Galaxies are natural laboratories for testing fundamental physics on the nature of the dark matter. MOdified Newtonian Dynamics (MOND) has been tested for over 20 years on small and large scales. While there are several versions of how MOND extrapolates to the large scales, and these versions are not yet fully successful, the original Bekenstein-Milgrom version of MOND is fully predictive and works very well on galaxy scales. However, little work has been done to explore this theory beyond fitting the rotation curves and Tully-Fisher relation of isolated disc galaxies. So far little is known of MONDian elliptical galaxies accelerating in any galaxy cluster. A defining feature of MOND is that internal dynamics of the galaxy depends on the overall acceleration of the galaxy. The existence of cuspy triaxial equilibria for elliptical galaxies is the minimal requirement to MOND. With the PhD project here, I constructed and then further studied the evolution and stability of gravitationally bound systems resembling like cuspy elliptical galaxies, both in isolation and when embedded in a uniform external field. I also studied the escape speeds from spiral galaxies, in particular by comparing the potentials of the Milky Way Galaxy in the Cold Dark Matter (CDM) and MOND frameworks.

We study the structure and substructure of Lambda-CDM halos using a suite of high-resolution cosmological N-body simulations. Our analysis of the substructure population of dark matter halos focuses on their mass and peak circular velocity functions, as well as their spatial distribution and dynamics. In our analysis, we consider the whole population of subhalos physically associated with the main halo, defined as those that have, at some time, crossed within the virial radius of the main progenitor. We find that this population extends beyond 3 times the virial radius and includes objects on unorthodox orbits, several of which travel at velocities approaching the nominal escape speed from the system. We trace the origin of these unorthodox orbits to the tidal dissociation of bound groups, which results in the ejection of some systems along tidal streams. This process primarily influences low-mass systems leading to clear mass-dependent biases in their spatial distribution and kinematics: the lower the subhalo mass at accretion time the more concentrated and kinematically hotter their descendant population. When quantified in terms of present day subhalo mass these trends disappear, presumably due to the increased effect of dynamical friction and tidal stripping on massive systems. We confirm several of these results using the ultra-high resolution Aquarius simulations, which extend the dynamic range of the subhalo mass function by nearly 3 orders of magnitude. Using these simulations we confirm that the substructure mass function follows a power-law, $dN/dM\propto M^{-1.9}$, and exhibits very little halo-to-halo scatter. This implies that the total mass in substructure within a given halo is bounded to a small fraction of the total halo mass, with the smooth component dominating the halo inner regions. Using the Aquarius simulations we study the structure of galaxy-sized Lambda-CDM halos. We find that the spherically averaged density profiles become increasingly shallow toward the halo center, with no sign of converging to an asymptotic power-law; a radial dependence accurately described by the Einasto profile. In our highest resolution run we resolve scales approaching 100 pc, at which point the maximum asymptotic slope is $\approx -0.89$, confidently ruling out recent claims for cusps as steep as $r^{-1.2}$. We find that the spherically averaged density and velocity dispersion profiles are not universal, but rather show subtle but significant deviations from self-similarity. Intriguingly, departures from self-similarity are minimized when cast in terms of the phase-space density profile, $\rho/\sigma^3$, suggesting an intimate scaling between densities and velocity dispersions across the system. The phase-space density profiles follow a power-law with radius, $r^{-1.875}$, identical to that of Bertschinger's similarity solution for self-similar infall onto a point mass in an otherwise unperturbed Einstein-de Sitter universe.

