Dust and gas in protoplanetary disks are the building blocks of planets. In this thesis, we study the dynamics of the gas and dust, which are crucial for the planet formation theory, using observational and numerical approaches. The observational part contains the case study of a rare circumtriple disk around the GW Ori hierarchical triple system. We present Atacama Large Millimeter/submillimeter Array (ALMA) observations of 1.3 mm dust continuum and 12CO J = 2-1 molecular gas emission of the disk. For the first time, we identify three dust rings in the GW Ori disk at ~46, 188, and 338 au, with the outermost ring being the largest dust ring ever found in protoplanetary disks. We use visibility modeling of the dust continuum and kinematics modeling of CO lines to show that the disk has misaligned parts, and the innermost dust ring is eccentric. We interpret these substructures as evidence of ongoing dynamical interactions between the triple stars and the circumtriple disk. In the numerical part, we study whether or not dust around gas gaps opened by planets can remain settled by performing three-dimensional, dust-plus-gas simulations of protoplanetary disks with an embedded planet. We find planets that open gas gaps 'puff up' small, sub-mm-sized grains at the gap edges, where the dust scale-height can reach 80% of the gas scale-height. We attribute this dust 'puff-up' to the planet-induced meridional gas flows previously identified by Fung and Chiang. We thus emphasize the importance of explicit 3D simulations to obtain the vertical distribution of sub-mm-sized grains around planet gaps. We caution that the gas-gap-opening planet interpretation of well-defined dust rings is only self-consistent with large grains exceeding mm in size. / Graduate

Methane/air premixed and partially premixed turbulent flames at high Reynolds number are characterized using Direct Numerical Simulations (DNS) with detailed chemistry in a spatially evolving slot Bunsen configuration. Two sets of simulations are performed. A first set of simulations with fully premixed inlet conditions is considered in order to assess the effect of turbulence on the flame. Four simulations are performed at increasing Reynolds number and up to 22400, defined based on the bulk velocity, slot width, and the reactants' properties, and 22 billion grid points, making it one of the largest simulations in turbulent combustion. The simulations feature finite rate chemistry with a 16 species mechanism. To perform these simulations, few preliminary steps were required: (i) two skeletal mechanisms were developed reducing GRI-3.0; (ii) a convergence study is performed to select the proper spatial and temporal discretization and (iii) simulations of fully developed turbulent channel flows are preformed to generate the inlet conditions of the jet. The study covers different aspects of flame-turbulence interaction. It is found that the thickness of the reaction zone is similar to that of a laminar flame, while the preheat zone has a lower mean temperature gradient, indicating flame thickening. The characteristic length scales of turbulence are investigated and the effect of the Reynolds number on these quantities is assessed. The tangential rate of strain is responsible for the production of flame surface in the mean and surface destruction is due to the curvature term. A second set of simulations with inhomogeneous inlet conditions is performed to study how partial premixing and turbulence interact with the flame and with each other. The jet Reynolds number is 5600, and a 33 species mechanism is used. The effect of the inlet fluctuations is reflected on heat release rate fluctuations, however the conditional mean is not affected. The flames show thickening of the preheat zone, and for the lowest level of mixing a slight thickening of the reaction zone is observed. The effect of partially mixed mixture on the NOx formation is analyzed and no major impact was found.

