Time-stepping methods for the simulation of the self-assembly of nano-crystals in MATLAB on a GPU

Partial differential equations describing the patterning of thin crystalline films are typically of fourth or sixth order, they are quasi- or semilinear and they are mostly defined on simple geometries such as rectangular domains. For the numerical simulation of these kind of problems spectral methods are an efficient approach. We apply several implicit-explicit schemes to one recently derived PDE that we express in terms of coefficients of trigonometric interpolants. While the simplest IMEX scheme turns out to have the mildest step-size restriction, higher order SBDF schemes tend to be more unstable and exponential time integrators are fastest for the calculation of very accurate solutions. We implemented a reduced model in the EXPINT package syntax and compared various exponential schemes. A convexity splitting approach was employed to stabilize the SBDF1 scheme. We show that accuracy control is crucial when using this idea, therefore we present a time-adaptive SBDF1/SBDF1-2-step method that yields convincing results reflecting the change in timescales during topological changes of the nanostructures. The implementation of all presented methods is carried out in MATLAB. We used the open source GPUmat package to gain up to 5-fold runtime benefits by carrying out calculations on a low-cost GPU without having to prescribe any knowledge in low-level programming or CUDA implementations and found comparable speedups as with MATLAB's PCT or with GPUmat run on Octave

Engineering Dynamic Behavior into Nucleic Acids Guided by Single Molecule Fluorescence Microscopy

Single-molecule fluorescence microscopy is a powerful technique that has been used for investigating the structural dynamics of biomolecules, and is particularly useful when ensemble averaging might obscure detailed information of the system under investigation. One application of single molecule measurement is to optimize the design of DNA nano-devices. Dynamic DNA nanotechnology has yielded nontrivial autonomous behaviours such as stimulus-guided locomotion, computation, and programmable molecular assembly. Despite these successes, DNA-based nanomachines suffer from slow kinetics, requiring several minutes or more to carry out a handful of operations. In this thesis, I have pursued the speed limit of an important class of reactions in DNA nanotechnology—toehold exchange—through the single-molecule optimization of a novel class of DNA walker that undergoes cartwheeling movements over a field of complementary oligonucleotides. I identified the walking mechanism by single-molecule fluorescence resonance energy transfer (smFRET) measurement, with the stepping rate constant approaching 1 s-1, which is 10- to 100-fold faster than prior DNA walkers. I also used single-particle tracking to demonstrate movement of the walker over hundreds of nanometers within 10 min, in quantitative agreement with predictions from the stepping kinetics. These results suggest that substantial improvements in the operating rates of broad classes of DNA nanomachines utilizing strand displacement are possible. Another application of single molecule measurements is kinetic fingerprinting detection. Conventional methods for detecting small quantities of nucleic acids require amplification by the polymerase chain reaction (PCR), which necessitates prior purification and introduces copying errors. While amplification-free methods do not have these shortcomings, they are generally orders of magnitude less sensitive and specific than PCR-based methods. In this thesis, I review important experimental tips and data analysis details to provide a practical guide to a novel amplification-free method, single-molecule recognition through equilibrium Poisson sampling (SiMREPS), that provides both single-molecule sensitivity and single-base selectivity by monitoring the repetitive interactions of fluorescent probes with immobilized targets. In addition to demonstrating how this kinetic fingerprinting filters out background arising from the inevitable nonspecific binding of probes, yielding virtually zero background signal, I also investigated the detection of epigenetic mutations such as CpG methylation using SiMREPS. The analysis of single-molecule microscopy data can be very time-consuming because there is no sufficiently robust automatic method for selection of qualified single-molecule fluorescence trajectories from the generally noisy and heterogeneous raw data, necessitating manual trace selection that can take hundreds of hours for large datasets. In this thesis, I discuss the innovative use of the popular convolutional neural network AlexNet and the recurrent neural network Long Short-Term Memory (LSTM) to develop an automatic selector for single-molecule fluorescence resonance energy transfer (smFRET) traces. The average prediction accuracy is above 90% when tested on datasets from different users and experimental systems. To boost the selection accuracy and increase the diversity of training datasets, simulation data were included into the training data set and tested for selection accuracy. I expect that this new method will not only greatly expedite analysis of smFRET data and increase analysis reliability of SiMREPS data, but also introduce and validate machine learning as an effective tool for analysis of single-molecule microscopy data more generally. Together, these results provide new insights into how single molecule microscopy can be used to engineer dynamic behaviors of nucleic acids.PHDChemistryUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/149970/1/jmli_1.pd