Absorption profiles are found in the observed spectra from quasars, and the most prominent of these are the Damped Lyman-alpha Absorbers (DLAs). They are caused by large collections of neutral hydrogen (HI) gas, which are thought to be housed in galaxies that lie along the line-of-sight to quasars. HI gas associated with DLAs contains most of the HI gas in the Universe during 2 < z < 5, and hence details about DLAs are important for understanding the history of star formation, as well as the formation and evolution of galaxies. Wyithe (2008) proposed a method of determining the characteristic mass of dark matter haloes that host DLAs. This involves generating an analytic power spectrum of the fluctuations in 21cm brightness temperature caused by the HI gas in the Universe. Calculating this analytic 21cm power spectrum requires a formalism for the HI mass weighted clustering bias of DLAs on both large and small scales. We include this DLA clustering bias by firstly generating an analytic galaxy power spectrum using the halo model of Peacock & Smith (2000), as well as including the occupation of haloes by galaxies -- using the Halo Occupation Distribution (HOD) weighting of Peacock (2003). This weighting is then adapted to account for the occupation of haloes by HI gas. / We then fit the analytic 21cm power spectrum generated using this formalism to a simulated 21cm power spectrum, with the characteristic mass of DLA host haloes being used as a fitting parameter. The DLA host halo mass is in turn dependent upon two parameters in our model: the minimum mass of haloes M_{min} included in our formalism, and the HI weighting index alpha_{HI}. The neutral hydrogen fraction is another parameter, which we can choose to be the same as that from our simulation volume. If we also choose a value for alpha_{HI} that is motivated by analysis of the dark matter and HI gas content of the haloes in the simulation, then we are able to fit the 21cm power spectrum at both large and small scales, with an M_{min} that is the same or similar to the lowest mass in the simulation's halo catalogue. This in turn gives a similar value for the DLA host halo mass that is known to be the case in the simulation. This demonstrates the viability of the Wyithe (2008) method for determining the DLA host halo mass using observations of 21cm fluctuations. However, degeneracies in the free parameters of our analytic formalism would hinder an accurate determination of the DLA host halo mass from actual future observations. This is due to the fact that the real space, spherically averaged 21cm power spectrum is used throughout this thesis. However, extending our analytic formalism to the redshift space, angular-dependent 21cm power spectrum should be capable of breaking the degeneracy between DLA host halo mass and neutral hydrogen fraction.

We study the structure and substructure of Lambda-CDM halos using a suite of high-resolution cosmological N-body simulations. Our analysis of the substructure population of dark matter halos focuses on their mass and peak circular velocity functions, as well as their spatial distribution and dynamics. In our analysis, we consider the whole population of subhalos physically associated with the main halo, defined as those that have, at some time, crossed within the virial radius of the main progenitor. We find that this population extends beyond 3 times the virial radius and includes objects on unorthodox orbits, several of which travel at velocities approaching the nominal escape speed from the system. We trace the origin of these unorthodox orbits to the tidal dissociation of bound groups, which results in the ejection of some systems along tidal streams. This process primarily influences low-mass systems leading to clear mass-dependent biases in their spatial distribution and kinematics: the lower the subhalo mass at accretion time the more concentrated and kinematically hotter their descendant population. When quantified in terms of present day subhalo mass these trends disappear, presumably due to the increased effect of dynamical friction and tidal stripping on massive systems. We confirm several of these results using the ultra-high resolution Aquarius simulations, which extend the dynamic range of the subhalo mass function by nearly 3 orders of magnitude. Using these simulations we confirm that the substructure mass function follows a power-law, $dN/dM\propto M^{-1.9}$, and exhibits very little halo-to-halo scatter. This implies that the total mass in substructure within a given halo is bounded to a small fraction of the total halo mass, with the smooth component dominating the halo inner regions. Using the Aquarius simulations we study the structure of galaxy-sized Lambda-CDM halos. We find that the spherically averaged density profiles become increasingly shallow toward the halo center, with no sign of converging to an asymptotic power-law; a radial dependence accurately described by the Einasto profile. In our highest resolution run we resolve scales approaching 100 pc, at which point the maximum asymptotic slope is $\approx -0.89$, confidently ruling out recent claims for cusps as steep as $r^{-1.2}$. We find that the spherically averaged density and velocity dispersion profiles are not universal, but rather show subtle but significant deviations from self-similarity. Intriguingly, departures from self-similarity are minimized when cast in terms of the phase-space density profile, $\rho/\sigma^3$, suggesting an intimate scaling between densities and velocity dispersions across the system. The phase-space density profiles follow a power-law with radius, $r^{-1.875}$, identical to that of Bertschinger's similarity solution for self-similar infall onto a point mass in an otherwise unperturbed Einstein-de Sitter universe.