Electric field can be a viable method in controlling various combustion properties. Comparing to traditional actuators, an application of electric field requires very small power consumption. Especially, alternating current (AC) has received attention recently, since it could modulate flames appreciably even for the cases when direct current (DC) has minimal effects. In this study, the effect of AC electric fields on small coflow diffusion flames is focused with applications of various laser diagnostic techniques. Flow characteristics of baseline diffusion flames, which corresponds to stationary small coflow diffusion flames when electric field is not applied, were firstly investigated with a particular focus on the flow field in near-nozzle region with the buoyancy force exerted on fuels due to density differences among fuel, ambient air, and burnt gas. The result showed that the buoyancy force exerted on the fuel as well as on burnt gas significantly distorted the near-nozzle flow-fields. In the fuels with densities heavier than air, recirculation zones were formed very close to the nozzle exit. Nozzle heating effect influenced this near-nozzle flow-field particularly among lighter fuels. Numerical simulations were also conducted and the results showed that a fuel inlet boundary condition with a fully developed velocity profile for cases with long fuel tubes should be specified inside the fuel tube to obtain satisfactory agreement in both the flow and temperature fields with those from experiment. With sub-critical AC applied to the baseline flames, particle image velocimetry (PIV), light scattering, laser-induced incandescence (LII), and laser-induced fluores- cence (LIF) techniques were adopted to identify the flow field and the structures of OH, polycyclic aromatic hydrocarbons (PAHs), soot zone. Under certain AC condi- tions of applied voltage and frequency, the distribution of PAHs and the flow field near the nozzle exit were drastically altered from the baseline case, leading to the formation of toroidal vortices. Increased residence time and heat recirculation inside the vortex resulted in appreciable formation of PAHs and soot near the nozzle exit. Decreased residence time along the jet axis through flow acceleration by the vortex led to a reduction in the soot volume fraction in the downstream sooting zone. Electromagnetic force generated by AC was proposed as a viable mechanism for the formation of the toroidal vortex. By varying applied AC in a wide range of frequency and voltage, several insta- bility modes were observed, including flicking flames, partial pinch-off of flames, and spinning flames. High speed imaging together with Mie scattering techniques were combined to reveal the flame dynamics as well as the flow structure inside the flames. Original steady toroidal vortices triggered by AC were noted to exhibit axisymmetric axial instability in the flicking and partial pinch-off modes and non-axisymmetric azimuthal instability in the spinning mode. Electrical measurements were also conducted simultaneously to identify the voltage, current, and electrical power responses. Integrated power was noted to be sensitive to indicate subtle variation of flames properties and to the occurrence of axial instability. Under low frequency AC forcing with electrical conditions not generating toroidal vortices, responses of flames were further investigated. Several nonlinear flame responses, including frequency doubling and tripling phenomena, were identified. Spectral analysis revealed that such nonlinear responses were attributed to the combined effects of triggering buoyancy-induced oscillation of the flame as well as the Lorenz force generated by applying AC. Phase delay behaviors between the applied voltage and the heat release rate (or flame size) were also studied to explore the potential of applying AC in controlling flame instability. It was found that the phase delay had large variations for AC frequency smaller than 80 Hz and became saturated at over 80 Hz, which has been explained based on the interaction between the buoyancy and ionic wind. Electrical measurement showed the power consumed by the AC was smaller than 0.01% of the heat release rate from the flame. To improve the understanding on the electric current resulting from applying electric field on flames, a simplified one-dimensional model was developed in that the reaction zone was modeled as a thin ionized layer. Model governing equations were derived from species equations by implementing mobility differences depending on the type of charged particles, especially between ions and electrons. The result showed that the sub-saturated current along with field intensity was significantly influenced by the polarity of DC due to the combined effect of non-equal mobility of charged particles as well as the position of the ionized layer in a gap relative to two electrodes. Experiments with quasi-one-dimensional flames under DC were conducted to substantiate the model and measured currents agreed qualitatively well with the model predictions.

