1,200 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

    Get PDF
    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    A modern analytic method to solve singular and non-singular linear and non-linear differential equations

    Get PDF
    This article circumvents the Laplace transform to provide an analytical solution in a power series form for singular, non-singular, linear, and non-linear ordinary differential equations. It introduces a new analytical approach, the Laplace residual power series, which provides a powerful tool for obtaining accurate analytical and numerical solutions to these equations. It demonstrates the new approach’s effectiveness, accuracy, and applicability in several ordinary differential equations problem. The proposed technique shows the possibility of finding exact solutions when a pattern to the series solution obtained exists; otherwise, only rough estimates can be given. To ensure the accuracy of the generated results, we use three types of errors: actual, relative, and residual error. We compare our results with exact solutions to the problems discussed. We conclude that the current method is simple, easy, and effective in solving non-linear differential equations, considering that the obtained approximate series solutions are in closed form for the actual results. Finally, we would like to point out that both symbolic and numerical quantities are calculated using Mathematica software

    2023-2024 Catalog

    Get PDF
    The 2023-2024 Governors State University Undergraduate and Graduate Catalog is a comprehensive listing of current information regarding:Degree RequirementsCourse OfferingsUndergraduate and Graduate Rules and Regulation

    Development, Implementation, and Optimization of a Modern, Subsonic/Supersonic Panel Method

    Get PDF
    In the early stages of aircraft design, engineers consider many different design concepts, examining the trade-offs between different component arrangements and sizes, thrust and power requirements, etc. Because so many different designs are considered, it is best in the early stages of design to use simulation tools that are fast; accuracy is secondary. A common simulation tool for early design and analysis is the panel method. Panel methods were first developed in the 1950s and 1960s with the advent of modern computers. Despite being reasonably accurate and very fast, their development was abandoned in the late 1980s in favor of more complex and accurate simulation methods. The panel methods developed in the 1980s are still in use by aircraft designers today because of their accuracy and speed. However, they are cumbersome to use and limited in applicability. The purpose of this work is to reexamine panel methods in a modern context. In particular, this work focuses on the application of panel methods to supersonic aircraft (a supersonic aircraft is one that flies faster than the speed of sound). Various aspects of the panel method, including the distributions of the unknown flow variables on the surface of the aircraft and efficiently solving for these unknowns, are discussed. Trade-offs between alternative formulations are examined and recommendations given. This work also serves to bring together, clarify, and condense much of the literature previously published regarding panel methods so as to assist future developers of panel methods

    Numerical methods for computing the discrete and continuous Laplace transforms

    Full text link
    We propose a numerical method to spline-interpolate discrete signals and then apply the integral transforms to the corresponding analytical spline functions. This represents a robust and computationally efficient technique for estimating the Laplace transform for noisy data. We revisited a Meijer-G symbolic approach to compute the Laplace transform and alternative approaches to extend canonical observed time-series. A discrete quantization scheme provides the foundation for rapid and reliable estimation of the inverse Laplace transform. We derive theoretic estimates for the inverse Laplace transform of analytic functions and demonstrate empirical results validating the algorithmic performance using observed and simulated data. We also introduce a generalization of the Laplace transform in higher dimensional space-time. We tested the discrete LT algorithm on data sampled from analytic functions with known exact Laplace transforms. The validation of the discrete ILT involves using complex functions with known analytic ILTs

    Neutrinos from horizon to sub-galactic scales

    Get PDF
    A first determination of the mass scale set by the lightest neutrino remains a crucial outstanding challenge for cosmology and particle physics, with profound implications for the history of the Universe and physics beyond the Standard Model. In this thesis, we present the results from three methodological papers and two applications that contribute to our understanding of the cosmic neutrino background. First, we introduce a new method for the noise-suppressed evaluation of neutrino phase-space statistics. Its primary application is in cosmological N-body simulations, where it reduces the computational cost of simulating neutrinos by orders of magnitude without neglecting their nonlinear evolution. Second, using a recursive formulation of Lagrangian perturbation theory, we derive higher-order neutrino corrections and show that these can be used for the accurate and consistent initialisation of cosmological neutrino simulations. Third, we present a new code for the initialisation of neutrino particles, accounting both for relativistic effects and the full Boltzmann hierarchy. Taken together, these papers demonstrate that with the combination of the methods described therein, we can accurately simulate the evolution of the neutrino background over 13.8 Gyr from the linear and ultra-relativistic regime at z=109z=10^9 down to the non-relativistic yet nonlinear regime at z=0z=0. Moreover, they show that the accuracy of large-scale structure predictions can be controlled at the sub-percent level needed for a neutrino mass determination. In a first application of these methods, we present a forecast for direct detection of the neutrino background, taking into account the gravitational enhancement (or indeed suppression) of the local density due to the Milky Way and the observed large-scale structure within 200 Mpc/h. We determine that the large-scale structure is more important than the Milky Way for neutrino masses below 0.1 eV, predict the orientation of the neutrino dipole, and study small-scale anisotropies. We predict that the angular distribution of neutrinos is anti-correlated with the projected matter density, due to the capture or deflection of neutrinos by massive objects along the line of sight. Finally, we present the first results from a new suite of hydrodynamical simulations, which includes the largest ever simulation with neutrinos and galaxies. We study the extent to which variations in neutrino mass can be treated independently of astrophysical processes, such as feedback from supernovae and black holes. Our findings show that baryonic feedback is weakly dependent on neutrino mass, with feedback being stronger for models with larger neutrino masses. By studying individual dark matter halos, we attribute this effect to the increased baryon density relative to cold dark matter and a reduction in the binding energies of halos. We show that percent-level accurate modelling of the matter power spectrum in a cosmologically interesting parameter range is only possible if the cosmology-dependence of feedback is taken into account