We present algorithms and implementations that overcome obstacles in the migration of the Fast Multipole Method (FMM), one of the most important algorithms in computational science and engineering, to exascale computing. Emerging architectural approaches to exascale computing are all characterized by data movement rates that are slow relative to the demand of aggregate floating point capability, resulting in performance that is bandwidth limited. Practical parallel applications of FMM are impeded in their scaling by irregularity of domains and dominance of collective tree communication, which is known not to scale well. We introduce novel ideas that improve partitioning of the N-body problem with boundary distribution through a sampling-based mechanism that hybridizes two well-known partitioning techniques, Hashed Octree (HOT) and Orthogonal Recursive Bisection (ORB). To reduce communication cost, we employ two methodologies. First, we directly utilize features available in parallel runtime systems to enable asynchronous computing and overlap it with communication. Second, we present Hierarchical Sparse Data Exchange (HSDX), a new all-to-all algorithm that inherently relieves communication by relaying sparse data in a few steps of neighbor exchanges. HSDX exhibits superior scalability and improves relative performance compared to the default MPI alltoall and other relevant literature implementations. We test this algorithm alongside others on a Cray XC40 tightly coupled with the Aries network and on Intel Many Integrated Core Architecture (MIC) represented by Intel Knights Corner (KNC) and Intel Knights Landing (KNL) as modern shared-memory CPU environments. Tests include comparisons of thoroughly tuned handwritten versus auto-vectorization of FMM Particle-to-Particle (P2P) and Multipole-to-Local (M2L) kernels. Scalability of task-based parallelism is assessed with FMM’s tree traversal kernel using different threading libraries. The MIC tests show large performance gains after adopting the prescribed techniques, which are inevitable in a world that is moving towards many-core parallelism.

In this thesis, we construct a new optimal contractivity-preserving (CP) explicit, 2-step, 6-stage, 6-derivative, Hermite--Birkhoff--Obrechkoff method of order 13, denoted by HBO(13) with nonnegative coefficients, for solving nonstiff first-order initial value problems y'=f(t,y), y(t_0)=y_0. This new method is the combination of a CP 2-step, 6-derivative, Hermite--Obrechkoff of order 9, denoted by HO(9), and a 6-stage Runge-Kutta method of order 5, denoted by RK(6,5). The new HBO(13) method has order 13. We compare this new method, programmed in Matlab, to Adams-Bashforth-Moulton method of order 13 in PECE mode, denoted by ABM(13), by testing them on several frequently used test problems, and show that HBO(13) is more efficient with respect to the CPU time, the global error at the endpoint of integration and the relative energy error. We show that the new HBO(13) method has a larger scaled interval of absolute stability than ABM(13) in PECE mode.

Title: Study of dark energy and modified gravity and their influence on the cosmological parameters of the universe Author: Michal Vraštil Institute: Institute of Physics of the Czech Academy of Sciences Supervisor: RNDr. Michael Prouza, Ph.D., Institute of Physics of the Czech Academy of Sciences Abstract: Discovery of the accelerated expansion of the Universe poses a major theoretical puzzle. Although the assumption of a non-zero cosmological constant provides a minimal extension of general relativity that is consistent with observational data, many theories of modified gravity have been suggested as possible alternatives due to serious problems connected with the cosmological constant. Numerical predictions of structure formation for these models in the fully non-linear regime are very expensive and it is difficult, if not impossible, to explore such a huge space of models and parameters using high-resolution N-body simulations. Even in the mildly nonlinear regime, perturbative methods can become extremely complex. We explore whether simplified dynamical approximations, applicable for a certain set of cosmological probes, can be used to investigate models of modified gravity with acceptable accuracy in the latter instance. For the case of chameleon gravity, we found that it is screened away on scales...

