X-ray optics has been serving the exploration of nature in synchrotron radiation for many decades. In recent years, X-ray free-electron lasers (XFELs) open a new era of X-ray based research by generating extremely intense X-ray flashes. The outstanding properties including extremely high brightness enable unprecedent discoveries in many research fields, such as structural biology, photochemistry, atomic, molecular and cluster physics. To assist research, the X-ray optics used in synchrotron radiation are either directly employed or modified for their utilizations in XFEL. One emerging challenge for the implementation of X-ray optics in XFEL is that the extremely bright photon beam introduces highly localized and strong thermal load on the X-ray optics, especially at high repetition rates. The thermal load induces severe non-uniform thermal deformation of the optics, degrading their ability to preserve the superior XFEL beam quality, such as high brightness and outstanding coherence.

To understand the thermal load effects and provide design principles to minimize these effects, in this study, we carry out coupled photo-thermal-mechanical analyses. We first provide necessary background and review of current studies on thermal load in X-ray optics. Next, we derive an analytical model to yield qualitative understanding on thermal load. According to the analytical model, the thermal load effects can be decomposed into two parts: the tunable part (due to the overall strain increase) and untunable part (due to the strain and surface slope inhomogeneity). We then further investigate and quantitatively evaluate the performance degradation of the optics due to thermal load in practical operating modes: pump-probe mode, pulse train mode and quasi-steady state. In pump-probe mode, the tunable part is invisible due to the limited amount of energy deposited, while the untunable part results in significant performance reduction for short delay time between the two pulses. For beamline monochromator, additional effects such as laser footprint distortion and tranverse coherence degradation are also harmful for photon science experiments. In pulse train mode where more than two pulses are incident, thermal load accumulates pulse by pulse. Both tunable and untunable parts are observable. The optics performance degrades dynamically due to continuing thermal load accumulation. Accordingly, the tuning needs to follow this dynamic behavior to recover the central photon energy shift and align the spectrum if multiple monochromators are cooperating in the system. At quasi-steady state, the performance is constantly affected and necessary design is needed to refrain the thermal load. Three designs of monochromators are proposed and analyzed for different repetition rate at different cooling temperatures. Critical repetition rate is accordingly determined. One desirable way to improve the thermal load tolerance of the X-ray optics is to operate them at cryogenic temperature, as confirmed by simulation. However, at cryogenic temperature, the emerging unconventional nondiffusive heat transfer phenomena may result in the performance deviation from designed status. We introduce and propose simplified nondiffusive models to characterize these new features and prepare for the experimental analysis with cryogenic cooling. Based on this study, the thermal load effects are be better understood. Design insights including geometry design and operation condition are also provided, contributing to the preparation for practical experimental test and maintaining the X-ray optics performance at high-brightness and high-repetition-rates.

With the progress of nanotechnologies for microelectronic and thermoelectric devices, a lack of understanding of the heat transfer in nano-/micro-scale creates the bottleneck for the applications. Although Fourier's law is able to describe the heat transfer in macroscale, it breaks down in nano-/micro-scale due to the nondiffusive heat transfer, which is still not well understood. Consequently, the objective for this thesis is to achieve a fundamental understanding of nondiffusive heat transfer.

Phonon is a quantum mechanical description of lattice oscillations, and it is the main heat carrier in insulators and semiconductors. When the system sizes are comparable or even smaller than the mean free path (MFP) of phonons, the heat transfer becomes nondiffusive due to the contribution from ballistic phonon transport. The phonon-mediated heat transfer in nanosystems and their interfaces is very complicated. In this thesis, we mainly focus on three problems: (1) there lacks a criterion to evaluate when Fourier's law breaks down; (2) the size-dependence of thermal interface resistivity is not clearly captured; (3) the ballistic heat transfer has not been directly observed at room temperature.

Accordingly, there are three goals for this thesis: (1) to find the criterion which is able to identify when Fourier's law breaks down; (2) to characterize how interface resistivity changes with the hotspot size; (3) to seek the possibility of a direct observation of ballistic heat transfer at room temperature.