Les virus sont connus pour infecter toutes les classes d’organismes vivants sur Terre, qu’elles soient végétales ou animales. Les virions consistent en un génome d'acide nucléique protégé par une enveloppe protéique unique ou multicouche appelée capside et, dans certains cas, par une enveloppe de lipides. La capside virale est généralement composée de centaines ou de milliers de protéines formant des structures ordonnées. La moitié des virus connus présentent une symétrie icosaédrique, les autres étant hélicoïdaux, prolats ou de structure irrégulière complexe. Récemment, les particules virales ont attiré une attention croissante en raison de leur structure extrêmement régulière et de leur utilisation potentielle pour la fabrication de nanostructures ayant diverses fonctions. Par conséquent, la compréhension des mécanismes d'assemblage sous-jacents à la production de particules virales est non seulement utile au développement d'inhibiteurs à des fins thérapeutiques, mais elle devrait également ouvrir de nouvelles voies pour l'auto-assemblage de matériaux supramoléculaires complexes. À ce jour, de nombreuses études expérimentales et théoriques sur l'assemblage de virus ont été effectuées. Des recherches expérimentales ont permis d'obtenir de nombreuses informations sur l'assemblage du virus, y compris les conditions appropriées requises pour l'assemblage et les voies cinétiques. En combinant ces informations et méthodes théoriques, une première compréhension du mécanisme d'assemblage des virus a été élaborée. Cependant, les informations provenant uniquement d'expériences ne peuvent donner une image complète, en particulier à l'échelle microscopique. Par conséquent, dans cette thèse, nous avons utilisé des simulations informatiques, y compris des techniques de Monte Carlo et de la dynamique moléculaire, pour sonder l’assemblage du virus, dans l’espoir de mieux comprendre les mécanismes moléculaires en jeu. / Viruses are known for infecting all classes of living organisms on Earth, whether vegetal or animal. Virions consist of a nucleic acid genome protected by a single or multilayered protein shell called capsid, and in some cases by an envelope of lipids. The viral capsid is generally made of hundreds or thousands of proteins forming ordered structures. Half of all known viruses exhibit an icosahedral symmetry, the rest being helical, prolate or having a complex irregular structure. Recently, viral particles have attracted an increasing attention due to their extremely regular structure and their potential use for fabricating nanostructures with various functions. Therefore, understanding the assembly mechanisms underlying the production of viral particles is not only helpful to the development of inhibitors for therapeutic purpose, but it should also open new routes for the self-assembly of complex supramolecular materials. To date, numerous experimental and theoretical investigations on virus assembly have been performed. Through experimental investigations, a lot of information have been obtained on virus assembly, including the proper conditions required for the assembly and the kinetic pathways. Combining those information and theoretical methods, an initial understanding of the assembly mechanism of viruses has been worked out. However, information coming purely from experiments cannot give the whole picture, in particular at a microscopic scale. Therefore, in this thesis, we employed computer simulations, including Monte Carlo and molecular dynamics techniques, to probe the assembly of virus, with the expectation to gain new insights into the molecular mechanisms at play.

Theory of turbulence at small scales plays a fundamental role in modeling turbulence and in retrieving information from physical measurements of turbulent flows. A systematic methodology based on direct numerical simulations of turbulent flows is developed to investigate universality of small scale turbulence. Understanding characteristics of the small scale intermittency in turbulent flows and the accuracy of the models, measurements, and theories in predicting it are the main objectives. The research is designed to address two central questions; 1) possible effects of large scale anisotropies on the small scale turbulence and 2) potential biases in characterizing small scale turbulence due to the nature of the quantities used to extract the information, known as surrogates. Direct numerical simulations of forced, isotropic homogeneous turbulence with extraordinarily fine spatial resolution on a periodic box up to 4096 × 4096 × 4096 grid points are analyzed first, to provide a clear insight to the small scale turbulence in the absence of large scale anisotropy. Direct numerical simulations of forced, homogeneous and axisymmetric density stratified flows on a periodic box up to 4096 × 4096 × 2048 grid points with the buoyancy Reynolds number ranging from 10 to 220 are considered next. Different levels of density stratification in the vertical direction cause different levels of large scale anisotropy in the flows. These unique simulations provide a clear picture of turbulent structures over an extensive range of scales. The dissipation rate of turbulent kinetic energy is chosen as the main descriptor of small scale structures. A comprehensive study on surrogates of energy dissipation rate is conducted to identify the best descriptor of the small scale turbulence based on easily measured quantities in physical experiments. In particular, the one-dimensional longitudinal and transverse surrogates, as well as a surrogate based on the asymmetric part of the strain rate tensor, are considered.The statistical analysis of local and locally averaged energy dissipation rate indicates that the small scale intermittency manifested in the energy dissipation rate is universal with intermittency exponent of μ = 0.25 ± 0.05, independent of flow conditions and measurement methods. In contrary, the general shape of the probability density functions of energy dissipation rate is strongly skewed to reflect all the existing dynamics in the flow. The surrogates are fundamentally different than the energy dissipation rate. The longitudinal and transverse surrogates overestimate the intermittency exponent by factors of 1.5 and 2.2, respectively. The scale dependency of the moments of locally averaged energy dissipation rate is proposed as a powerful technique to identify the dominant dynamics of the complex flows for a specific range of scales in physical space. Specifically, for the stratified turbulence, this method suggests a superposition of patches of three-dimensional turbulence superimposed on the background semi two-dimensional stratified flow.