Star clusters are thought to be the birthplaces of stars as well as the building blocks of galaxies. They typically consist of thousands to millions of stars bound together by self-gravity. These systems evolve on the scale of Myr to Gyr, there- fore, it is impossible for us to see any change in their global evolution even within hundreds of human lifetimes. Although the equations of motion of stars in a star cluster are simple New- tonian, it is impossible to predict precisely history of any star within them to any point in the future. Therefore, we may either compare the observations of different star clusters at different age, we may invent theoretical approaches and analytical predictions, or we must follow their evolution numerically (e.g. with direct N-body integrators) which is the main focus of my research and this thesis. First, we follow the evolution of star clusters in general while coming up with a novel method to estimate their characteristic timescale (i.e. the time of core collapse) based on global parameters. The core collapse is directly linked to the formation of hard binary stars, thus, we focus on their analysis as well. We also follow several recent observational results: (i) ALMA observations of the Serpens South star-forming region indicate that star clusters are born mass...

We present new N-body, hydrodynamical simulations of the interaction between the starburst galaxy NGC 7714 and its poststarburst companion NGC 7715, focusing on the formation of the collisional features, including (1) the gas-rich star-forming bridge, (2) the large gaseous loop (and stellar tails) to the west of the system, (3) the very extended H I tail to the west and north of NGC 7714, and (4) the partial stellar ring in NGC 7714. Our simulations confirm the results of earlier work that an off-center inclined collision between two disk galaxies is almost certainly responsible for the peculiar morphologies of this system. However, we have explored a wider set of initial galaxy and collisional encounter parameters than previously and have found a relatively narrow range of parameters that reproduce all the major morphologies of this system. The simulations suggest specific mechanisms for the development of several unusual structures. We find that the complex gas bridge has up to four distinct components, with gas contributed from two sides of NGC 7715, as well as from NGC 7714. The observed gas-star offset in this bridge is accounted for in the simulations by the dissipative evolution of the gas. The models suggest that the most recently formed gas bridge component from NGC 7715 is interacting with gas from an older component. This interaction may have stimulated the band of star formation on the north side of the bridge. The models also indicate that the low surface brightness H I tail to the far west of NGC 7714 is the end of the NGC 7715 countertail, curved behind the two galaxies. The sensitivity of the tidal structures to collision parameters is demonstrated by comparisons between models with slightly different parameter values. Comparison of model and observational (H I) kinematics provides an important check that the morphological matches are not merely fortuitous. Line-of-sight velocity and dispersion fields from the model are found to match those of the observations reasonably well at current resolutions. Spectral evolutionary models of the NGC 7714 core by Lançon et al. suggest the possibility of multiple starbursts in the last 300 Myr. Our hydrodynamic models suggest that bursts could be triggered by induced ringlike waves and a postcollision buildup of gas in the core of the galaxy.

The recent boom in 21cm astronomy has piqued the interest of many, especially cosmologists realizing its applications in their field. This study aims to determine if 21cm astronomy is a good tool for testing the validity of keV WDM models, as well as creating a code capable of simulating keV WDM models from an existing CDM code. The assumed WDM models vary only in dark matter particle mass and assume a single-species dark matter case as well as totally thermalized particles, such as gravitinos. Small-scale simulations of approximately 183Mpc3, as well as large-scale simulations of approximately 1503Mpc3-1793Mpc3, indicated that the CDM code was successfully modified to simulate WDM through the total dark matter power spectrum and the halo-mass function. Additionally, the large-scale simulations hinted at a positive use of 21cm astronomy for the restriction of keV WDM models, due to the existence of a distinct CDM HI power spectrum as compared to the 0.5keV WDMHI power spectrum. A discernable difference between CDM and keV WDM galactic HI power spectra would provide a step towards a confirmation or falsification of keV WDM models if supplied with a large-scale galactic HI power spectrum study