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Perturbed Strong Stability Preserving Time-Stepping Methods For Hyperbolic PDEsHadjimichael, Yiannis 30 September 2017 (has links)
A plethora of physical phenomena are modelled by hyperbolic partial differential
equations, for which the exact solution is usually not known. Numerical methods
are employed to approximate the solution to hyperbolic problems; however, in many
cases it is difficult to satisfy certain physical properties while maintaining high order
of accuracy. In this thesis, we develop high-order time-stepping methods that
are capable of maintaining stability constraints of the solution, when coupled with
suitable spatial discretizations. Such methods are called strong stability preserving
(SSP) time integrators, and we mainly focus on perturbed methods that use both
upwind- and downwind-biased spatial discretizations.
Firstly, we introduce a new family of third-order implicit Runge–Kuttas methods
with arbitrarily large SSP coefficient. We investigate the stability and accuracy of
these methods and we show that they perform well on hyperbolic problems with large
CFL numbers. Moreover, we extend the analysis of SSP linear multistep methods to
semi-discretized problems for which different terms on the right-hand side of the
initial value problem satisfy different forward Euler (or circle) conditions. Optimal
perturbed and additive monotonicity-preserving linear multistep methods are studied
in the context of such problems. Optimal perturbed methods attain augmented
monotonicity-preserving step sizes when the different forward Euler conditions are
taken into account. On the other hand, we show that optimal SSP additive methods achieve a monotonicity-preserving step-size restriction no better than that of the corresponding
non-additive SSP linear multistep methods. Furthermore, we develop the
first SSP linear multistep methods of order two and three with variable step size, and
study their optimality. We describe an optimal step-size strategy and demonstrate
the effectiveness of these methods on various one- and multi-dimensional problems.
Finally, we establish necessary conditions to preserve the total variation of the solution
obtained when perturbed methods are applied to boundary value problems.
We implement a stable treatment of nonreflecting boundary conditions for hyperbolic
problems that allows high order of accuracy and controls spurious wave reflections.
Numerical examples with high-order perturbed Runge–Kutta methods reveal that this
technique provides a significant improvement in accuracy compared with zero-order
extrapolation.
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Analysis of Regulated Drugs Using Chromatographic and Spectrophotometric Techniques Coupled with Spectroscopy An Orthogonal Approach to Protecting Public HealthNickum, Elisa A. 30 October 2017 (has links)
No description available.
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AKAP7 Degrades 2-5A Mediators of the Interferon Antiviral ResponseGusho, Elona 08 December 2015 (has links)
No description available.
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Investigation of Sustained Detonation Devices: the Pulse Detonation Engine-Crossover System and the Rotating Detonation Engine SystemDriscoll, Robert B. 26 May 2016 (has links)
No description available.
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Cyclic di-GMP Regulates Motility, Biofilm Formation, and Desiccation Tolerance in Acinetobacter baumanniiReynolds, Garrett 01 August 2022 (has links)
Acinetobacter baumannii is an increasingly multidrug-resistant pathogen contributing to hospital-acquired infections necessitating the discovery of novel treatments. A bacterial second messenger, cyclic diguanosine monophosphate (cyclic di-GMP), can regulate various persistence factors that are potentially advantageous for survival in hospital environments. Cyclic di-GMP–modulating enzymes and cyclic di-GMP–binding effectors predictively are encoded in the Acinetobacter baumannii genome. I hypothesized that cyclic di-GMP controls motility, biofilm formation, and desiccation tolerance in Acinetobacter baumannii. Disrupting cyclic di-GMP–modulating enzymes or cyclic di-GMP–binding effectors should alter the regulatory effectiveness of these phenotypes. I tested the multidrug-resistant isolate Acinetobacter baumannii strain AB5075 and identified several transposon mutants that altered twitching motility, biofilm formation, and desiccation tolerance; these results suggest that cyclic di-GMP plays a role during these three responses in Acinetobacter baumannii AB5075. Inhibiting these cyclic di-GMP signaling pathways could produce novel mechanisms to combat this pathogen in the hospital environment.
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Singularity Formation in the Deterministic and Stochastic Fractional Burgers EquationsRamírez, Elkin Wbeimar January 2020 (has links)
Motivated by the results concerning the regularity of solutions to the fractional Navier-Stokes system and questions about the influence of noise on the formation of singularities in hydrodynamic models, we have explored these two problems in the context of the fractional 1D Burgers equation. First, we performed highly accurate numerical computations to characterize the dependence of the blow-up time on the the fractional dissipation exponent in the supercritical regime. The problem was solved numerically using a pseudospectral method where integration in time was performed using a hybrid method combining the Crank-Nicolson and a three-step Runge-Kutta techniques. A highlight of this approach is automated resolution refinement. The blow-up time was estimated based on the time evolution of the enstrophy (H1 seminorm) and the width of the analyticity strip. The consistency of the obtained blow-up times was verified in the limiting cases. In the second part of the thesis we considered the fractional Burgers equation in the presence of suitably colored additive noise. This problem was solved using a stochastic Runge-Kutta method where the stochastic effects were approximated using a Monte-Carlo method. Statistic analysis of ensembles of stochastic solutions obtained for different noise magnitudes indicates that as the noise amplitude increases the distribution of blow-up times becomes non-Gaussian. In particular, while for increasing noise levels the mean blow-up time is reduced as compared to the deterministic case, solutions with increased existence time also become more likely. / Thesis / Master of Science (MSc)
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On harmonic and biharmonic Bezier surfacesMonterde, J., Ugail, Hassan January 2004 (has links)
Yes
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Implementing automatic design optimisation in an interactive environmentUgail, Hassan, Bloor, M.I.G., Wilson, M.J. January 2000 (has links)
Yes
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Optimal design of thin-walled structures by means of efficient parameterizationUgail, Hassan January 2002 (has links)
Yes
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Method of modelling the compaction behaviour of cylindrical pharmaceutical tabletsAhmat, Norhayati, Ugail, Hassan, Gonzalez Castro, Gabriela January 2010 (has links)
No / The mechanisms involved for compaction of pharmaceutical powders have become a crucial step in the development cycle for robust tablet design with required properties. Compressibility of pharmaceutical materials is measured by a force-displacement relationship which is commonly analysed using a well known method, the Heckel model. This model requires the true density and compacted powder mass value to determine the powder mean yield pressure. In this paper, we present a technique for shape modelling of pharmaceutical tablets based on the use of partial differential equations (PDEs). This work also presents an extended formulation of the PDE method to a higher dimensional space by increasing the number of parameters responsible for describing the surface in order to generate a solid tablet. Furthermore, the volume and the surface area of the parametric cylindrical tablet have been estimated numerically. Finally, the solution of the axisymmetric boundary value problem for a finite cylinder subject to a uniform axial load has been utilised in order to model the displacement components of a compressed PDE-based representation of a tablet. The Heckel plot obtained from the developed model shows that the model is capable of predicting the compaction behaviour of pharmaceutical materials since it fits the experimental data accurately.
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