Granular materials are characterized by its discrete nature which makes their behaviour very complex to understand when subjected to various loading situations. Comparing other materials, the understanding of granular materials is poor. This is because experimental analysis provides the macroscopic responses of the considered assembly whereas the discrete nature of the particles point to the fact of understanding the micro scale details and correlating it with the overall behaviour. Among the various modeling tools viz. analytical, physical or numerical, Discrete Element Method (DEM) a numerical technique, originally developed by Cundall (1971, 1974) and modified by Cundall and Strack (1979a, 1979b) is widely used for granular materials. Later a thorough description of DEM was given by Cundall (1988) and Hart et al (1988). Moreover Cundall & Hart (1992) reported discrete element code as one which allows finite displacements and rotations of discrete bodies along with recognition of new contacts as the calculation progresses which is followed in particle flow code and is used for this study. Generally the discrete particles are modeled as discs or spheres in 2-D and 3-D simulations respectively. The discs or spheres were considered as it is very easy to characterize the grain interactions and the contact detection. Even though the significance of particle shape has been reported in literature, a comprehensive 3-D study of the effect of particle shape on the various aspects of soil behaviour is lacking and is not reported. Particle shape is generally defined in terms of elongation, roundness and texture. Elongation is an indication of the particle aspect ratio whereas roundness measures the sharpness or angularity of particle’s edges and corners. Texture is related to the roughness of the surface. Particle gradation also plays a role in the mechanical behaviour. The influence of each of these factors on the mechanical behaviour of the assembly is important. Hence the major factors like elongation, texture etc which are used to define the particle shape are incorporated in this study. Evaluating the particle shape is another hurdle. In this study, the particle shape is analyzed using a 3D laser scanner which helps to identify the major and minor axis lengths of the particle. Additionally, the effective use of 3D DEM on large scale real life applications incorporating the particle shape effect is also not dealt with very extensively. Hence in this research, a comprehensive study on the calibration of DEM using glass beads, effect of particle shape on drained and undrained monotonic behaviour, liquefaction, post liquefaction and dynamic properties and the application of DEM to a grain polishing machine and an underground tunnel assembly is presented. In the present study, a set of drained triaxial tests were done on glass bead assembly using a laboratory triaxial set up. The glass beads used for the test were spherical and ellipsoidal in shape. The shape of glass beads was characterized through a sophisticated method of 3D laser scanning. In this scanning, the shape of the image of the glass bead is captured through an array of digitized points. These images obtained as unstructured 3D triangular meshes on processing will render the long and short axes of the particle which can be used for proper modeling of the particle shape. After obtaining the long and short axes for the particles, the same is used for the numerical modeling of the glass beads. The numerical simulation results have shown that the assembly modeled with clumped particles gives results qualitatively and quantitatively similar to the observed experimental macro responses. Hence this is used to demonstrate the power of DEM to realistically model the granular behaviour by incorporating the particle shape effect. In addition, undrained simulation of granular material has been numerically predicted from drained triaxial tests which are similar to the approach proposed by Norris et al (1997). An excellent correlation between undrained results predicted from drained triaxial test and undrained test (performed under constant volume conditions) has been observed. This further underlines the fact that the constant volume simulations are equivalent to undrained tests. Having validated the DEM results to the values obtained from the experiments on glass beads, a series of monotonic drained and undrained triaxial tests were performed on cylindrical assemblies of height to diameter ratio 2:1. Four different sets of assemblies were prepared which consists of particles of different aspect ratio to study the influence of particle shape. The behaviour of these assemblies under drained shearing indicates that the strength of the clumped assemblies is higher than that of the spherical assembly at all confining pressures. This has been explained from the magnitude of the anisotropic vi coefficients associated with the fabric and normal contact force tensors. It is also noted