To achieve the first goal, a criterion is proposed based on the nondimensional parameter defined in the Two-Parameter Heat Conduction (TPHC) model, to predict the breakdown of Fourier's law. The physical interpretation of this nondimensional parameter is a product of the nondimensional diffusive phonon MFP and ballistic phonon MFP. To validate this criterion, both Fourier's law and the TPHC model are analytically or numerically solved for multiple experiments on different materials. These experiments include the one-dimensional and two-dimensional transient thermal grating (1D/2D TTG) experiments on silicon and gallium arsenide, and the metallic grating (MG) experiments on sapphire. The comparison results indicate that this criterion is able to identify the breakdown of Fourier's law.

To achieve the second goal, the TPHC model and the enhanced gray Boltzmann transport equation (EG-BTE) are numerically solved on the MG experiments by finite difference method and lattice Boltzmann method, respectively. Current study of the interface resistivity is based on Fourier's law, which fails to decouple the size-dependence of the thermal conductivity (material thermal property defined by Fourier's law) and the interface resistivity. While the TPHC model and EG-BTE are able to exclude the size-dependence of the thermal conductivity, and thus extract a clean size-dependence of the interface resistivity. Based on these two models, a monotonically change of the interface resistivity with the size of interface is captured, which is different from but more reliable than the results by Fourier's law.

To achieve the third goal, we focus on the thermal wave, the direct evidence of ballistic heat transfer. Although ballistic heat transfer is believed to be the cause of nondiffusive heat transfer, so far only the deviation from prediction by Fourier's law is reported as the evidence of nondiffusive heat transfer at room temperature. To study the thermal wave, the EG-BTE is applied on the thermal wave experiments in cryogenic crystal. In these cases, the EG-BTE is numerically solved by an in-house numerical scheme developed called the discrete ordinates method for phonon transport, which is validated by other theoretical study in this thesis. The results are compared with the experiments and indicate a successful reproduction of the thermal wave. Based on the proved capability of describing the thermal wave, the EG-BTE is extensively applied to identify the length and time scale to observe the thermal wave at room temperature.

In conclusion, the criterion proposed in this thesis facilitates the choice of models between the efficient Fourier's law and the accurate nondiffusive models, benefiting the engineering use in multiscale situations. Secondly, the monotonic behavior of interface resistivity offers new insights of the physics of nondiffusive heat transfer across the interface. At last, the prediction of the thermal wave at room temperature provides potential guidance for the design of experiments to directly observe the thermal wave at room temperature, opening up a new gate to study the unique features of the ballistic heat transfer.

Manipulation of microparticles by droplets is a very useful and important technique for many microfluidics applications. Due to the large specific surface necessary for chemical binding and easy recovery from a dispersion, utilization of nanospheres or microspheres has become more and more popular for different medical, biological, and optical applications. The goal of this research is to understand the mechanism for the manipulation of microparticles by droplets. Dissipative particle dynamics (DPD), which is extensively used to model mesoscale flow phenomena, is applied as the numerical tool for this study. A model for solid microparticles is designed to study the interactions among microparticles, liquid droplets, and solid substrates. A spherical shell is used to represent the microparticle, and the shell surface is packed by dense enough beads to avoid undesired penetration of liquid beads into solid microparticles, conserving the momentum automatically. After that, the interaction between a rigid microparticle and a solid substrate is modeled based on contact mechanics, including adhesion forces, normal forces, and friction forces. After the model for microparticles is built, a baseline case simulating the pickup and transport of a hydrophobic microparticle by a droplet is demonstrated and compared with experimental observations. Then, the flow structures within a droplet containing a hydrophobic microparticle are revealed.

With this developed numerical tool, parametric studies are conducted to investigate the effect on the manipulation processes (including pickup, transport, and drop off) of a microparticle by droplet sizes, wetting properties of microparticles, and particle-substrate friction coefficients. The increase of droplet size can speed up the transport of microparticles. However, the increase of particle-substrate friction coefficients can lead to drop-off of a hydrophobic microparticle. The mechanism for the drop-off, or delivery, is analyzed by checking the development of the friction force and driving force on the microparticle during the transport process. The critical velocity, defined as the instantaneous velocity of the microparticle right before the occurrence of delivery, is measured, and it is found that the critical velocity is about same for different sizes of droplets. Based on the numerical results, two different designs, namely passive delivery and active delivery, have been demonstrated to be capable of controlling the location for the delivery of single hydrophobic microparticle without any trap design or external field forces. These numerical results provide a fundamental understanding of interactions among the microparticle, the droplet and the substrate to facilitate the optimal experimental design of digital microfluidic system utilizing microparticles.