X-ray Bragg Projection Ptychography for nano-materials

Progress in nanotechnology critically relies on high resolution probing tools, and X-ray coherent diffraction imaging (CDI) is certainly an attractive method for exploring science at such small scales. Thus, the aim of this PhD is to study structural properties of nano-materials using X-ray CDI, with a special motivation to combine Bragg CDI with ptychography. The former has ability to retrieve the complex density and strain maps of nano-meso crystalline objects, and the latter uses translational diversity to produce quantitative maps of the complex transmission function of non-crystalline objects. As both techniques promote highly sensitive phase-contrast properties, the thesis exploits their agreement to reveal the morphology of domain structures in metallic thin films. Additionally, it is demonstrated that Bragg-ptychography is an evolutionary improvement to probe the structure of ’highly’ strained crystals, with respect to its Bragg-CDI counterpart. However, the adaptation of ptychography to the Bragg geometry is not without difficulties and comes with more experimental cost. Therefore, the effects of experimental uncertainties, e.g., scan positions undetermination, partial coherence, and time-varying probes are assessed throughout the thesis and corrected for by implementation of suitable refinement methods. Furthermore, it is shown how the set-up at beamline 34-ID-C at the Advanced Photon Source, used for the experimental measurements can be optimized for better ptychographical reconstructions

Artificial Intelligence in Materials Science: Applications of Machine Learning to Extraction of Physically Meaningful Information from Atomic Resolution Microscopy Imaging

Materials science is the cornerstone for technological development of the modern world that has been largely shaped by the advances in fabrication of semiconductor materials and devices. However, the Moore’s Law is expected to stop by 2025 due to reaching the limits of traditional transistor scaling. However, the classical approach has shown to be unable to keep up with the needs of materials manufacturing, requiring more than 20 years to move a material from discovery to market. To adapt materials fabrication to the needs of the 21st century, it is necessary to develop methods for much faster processing of experimental data and connecting the results to theory, with feedback flow in both directions. However, state-of-the-art analysis remains selective and manual, prone to human error and unable to handle large quantities of data generated by modern equipment. Recent advances in scanning transmission electron and scanning tunneling microscopies have allowed imaging and manipulation of materials on the atomic level, and these capabilities require development of automated, robust, reproducible methods.Artificial intelligence and machine learning have dealt with similar issues in applications to image and speech recognition, autonomous vehicles, and other projects that are beginning to change the world around us. However, materials science faces significant challenges preventing direct application of the such models without taking physical constraints and domain expertise into account.Atomic resolution imaging can generate data that can lead to better understanding of materials and their properties through using artificial intelligence methods. Machine learning, in particular combinations of deep learning and probabilistic modeling, can learn to recognize physical features in imaging, making this process automated and speeding up characterization. By incorporating the knowledge from theory and simulations with such frameworks, it is possible to create the foundation for the automated atomic scale manufacturing

Modeling dewetting, demixing, and thermal effects in nanoscale metal films

Thin film dynamics, particularly on the nanoscale, is a topic of extensive interest. The process by which thin liquids evolve is far from trivial and can lead to dewetting and drop formation. Understanding this process involves not only resolving the fluid mechanical aspects of the problem, but also requires the coupling of other physical processes, including liquid-solid interactions, thermal transport, and dependence of material parameters on temperature and material composition. The focus of this dissertation is on the mathematical modeling and simulation of nanoscale liquid metal films, which are deposited on thermally conductive substrates, liquefied by laser heating, and subsequently dewet into nanoparticles, before cooling and resolidifying. Both single- and multi-metal configurations are considered. In the former case, continuum theory is used to describe the thermohydrodynamics. Separation of length scales (in-plane length scales are larger than those in the out-of-plane direction) allows for formulation of asymptotic theory that reduces the fluid dynamics problem, involving Navier-Stokes equations in evolving domains, to a fourth order nonlinear partial differential equation for the fluid thickness. Similarly, a leading order thermal model is developed that is novel, computationally efficient, and accurate. The resulting coupled fluid dynamics and thermal transport model is then used to simulate metal film evolution in both two and three dimensional domains, and to investigate the role of various material parameters. Thermal effects are found to play an important role; in particular it is found that the inclusion of temperature dependence in the metal viscosity modifies the time scale of the evolution significantly. On the other hand, in the considered setup the Marangoni (thermocapillary) effect turns out to be insignificant. The rate of heat lost in the substrate, measured by a Biot number (Bi) is found to influence peak metal film temperatures and liquid lifetimes (time from film melting to resolidification) more strongly than substrate thickness (H s ). Nevertheless, changes in both Bi and H s can lead to films that freeze in place prior to full dewetting due to the strong dependence of viscosity on temperature. n the case of multi-metal configurations, molecular dynamics simulations are used to investigate the competition between chemical instabilities and Rayleigh-Plateau type dewetting behavior in NiAg alloys of various geometries. Phase separation occurs for decreasing temperatures and results in Ag@Ni core-shell particles. During the breakup, phase separation and the Rayleigh-Plateau instability either compete or cooperate depending on the relative positioning of Ag and Ni. When the phase separation length scale is sufficiently large, axial migration of Ag onto Ni can result in both Ag@Ni core-shell and pure Ag nanoparticles. Chemical instabilities, therefore, can strongly affect the dewetting mechanism