that eventhough both assemblies reach the peak strength at the same axial strain, the strain softening associated with the clumped assembly is very rapid which is due to the fact that clumps try to push each other apart as it offers more resistance to rotation resulting in dilation. Another significant observation is that a general increase in aspect ratio will not keep on increasing the strength. As the aspect ratio increases, the particles have a tendency to orient along their larger dimensions. This helps them to attain the lowest potential energy leading to a stable equilibrium and resulting in inherent fabric anisotropy. But when the particles try to align along the larger dimension, the formation of strong contact forces along the direction of loading is hindered. In addition, the lower strength associated with the higher aspect ratio particle assembly can also be attributed to the formation of unexpected void spaces when these longer particles bridge gaps over the underlying grains. The critical state studies indicate that the clumped assembly is having a higher residual strength compared to that of the spherical assembly. In the case of clumped assemblies also, irrespective of the initial loose or dense state of the assembly and the confining pressure applied, the samples reached the same critical state which underlines that the critical state is unique for a granular material. Moreover, the critical state line is non-linear for both the spherical and clumped assemblies. The studies conducted on the liquefaction behaviour indicates that at lower confining pressures the assemblies with particles consisting of lower aspect ratios loses its strength at less number of cycles which can be attributed to the interlocking of non-spherical particles resulting in higher number of contacts per particle. Moreover, during the initial cycles of loading, it is seen that the strong contacts are predominantly in the vertical direction or more precisely along the direction of maximum axial strain. But the plots extracted at higher cycles indicated that the strong contacts along the vertical direction have diminished considerably. This reduction in contact force magnitude and force chain indicates a drop in the number of contacts and is clearly visible in the gradual decrease of average coordination number. Another significant observation is that as the confining stresses increases, the rate of pore pressure generation of the assembly vii consisting of only spherical particles is less compared to the other two samples. Furthermore, at higher confining pressures, when the load direction reverses, the fabric of the clumped assemblies fails to change to a new orientation immediately. But to retain equilibrium the force anisotropy will quickly adjust itself. This mismatch results in losing the contacts and resulting in lower strength and less resistance to liquefaction at higher stresses for assemblies consisting of clumped particles. The post liquefaction study of the numerically liquefied samples shows that the assembly consisting of clumped shaped particles gained strength at a much faster rate compared to the assembly consisting of only spheres. This may be attributed to the ability of the clumps to rearrange themselves on a faster rate compared to that of the spherical particles. The rate of development of average coordination number is very significant as it explains the ability of the assembly to build up the deviatoric stress from a complete collapsed structure. As the contacts develop, the average coordination number as well as the deviatoric stress starts increasing with both the values higher for the assembly consisting of clumped particles. The evaluation of the dynamic properties viz. shear modulus and damping ratio showed a trend similar to the experimental observations on real granular materials. It is observed that the normalized shear modulus reduces with an increase in shear strain and the rate of reduction is very high at low strains for all the samples. It can be seen that as the confining pressure increases, the normalized shear modulus value also increases and the rate of increment is higher for the assemblies consisting of non-spherical particles. Furthermore, for all the samples the threshold shear strain is about 0.001 up to which the behaviour is elastic. Beyond the threshold shear strain, the variation of the normalized shear modulus ratio is non-linear. At small shear strains, the energy dissipation is low resulting in smaller values of damping. As the strains increase, the non-linearity in the constitutive behaviour results in higher material damping leading to high damping value. The simulations of the food polishing machine helps to understand the pattern of hitting of clumped grains on the wall with due importance to the velocity of hit, angle of hit, force of hit, and the number of grains hitting the wall. The modeling and subsequent extraction of the data helped to identify that the wear and tear of