Rapid progress has been made in the manufacture of microelectronic and thermoelectric devices. With continuous decrease in the size of devices and structures, the manipulation and control of phonon-mediated heat transfer on the nano-/micro-scale is becoming a bottleneck for the development of many nano-/micro-technologies. To advance these technologies, it is necessary to understand the fundamental mechanisms of thermal transport at nano-/micro-scale. The new feature of heat transfer in nano-/micro-scale systems is non-diffusive thermal transport which cannot be described by Fourier’s law. However, current nano-thermometry of non-diffusive heat transfer still focuses on studying the effective thermal conductivity within the framework of Fourier’s law due to a lack of a well-accepted non-diffusive model. The molecular dynamics (MD) and full spectral Boltzmann transport equation (BTE) are unpractical to be applied for experimental data analysis due to their prohibited computational cost. For Gray BTE and other macroscopic models such as Cattaneo-Vernotte (CV) equation, Guyer-Krumhansl (GK) equation, Dual-phase-lag (DPL) equation and et al., they cannot capture the non-diffusive heat transport accurately.

In this thesis we will develop a high-fidelity model that can accurately describe phonon transport at nano-/micro-scale regime and can replace Fourier’s law for experimental data analysis. The new model named enhanced gray (EG) model is derived from the phonon Boltzmann transport equation (BTE) by considering the second-order terms in Taylor expansion of phonon density distribution. In the proposed enhanced gray BTE (EG-BTE), two parameters associated with inherent material properties, i.e., the ballistic mean free time and the diffusive relaxation time, are used to characterize the non-diffusive nature of heat conduction. Theoretical solutions of EG-BTE

based on Fourier transform are presented in three-dimensional domain for transient thermal grating (TTG) experiments and time domain thermo-reflectance (TDTR) experiments. The reconstructed thermal decays by EG-BTE are in excellent match with the measured signal traces in TTG and TDTR experiments, which demonstrates the validity of our new model. For problems where analytical solutions are not available, an implicit lattice Boltzmann method (LBM) is developed to solve the EG-BTE, which is unconditionally stable and computationally efficient. As an illustrative application, the phonon transport in cryogenic crystals is studied by implicit LBM simulation based on EG-BTE. The heat-pulse experiment conducted in cryogenic crystals observed the only direct evidence of ballistic heat transport. The successive interpretation of this benchmark case by EG-BTE provides a better understanding of the physical nature of non-diffusive heat transfer.

The proposed EG-BTE opens a new avenue to study the unique features of non-diffusive heat transfer. The current interpretations of TDTR experiments is limited by Fourier’s law. For example, the measurements of effective thermal conductivity within the framework of Fourier’s law will provide little insight for non-diffusive heat transfer. By deriving the analytical solution of EG-BTE for TDTR experiments, a new theoretical framework based on EG-BTE that can remove the limit of Fourier law for experimental data analysis is developed and proved. Some unique material thermal properties of non-diffusive heat conduction can be characterized, such as the ballistic mean free time and the diffusive relaxation time. But further development and improvement of the theoretical tool are required to understand other features of non-diffusive heat transfer, such as the interfacial thermal conductance, which can be our future work.