    The Forward Physics Facility at the High-Luminosity LHC

    Get PDF
    High energy collisions at the High-Luminosity Large Hadron Collider (LHC) produce a large number of particles along the beam collision axis, outside of the acceptance of existing LHC experiments. The proposed Forward Physics Facility (FPF), to be located several hundred meters from the ATLAS interaction point and shielded by concrete and rock, will host a suite of experiments to probe standard model (SM) processes and search for physics beyond the standard model (BSM). In this report, we review the status of the civil engineering plans and the experiments to explore the diverse physics signals that can be uniquely probed in the forward region. FPF experiments will be sensitive to a broad range of BSM physics through searches for new particle scattering or decay signatures and deviations from SM expectations in high statistics analyses with TeV neutrinos in this low-background environment. High statistics neutrino detection will also provide valuable data for fundamental topics in perturbative and non-perturbative QCD and in weak interactions. Experiments at the FPF will enable synergies between forward particle production at the LHC and astroparticle physics to be exploited. We report here on these physics topics, on infrastructure, detector, and simulation studies, and on future directions to realize the FPF's physics potential

    The Forward Physics Facility at the High-Luminosity LHC

    Get PDF
    High energy collisions at the High-Luminosity Large Hadron Collider (LHC) produce a large number of particles along the beam collision axis, outside of the acceptance of existing LHC experiments. The proposed Forward Physics Facility (FPF), to be located several hundred meters from the ATLAS interaction point and shielded by concrete and rock, will host a suite of experiments to probe standard model (SM) processes and search for physics beyond the standard model (BSM). In this report, we review the status of the civil engineering plans and the experiments to explore the diverse physics signals that can be uniquely probed in the forward region. FPF experiments will be sensitive to a broad range of BSM physics through searches for new particle scattering or decay signatures and deviations from SM expectations in high statistics analyses with TeV neutrinos in this low-background environment. High statistics neutrino detection will also provide valuable data for fundamental topics in perturbative and non-perturbative QCD and in weak interactions. Experiments at the FPF will enable synergies between forward particle production at the LHC and astroparticle physics to be exploited. We report here on these physics topics, on infrastructure, detector, and simulation studies, and on future directions to realize the FPF's physics potential

    Forested Watersheds and Water Supply: Exploring Effects of Wildfires, Silviculture, and Climate Change on Downstream Waters

    Get PDF
    Drinking water supplies for much of society originate in forests. To preserve the capability of these forests to produce clean and easily treatable water, source water supply and protection strategies focus in particular on potential disturbances to the landscape, which include prescribed forest harvesting and wildfires of varying intensity. While decades of work have revealed relationships between forest harvesting and stream flow response, there is a considerable lack of synthesis disentangling the interactions of climate, wildfires, stream flow, and water quality. Revealing the mechanisms for impacts on downstream waters after disturbances of harvesting and wildfire will greatly improve land and water management. In this dissertation, I combined synthesis of previously published or available data, novel mathematical analyses, and deterministic modeling to disentangle various disturbance effects and further our understanding of processes in forested watersheds. I broadly sought to explore how streamflow and water quality change after forest disturbances, and how new methods and analyses can provide insight into the biogeochemical and ecohydrologic processes changing during disturbances. First, I examined the effect of wildfire on hydrology, and developed a novel Budyko decomposition method to separate climatic and disturbance effects on streamflow. Using a set of 17 watersheds in southern California, I showed that while traditional metrics like changes in flow or runoff ratio might not detect a disturbance effect from wildfire due to confounding climate signals, the Budyko framework can be used successfully for statistical change detection. The method was used to estimate hydrologic recovery timescales that varied between 5 and 45 years, with an increase of about 4 years of recovery time per 10% of the watershed burned. Next, in Chapter 3 I used a meta-analysis approach to examine the effect of wildfire on water quality, using data from 121 catchments around the world. Analyzing the changes in concentrations of stream water nutrients, including carbon, nitrogen, and phosphorus, I showed that concentrations generally increased after fire. While a large amount of variability existed in the data, we found concurrent increases in the constituents after fire highlighting tight coupling of the biogeochemical cycles. Most interestingly, we found fire to increase the concentrations of biologically active nutrients like nitrate and phosphate at a greater rate than total nitrogen and phosphorus, with median increases of 40-60% in the nitrate to TN, and SRP to TP ratios. Next, I conducted an analysis of both water quality and hydrology together after fire in Chapter 4, using a set of 29 wildfire-impacted watersheds in the United States. Concentration-discharge relationships can be used to reveal pathways and sources of elements exported from watersheds, and my overall hypothesis was that these relationships change in post-fire landscapes. I developed a new methodology, using k-means clustering, to classify watersheds as chemostatic, dilution, mobilization and chemodynamic, and explored how their position within the cluster changed in post-fire landscapes. I found that the behavior of nitrate and ammonium was increasingly chemostatic after fire, while behavior of total nitrogen, phosphorus, and organic phosphorus was increasingly mobilizing after fire. Finally, I developed a coupled hydrology-vegetation-biogeochemistry model to simulate and elucidate processes controlling the impact of harvesting on downstream waters. I focused on the Turkey Lakes watershed where a significant amount of data has been collected on vegetation and soil nutrient dynamics, in addition to traditional streamflow and water quality metrics, and developed a novel multi-part calibration process that used measured data on stream, forest, and soil characteristics and dynamics. Future work would involve using the model to explore the data driven relationships that have been developed in the earlier chapters of the paper. The work presented in this dissertation highlights new small and large-scale relationships between disturbances in forested watersheds and effects on downstream waters. With more threats predicted to escalate and overlap in the coming years, the novel results and methodologies that I have presented here should contribute to improving land and water management
    • …
    corecore