the machine was not uniform and was clustered to specific regions due to the non-uniform distribution of the considered parameters. This helped to design a more sophisticated system such that the parts which are subjected to more deterioration are provided with additional support. To bring out the effect of the particle shape, simulations are performed using spherical particles and the results show that the pattern of variation is same, but the magnitudes are different owing to the less surface area associated with the spherical particles. The 3-D simulations of an underground tunnel assembly in a weak weathered rock helped to understand the variation in the stability of the system with and without lining. It was observed that the introduction of lining resulted in a more stable configuration and the circumferential stresses were found to be distributed uniformly around the tunnel. FEM simulations also show a similar trend of stress and strain variations but were unable to capture the ground loosening around the tunnel and the formation of the ground arch whereas DEM could realistically capture all these phenomena. It was observed that as the shape changes from sphere to non-spherical particles, circumferential stresses around the tunnels increased. In addition, as the distance from the tunnel face increases, the strains are reduced. The maximum vertical strain near the crown of the tunnel is observed for the assembly consisting of spherical particles. In short, this research is focused on a comprehensive understanding of the particle shape effect on the mechanical behaviour of granular mass. Numerical simulations incorporating the shape effect has been done on drained and undrained monotonic shear tests, critical state, liquefaction, post liquefaction and dynamic properties. Besides, the granular dynamics simulation of the movement of long food grains in a food polishing machine and the behaviour of an underground tunnel in a granular assembly is also reported.

The main goal of my studies has been to search for the optimal control strategy of controlling epidemics when taking into account both economical and social costs of the disease. Three control scenarios emerge with treating the whole population (global strategy, GS), treating a small number of individuals in a well-defined neighbourhood of a detected case (local strategy, LS) and allowing the disease to spread unchecked (null strategy, NS). The choice of the optimal strategy is governed mainly by a relative cost of palliative and preventive treatments. Although the properties of the pathogen might not be known in advance for emerging diseases, the prediction of the optimal strategy can be made based on economic analysis only. The details of the local strategy and in particular the size of the optimal treatment neighbourhood weakly depends on disease infectivity but strongly depends on other epidemiological factors (rate of occurring the symptoms, spontaneously recovery). The required extent of prevention is proportional to the size of the infection neighbourhood, but this relationship depends on time till detection and time till treatment in a non-nonlinear (power) law. The spontaneous recovery also affects the choice of the control strategy. I have extended my results to two contrasting and yet complementary models, in which individuals that have been through the disease can either be treated or not. Whether the removed individuals (i.e., those who have been through the disease but then spontaneously recover or die) are part of the treatment plan depends on the type of the disease agent. The key factor in choosing the right model is whether it is possible - and desirable - to distinguish such individuals from those who are susceptible. If the removed class is identified with dead individuals, the distinction is very clear. However, if the removal means recovery and immunity, it might not be possible to identify those who are immune. The models are similar in their epidemiological part, but differ in how the removed/recovered individuals are treated. The differences in models affect choice of the strategy only for very cheap treatment and slow spreading disease. However for the combinations of parameters that are important from the epidemiological perspective (high infectiousness and expensive treatment) the models give similar results. Moreover, even where the choice of the strategy is different, the total cost spent on controlling the epidemic is very similar for both models. Although regular and small-world networks capture some aspects of the structure of real networks of contacts between people, animals or plants, they do not include the effect of clustering noted in many real-life applications. The use of random clustered networks in epidemiological modelling takes an impor- tant step towards application of the modelling framework to realistic systems. Network topology and in particular clustering also affects the applicability of the control strategy.