Continuum methods have been used for numerical simulation of solid and fluid for a long time but they have several constraints. For complex fluids, numerical simulations using continuum assumptions are very challenging especially when the phenomena occurring in the system are smaller than the continuum — limit below which fluid cannot be considered as a continuum. Thermal fluctuation (due to Brownian motion) become significant at micro and nanoscale. As a result, continuum methods are not directly applicable at these scales. On the other hand, when the continuum simulations work for simulations at other scales, they have an additional challenge (especially in structural dynamics simulations). When the dynamics of the solid simulations are extreme and high deformations occur in the system, the continuum methods that are based on the idea of small element/mesh fail. Generating a mesh, that can be adequate to the dynamics is very difficult and still one of the big challenges of the continuum simulations. Even if a high-quality mesh is generated, a severe mesh distortion may occur for certain dynamics. In those cases, it is important to remesh the system. Thus, having a good quality mesh is not enough, the meshing process should also be extremely fast. Furthermore, the frequency of remeshing depends on the quality of the mesh, so there needs to be a balance of quality and efficiency. In fluid simulations, most continuum methods are based on the Eulerian approach of the flow field, i.e. system is studied by dividing into small elements/mesh (typically fixed) and fluid motion is studied through those points. In the Lagrangian specification of the flow field, fluid is assumed to be made of small particles. These particles are then tracked throughout the simulation to study the system behavior. These second methods of simulating fluid/solid fall into a general class called Particle methods. There are several kinds of particle methods such as Brownian Dynamics, Smoothed Particle Hydrodynamics, and Dissipative Particle Dynamics(DPD) that vary from each other on length scale, time scale, and model but have some similarities. Particle methods are very powerful and can be used to solve the challenges that are faced in the continuum method. In this dissertation, two problems that are encountered in simulating fluid and solid are tackled and solutions are proposed. In simulating fluid using particle methods such as DPD, two major problems occur. First, particle density fluctuations near the solid-liquid interface, and second high computational cost due to solid wall. Particle density in DPD is defined as the local density of the particle. Density fluctuations occur due to the low solid wall particle density. One way to tackle it is increasing the solid wall particle density but that results in even higher computational cost. In this dissertation, first modified version of DPD — multibody Dissipative Particle Dynamics(MDPD)— is chosen due to its capability of handling the free liquid surface. In the context of MDPD, a closed-form mathematical framework is developed to model the solid wall and the original particle wall is replaced by this proposed model. The model is derived using a modified conservative force and a combination of analytical and numerical integration. The wall model is simpler and computationally efficient than traditional approaches of modeling the wall. The proposed wall model is also capable of mimicking the high-density computational wall that results into extremely low (less than 1%) density fluctuations. Furthermore, another challenge in MDPD and particle method community, a discrepancy in wall density is also solved by normalizing the wall density with fluid density. Several examples of fluid-solid interaction are used and the superiority of the wall boundary model is demonstrated. Computational time using wall model is only 30% − 50% of the computational time using the traditional particle wall. A dynamic case of solid sphere transport inside a water droplet due to wettability gradient is also demonstrated. In that example, several parametric studies such as the effect of wettability gradient, droplet radius and solid sphere radius is studied. The proposed wall model can easily be extended to other particle-based methods such as SPH and density fluctuations can be reduced. Furthermore, lower computational time will enable to simulate larger systems for longer times. In solid mechanics and structural dynamics simulation, there are three steps, pre-processing(creating the geometry and mesh), numerical simulation, and postprocessing (analyzing the results from obtained data). Mesh generation is one of the critical stages in numerical simulation and it is still very challenging depending on the geometry and mesh requirement. The process of mesh generation becomes even more challenging when there is high deformation physics. In those cases, the mesh needs to be of high quality and sometimes even after that, remeshing is required. In this dissertation, a novel, simple and efficient model based on the particle method for isotropic unstructured mesh generation is proposed. The proposed method uses simple point particles with varying cutoff radii and densities. The cutoff radii dictate which surrounding particles exert force on the particle. Several force models are also proposed that affect the convergence speed and accuracy of the system. The mesh generation process follows these steps. First, a target number density of the particles is defined based on the desired refinement in the system. Next, a total number of particles is calculated which is a function of density contour and the system volume. The system is then filled with particles randomly and is set to reach equilibrium. Furthermore, several numerical schemes such as implicit and semi-implicit, and their effect on convergence speed and accuracy are also described. A Voronoi-Tessellation-Delaunay-Triangulation(VT-DT) is developed for two dimensions and three dimensions. VT-DT is used to create mesh from the particle position. The obtained mesh consists of triangular (two dimensions) and tetrahedral (three dimensions) elements. This proposed mesh generation method achieves higher mesh qualities than do its counterparts in prior works. For the mesh, several 2D and 3D benchmark cases are used to demonstrate the capability of the proposed method. Some non-engineering mesh examples are also demonstrated to showcase the robustness of the method. The proposed mesh generation model is simple, efficient, and can be used to generate mesh for any geometry and any level of refinement. Furthermore, the speed of the mesh generation enables this method to be used on applications where remeshing is needed.