proxy surface method is effective for the RPY tensor with polydisperse particle radii. • Software for RPY summations is available for large-scale Brownian simulations. For simulations of large numbers of small, spherical particles in a Stokes flow, the long-range hydrodynamic interactions approximated by the Rotne–Prager–Yamakawa (RPY) kernel can be summed rapidly using, for example, the fast multipole method (FMM) or the particle-mesh Ewald (PME) method. In this paper, we develop new fast methods for computing these sums using the H 2 hierarchical matrix representation, for open and for periodic boundary conditions. To the best of our knowledge, the method for infinite periodic sums using the H 2 hierarchical matrix representation is the first such method developed. We also consider a more general RPY kernel that handles polydisperse particle radii, and show analytically and experimentally that the proxy surface method for efficiently constructing the H 2 hierarchical matrix representation remains effective in this case. Numerical tests demonstrate the well-controlled accuracy of the H 2 summation methods and their linear-scaling computation and storage cost. We find that the H 2 matrix approach has lower cost for computing the summations compared to FMM and PME, but higher precomputation cost (required for each particle configuration). This precomputation cost can be amortized over several summations when computing Brownian displacements or forces in Brownian and Stokesian dynamics simulations with very large numbers of particles. [ABSTRACT FROM AUTHOR]

Abstract: We report on time-resolved label-free monitoring of protein binding in a physiological buffer using a photonic crystal microcavity sensor of total area 50μm2 with an effective detection area of 0.272μm2. We use this ultracompact sensor to monitor the binding of anti-biotin to biotinylated-bovine serum albumin (b-BSA), and measure an affinity constant of 6.94×107 M−1. We show that this photonic crystal sensor can be used for anti-biotin detection at concentrations ranging from picomolar to micromolar. The lower limit of detection for anti-biotin is less than 20pM, corresponding to less than 4.5fg of bound material on the sensor surface and fewer than 80 molecules in the modal volume of the microcavity. The sensor also has the capability of measuring binding of small molecular species such as aromatic rings (98Da). Furthermore, we show that the active surface of the sensor can be successfully regenerated and re-used in subsequent protein binding experiments. A comparison of experimental and theoretical data is given, and the current experimental limitations of the sensor with regard to noise are discussed. [Copyright &y& Elsevier]

Na+/H+ antiporters are central to cellular salt and pH homeostasis. The structure of Escherichia coli NhaA was recently determined, but its mechanisms of transport and pH regulation remain elusive. We performed molecular dynamics simulations of NhaA that, with existing experimental data, enabled us to propose an atomically detailed model of antiporter function. Three conserved aspartates are key to our proposed mechanism: Asp164 (D164) is the Na+-binding site, D163 controls the alternating accessibility of this binding site to the cytoplasm or periplasm, and D133 is crucial for pH regulation. Consistent with experimental stoichiometry, two protons are required to transport a single Na+ ion: D163 protonates to reveal the Na+-binding site to the periplasm, and subsequent protonation of D164 releases Na+. Additional mutagenesis experiments further validated the model. [ABSTRACT FROM AUTHOR]

Colloidal quantum dots display a wide range of novel optical properties that could prove useful for many applications in photonics. Here, we report the enhancement of fluorescence emission from colloidal quantum dots on the surface of two-dimensional photonic crystal slabs. The enhancement is due to a combination of high-intensity near fields and strong coherent scattering effects, which we attribute to leaky eigenmodes of the photonic crystal. By fabricating two-dimensional photonic crystal slabs that operate at visible wavelengths and engineering their leaky modes so that they overlap with the absorption and emission wavelengths of the quantum dots, we demonstrate that the fluorescence intensity can be enhanced by a factor of up to 108 compared with quantum dots on an unpatterned surface. [ABSTRACT FROM AUTHOR]