Optical coupler design and experimental demonstration for 2.5D/3D heterogeneous integrated electronics

The objective of the dissertation is to theoretically design and experimentally demonstrate optical couplers for 2.5D/3D heterogeneous integrated electronics. In the first part, a new concept, "Equivalent Index Slab (EIS)" method, is proposed to extend the application of Rigorous Coupled-Wave Analysis (RCWA) to rectangular waveguide grating diffraction involving surface waves. RCWA-EIS method can be applied to optimize rectangular grating couplers with arbitrary profiles and to analyze the effects of angular misalignments on the coupling efficiency. In the second part, a fundamentally new coupling structure, Grating-Assisted-cylindrical-Resonant-Cavities (GARC) coupler, is introduced to achieve efficient and broadband interlayer coupling. GARC coupler is based on evanescent field coupling between waveguides and the interconnecting via, and the via serves as a cylindrical resonant cavity which is further assisted by the circular gratings to enhance the field. In the third part, a passive fiber alignment and assembly approach, Fiber-Interconnect Silicon Chiplet Technology (FISCT), is demonstrated using a combination of silicon micromachining and 3D printing to achieve efficient and convenient near-vertical fiber-to-chip coupling.Ph.D

In situ Laser Synthesis, Processing and Characterization in the TEM

Rapid materials synthesis, processing and characterization enables a wide variety of materials systems with tuned properties. The objective of this dissertation is to demonstrate how a prototype setup allows laser illumination to be coupled into a (scanning) transmission electron microscope (TEM) for real-time observations of synthesis, processing, and characterization. The laser synthesis of two-dimensional (2D) crystals and van der Waals (vdW) heterostructures is investigated through stepwise laser crystallization within a TEM. Amorphous tungsten selenide that was deposited by pulsed laser deposition (PLD) evolves through a series of metastable nanophases as crystallizing and coalescing into continuous 2D WSe2 domains on monolayer graphene or MoSe2 substrates. The lattice-matched MoSe2 substrate is shown to play a guiding role in the formation of heteroepitaxial vdW WSe2/MoSe2 bilayers both during the crystallization process and afterwards, when crystalline nanosized domains are observed to coalesce by rotation, and grain boundary migration processes. In addition, the controllable implantation of hyperthermal species from PLD plasmas is introduced as a top-down method to compositionally engineer 2D monolayers and form Janus monolayers using in situ diagnostics. The chalcogen atoms on both sides of transition metal dichalcogenide (TMD) were resolved by grid tilting and the Janus structure of TMD was confirmed in atomic resolution for the first time. These in situ studies of pulsed laser-driven crystallization and implantation represent a transformational tool for the rapid exploration of synthesis pathways and lend insight to the growth of 2D crystals by PLD and laser processing methods. Laser characterization within the TEM is demonstrated via experimentally accessing photon-stimulated electron energy-loss (sEEL) and electron energy-gain (EEG) responses of individual plasmonic nanoparticles via photon-plasmon-electron interactions induced by simultaneous irradiation of a continuous wave laser and continuous current electron probe. EEG and sEEL probabilities are equivalent and increase linearly in the low irradiance range; importantly the photon energy must be tuned in resonance with the plasmon energy for the sEEG and sEEL peaks to emerge. This study opens a fundamentally new approach to explore the quantum physics of excited-state plasmon resonances that does not rely on high intensity laser pulses or any modification to the EELS detector

Analysis and simulation for an isotropic phase-field model describing grain growth

A phase-field system of coupled Allen-Cahn type PDEs describing grain growth is analyzed and simulated. In the periodic setting, we prove the existence and uniqueness of global weak solutions to the problem. Then we investigate the long-time behavior of the solutions within the theory of infinite-dimensional dissipative dynamical systems. Namely, the problem possesses a global attractor as well as an exponential attractor, which entails that the global attractor has finite fractal dimension. Moreover, we show that each trajectory converges to a single equilibrium. A time-adaptive numerical scheme based on trigonometric interpolation is presented. It allows to track the approximated long-time behavior accurately and leads to a convergence rate. The scheme exhibits a physically aspired discrete free energy dissipation