The present thesis is devoted to an application of the ideas of complex networks theory for analysing, modelling, and, finally, optimising different processes that occur in transportation networks.

No description available.

Turbulent magnetic fields are ubiquitous in space physics and astrophysics. The influence of magnetic turbulence on the motions of charged particles contains the essential physics of the transport and acceleration of energetic charged particles in the heliosphere, which is to be explored in this thesis. After a brief introduction on the energetic charged particles and magnetic fields in the heliosphere, the rest of this dissertation focuses on three specific topics: 1. the transport of energetic charged particles in the inner heliosphere, 2. the acceleration of ions at collisionless shocks, and 3. the acceleration of electrons at collisionless shocks. We utilize various numerical techniques to study these topics. In Chapter 2 we study the propagation of charged particles in turbulent magnetic fields similar to the propagation of solar energetic particles in the inner heliosphere. The trajectories of energetic charged particles in the turbulent magnetic field are numerically integrated. The turbulence model includes a Kolmogorov-like magnetic field power spectrum containing a broad range of scales from those that lead to large-scale field-line random walk to small scales leading to resonant pitch-angle scattering of energetic particles. We show that small-scale variations in particle intensities (the so-called "dropouts") and velocity dispersions observed by spacecraft can be reproduced using this method. Our study gives a new constraint on the error of "onset analysis", which is a technique commonly used to infer information about the initial release of energetic particles. We also find that the dropouts are rarely produced in the simulations using the so-called "two-component" magnetic turbulence model (Matthaeus et al., 1990). The result questions the validity of this model in studying particle transport. In the first part of Chapter 3 we study the acceleration of ions in the existence of turbulent magnetic fields. We use 3-D self-consistent hybrid simulations (kinetic ions and fluid electrons) to investigate the acceleration of low-energy particles (often termed as "injection problem") at parallel shocks. We find that the accelerated particles always gain the first amount of energy by reflection and acceleration at the shock layer. The protons can move off their original field lines in the 3-D electric and magnetic fields. The results are consistent with the acceleration mechanism found in previous 1-D and 2-D simulations. In the second part of Chapter 3, we use a stochastic integration method to study diffusive shock acceleration in the existence of large-scale magnetic variations. We show that the 1-D steady state solution of diffusive shock acceleration can be significantly modified in this situation. The results suggest that the observations of anomalous cosmic rays by Voyager spacecraft can be explained by a 2-D shock that includes the large-scale magnetic field variations. In Chapter 4 we study electron acceleration at a shock passing into a turbulent magnetic field by using a combination of hybrid simulations and test-particle electron simulations. We find that the acceleration of electrons is greatly enhanced by including the effect of large-scale magnetic turbulence. Since the electrons mainly follow along the magnetic lines of force, the large-scale braiding of field lines in space allows the fast-moving electrons interacting with the shock front multiple times. Ripples in the shock front occurring at various scales also contribute to the acceleration by mirroring the electrons. Our calculation shows that this process favors electron acceleration at perpendicular shocks. We discuss the application of this process in interplanetary shocks and flare termination shocks. We also discuss the implication of this study to solar energetic particles (SEPs) by comparing the acceleration of electrons with that of protons. The intensity correlation of electrons and ions in SEP events indicates that perpendicular or quasi-perpendicular shocks play an important role in accelerating charged particles. In Chapter 5 we summarize the results of this thesis and discuss possible future work.