Highly linear electro-optic modulators are key components in analog microwave photonic links, offering on-chip direct mixing of optical and RF fields. In this work, we demonstrate a monolithic integrated Michelson interferometer modulator on thin-film lithium niobate (LN), that achieves linearized performance by modulating Bragg grating reflectors placed at the end of Michelson arms. The modulator utilizes spiral-shaped waveguide Bragg gratings on Z-cut LN with top and bottom electrodes to realize extensive reflectors, essential for linearized performance, in a highly integrated form. Optical waveguides are realized using rib etching of LN with precisely engineered bottom and top cladding layers made of silicon dioxide and SU-8 polymer, respectively. The compact design fits a 3 mm long grating in an 80 µm × 80 µm area, achieving a broad operating bandwidth up to 18 GHz. A spurious free dynamic range (SFDR) of 101.2 dB·Hz 2/3 is demonstrated at 1 GHz, compared to 91.5 dB·Hz 2/3 for a reference Mach-Zehnder modulator fabricated on the same chip. Further enhancement in SFDR could be achieved by reducing fiber-to-chip coupling loss. The proposed demonstration could significantly improve the linearity of analog modulator-based integrated optical links.

In density functional theory, each self-consistent field (SCF) nonlinear step updates the discretized Kohn-Sham orbitals by solving a linear eigenvalue problem. The concept of pseudodiagonalization is to solve this linear eigenvalue problem approximately and specifically utilizing a method involving a small number of Jacobi rotations that takes advantage of the good initial guess to the solution given by the approximation to the orbitals from the previous SCF iteration. The approximate solution to the linear eigenvalue problem can be very rapid, particularly for those steps near SCF convergence. We adapt pseudodiagonalization to finite-temperature and metallic systems, where partially occupied orbitals must be individually resolved with some accuracy. We apply pseudodiagonalization to the subspace eigenvalue problem that arises in Chebyshev-filtered subspace iteration. In tests on metallic and other systems for a range of temperatures, we show that pseudodiagonalization achieves similar rates of SCF convergence to exact diagonalization.

In this paper, we designed, implemented, and characterized compact Mach-Zehnder interferometer-based electro-optic modulators. The modulator utilizes spiral-shaped optical waveguides on Z-cut lithium niobate and the preeminent electro-optic effect which is applied using top and bottom electrodes. Optical waveguides are made of rib etched lithium niobate waveguides with bottom silicon oxide cladding, while SU8 polymer covers the top and sides of the rib waveguides. The proposed implementation resulted in low optical losses < 1.3 dB/cm. Moreover, we achieved compact modulators that fit 0.286 cm and 2 cm long optical waveguides in 110 µm × 110 µm and 300 µm × 300 µm areas, respectively. For single arm modulation, the modulators achieved a VπL of 7.4 V.cm and 6.4 V.cm and 3-dB bandwidths of 9.3 GHz and 2.05 GHz, respectively. Push-pull modulation is expected to cut these VπL in half. The proposed configuration avoids traveling wave modulation complexities and represents a key development towards miniature and highly integrated photonic circuits.

Efficient representations of the electron repulsion integral (ERI) tensor and fast algorithms for contractions with the ERI tensor often employ a low-rank approximation of the tensor or its sub-blocks. Such representations include density fitting (DF), the continuous fast multipole method (CFMM), and, more recently, hierarchical matrices. We apply the H 2 hierarchical matrix representation to the ERI tensor with Gaussian basis sets to rapidly calculate the Coulomb matrices in Hartree-Fock and density functional theory calculations. The execution time and storage requirements of the hierarchical matrix approach and the DF approach are compared. The hierarchical matrix approach has very modest storage requirements, allowing large calculations to be performed in memory without recomputing ERIs. We interpret the hierarchical matrix approach as a multilevel, localized DF method and also discuss the close relationship between the hierarchical matrix approaches with CFMM. Like CFMM, the hierarchical matrix approach is asymptotically linear scaling, but the latter requires severalfold less memory (or severalfold less computation, if quantities are computed dynamically) due to being able to efficiently employ low-rank approximations for far more blocks.

This paper presents techniques for Fock matrix construction that are designed for high performance on shared and distributed memory parallel computers when using Gaussian basis sets. Four main techniques are considered. (1) To calculate electron repulsion integrals, we demonstrate batching together the calculation of multiple shell quartets of the same angular momentum class so that the calculation of large sets of primitive integrals can be efficiently vectorized. (2) For multithreaded summation of entries into the Fock matrix, we investigate using a combination of atomic operations and thread-local copies of the Fock matrix. (3) For distributed memory parallel computers, we present a globally accessible matrix class for accessing distributed Fock and density matrices. The new matrix class introduces a batched mode for remote memory access that can reduce the synchronization cost. (4) For density fitting, we exploit both symmetry (of the Coulomb and exchange matrices) and sparsity (of 3-index tensors) and give a performance comparison of density fitting and the conventional direct calculation approach. The techniques are implemented in an open-source software library called GTFock.

The motions of particles in a viscous fluid confined within a spherical cell have been simulated using Brownian and Stokesian dynamics simulations. High volume fractions mimicking the crowded interior of biological cells were used. Importantly, although confinement yields an overall slowdown in motion, the qualitative effects of motion in the interior of the cell can be effectively modeled as if the system were an infinite periodic system. However, we observe layering of particles at the cell wall due to steric interactions in the confined space. Motions of nearby particles are also strongly correlated at the cell wall, and these correlations increase when hydrodynamic interactions are modeled. Further, particles near the cell wall have a tendency to remain near the cell wall. A consequence of these effects is that the mean contact time between particles is longer at the cell wall than in the interior of the cell. These findings identify a specific way that confinement affects the interactions between particles and points to a previously unidentified mechanism that may play a role in signal transduction and other processes near the membrane of biological cells.

Quantum chemistry is increasingly performed using large cluster computers consisting of multiple interconnected nodes. For a fixed molecular problem, the efficiency of a calculation usually decreases as more nodes are used, due to the cost of communication between the nodes. This paper empirically investigates the parallel scalability of Hartree-Fock calculations. The construction of the Fock matrix and the density matrix calculation are analyzed separately. For the former, we use a parallelization of Fock matrix construction based on a static partitioning of work followed by a work stealing phase. For the latter, we use density matrix purification from the linear scaling methods literature, but without using sparsity. When using large numbers of nodes for moderately sized problems, density matrix computations are network-bandwidth bound, making purification methods potentially faster than eigendecomposition methods.

Over the last decade, field-effect transistors (FETs) with nanoscale dimensions have emerged as possible label-free biological and chemical sensors capable of highly sensitive detection of various entities and processes. While significant progress has been made towards improving their sensitivity, much is yet to be explored in the study of various critical parameters, such as the choice of a sensing dielectric, the choice of applied front and back gate biases, the design of the device dimensions, and many others. In this work, we present a process to fabricate nanowire and nanoplate FETs with Al(2)O(3) gate dielectrics and we compare these devices with FETs with SiO(2) gate dielectrics. The use of a high-k dielectric such as Al(2)O(3) allows for the physical thickness of the gate dielectric to be thicker without losing sensitivity to charge, which then reduces leakage currents and results in devices that are highly robust in fluid. This optimized process results in devices stable for up to 8 h in fluidic environments. Using pH sensing as a benchmark, we show the importance of optimizing the device bias, particularly the back gate bias which modulates the effective channel thickness. We also demonstrate that devices with Al(2)O(3) gate dielectrics exhibit superior sensitivity to pH when compared to devices with SiO(2) gate dielectrics. Finally, we show that when the effective electrical silicon channel thickness is on the order of the Debye length, device response to pH is virtually independent of device width. These silicon FET sensors could become integral components of future silicon based Lab on Chip systems.

Na+/H+ antiporters are central to cellular salt and pH homeostasis. The structure of Escherichia coli NhaA was recently determined, but its mechanisms of transport and pH regulation remain elusive. We performed molecular dynamics simulations of NhaA that, with existing experimental data, enabled us to propose an atomically detailed model of antiporter function. Three conserved aspartates are key to our proposed mechanism: Asp164 (D164) is the Na+-binding site, D163 controls the alternating accessibility of this binding site to the cytoplasm or periplasm, and D133 is crucial for pH regulation. Consistent with experimental stoichiometry, two protons are required to transport a single Na+ ion: D163 protonates to reveal the Na+-binding site to the periplasm, and subsequent protonation of D164 releases Na+. Additional mutagenesis experiments further validated the model.