Current Search: Hoflich, Peter A. (x)
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 Title
 Diffuse Interface Method for TwoPhase Incompressible Flows.
 Creator

Han, Daozhi, Wang, Xiaoming, Höflich, Peter, Gallivan, Kyle A., Kopriva, David A., Oberlin, Daniel M., Sussman, Mark, Florida State University, College of Arts and Sciences,...
Show moreHan, Daozhi, Wang, Xiaoming, Höflich, Peter, Gallivan, Kyle A., Kopriva, David A., Oberlin, Daniel M., Sussman, Mark, Florida State University, College of Arts and Sciences, Department of Mathematics
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In this contribution, we focus on the study of multiphase flow using the phase field approach. Multiphase flow phenomena are ubiquitous. Common examples include coupled atmosphere and ocean system (air and water), oil reservoir (water, oil and gas), cloud and fog (water vapor, water and air). Multiphase flows also play an important role in many engineering and environmental science applications. For two fluids with matched density, the CahnHilliardNavierStokes system (CHNS) is a well...
Show moreIn this contribution, we focus on the study of multiphase flow using the phase field approach. Multiphase flow phenomena are ubiquitous. Common examples include coupled atmosphere and ocean system (air and water), oil reservoir (water, oil and gas), cloud and fog (water vapor, water and air). Multiphase flows also play an important role in many engineering and environmental science applications. For two fluids with matched density, the CahnHilliardNavierStokes system (CHNS) is a well accepted phase field model. We propose a novel second order in time numerical scheme for solving the CHNS system. The scheme is based on a second order convexsplitting for the CahnHilliard equation and pressureprojection for the NavierStokes equation. We show that the scheme is massconservative, satisfies a modified energy law and is therefore unconditionally stable. Moreover, we prove that the scheme is unconditionally uniquely solvable at each time step by exploring the monotonicity associated with the scheme. Thanks to the simple coupling of the scheme, we design an efficient Picard iteration procedure to further decouple the computation of CahnHilliard equation and NavierStokes equation. We implement the scheme by the mixed finite element method. Ample numerical experiments are performed to validate the accuracy and efficiency of the numerical scheme. In addition, we propose a novel decoupled unconditionally stable numerical scheme for the simulation of twophase flow in a HeleShaw cell which is governed by the CahnHilliardHeleShaw system (CHHS). The temporal discretization of the CahnHilliard equation is based on a convexsplitting of the associated energy functional. Moreover, the capillary forcing term in the Darcy equation is separated from the pressure gradient at the time discrete level by using an operatorsplitting strategy. Thus the computation of the nonlinear CahnHilliard equation is completely decoupled from the update of pressure. Finally, a pressurestabilization technique is used in the update of pressure so that at each time step one only needs to solve a Poisson equation with constant coefficient. We show that the scheme is unconditionally stable. Numerical results are presented to demonstrate the accuracy and efficiency of our scheme. The CHNS system and CHHS system are two widely used phase field models for twophase flow in a single domain (either conduit or HeleShaw cell/porous media). There are applications such as flows in unconfined karst aquifers, karst oil reservoir, proton membrane exchange fuel cell, where multiphase flows in conduits and in porous media must be considered together. Geometric configurations that contain both conduit (or vug) and porous media are termed karstic geometry. We present a family of phase field (diffusive interface) models for two phase flow in karstic geometry. These models, the socalled CahnHilliardStokesDarcy system, together with the associated interface boundary conditions are derived by utilizing Onsager's extremum principle. The models derived enjoy physically important energy laws and are consistent with thermodynamics. For the analysis of the CahnHilliardStokesDarcy system, we show that there exists at least a global in time finite energy solution by the compactness argument. A weakstrong uniqueness result is also established, which says that the strong solution, if exists, is unique in the class of weak solutions. Finally, we propose and analyze two unconditionally stable numerical algorithms of first order and second order respectively, for solving the CHSD system. A decoupled numerical procedure for practical implementation of the schemes are also presented. The decoupling is realized through explicit discretization of the velocity in the CahnHilliard equation and extrapolation in time of the interface boundary conditions. At each time step, one only needs to solve a CahnHilliard type equation in the whole domain, a Darcy equation in porous medium, and a Stokes equation in conduit in a separate and sequential fashion. Two numerical experiments, boundary driven and buoyancy driven flows, are performed to illustrate the effectiveness of our scheme. Both numerical simulations are of physical interest for transport processes of twophase flow in karst geometry.
Show less  Date Issued
 2015
 Identifier
 FSU_migr_etd9609
 Format
 Thesis
 Title
 Imprints of Explosion Conditions on LateTime Spectra of Type Ia Supernovae.
 Creator

Diamond, Tiara R., Höflich, Peter, Chicken, Eric, Collins, David C., Prosper, Harrison B., Riley, Mark A., Florida State University, College of Arts and Sciences, Department of...
Show moreDiamond, Tiara R., Höflich, Peter, Chicken, Eric, Collins, David C., Prosper, Harrison B., Riley, Mark A., Florida State University, College of Arts and Sciences, Department of Physics
Show less  Abstract/Description

Type Ia supernovae (SNe Ia) play a vital role in the discrimination of different cosmological models. These events have been shown to be standardizable based on properties of their light curves during the earlytime photospheric phase. However, the distribution of types of progenitor system, the explosion trigger, and the physics of the explosion are still an active topic of discussion. The details of the progenitors and explosion may provide insight into the variation seen in Type Ia...
Show moreType Ia supernovae (SNe Ia) play a vital role in the discrimination of different cosmological models. These events have been shown to be standardizable based on properties of their light curves during the earlytime photospheric phase. However, the distribution of types of progenitor system, the explosion trigger, and the physics of the explosion are still an active topic of discussion. The details of the progenitors and explosion may provide insight into the variation seen in Type Ia supernova light curves and spectra, and therefore, allow for additional methods of standardization among the group. Latetime nearinfrared spectral observations for SNe Ia show numerous strong emission features of forbidden line transitions of cobalt and iron, tracing the central distribution of irongroup burning products. As the spectrum ages, the cobalt features fade as expected from the decay of 56Co to 56Fe. This work will show that the strong and isolated [Fe II] emission line at 1.644 μm provides a unique tool to analyze nearinfrared spectra of SNe Ia. Several new methods of analysis will be demonstrated to determine some of the initial conditions of the system. The initial central density, ρc, and the extent of mixing in the central regions of the explosion have signatures in the line profiles of latetime spectra. An embedded magnetic field, B, of the white dwarf can be determined using the evolution of the lines profiles. Currently magnetic field effects are not included in the hydrodynamics and radiation transport of simulations of SNe Ia. Normalization of spectra to the 1.644 μm line allows separation of features produced by stable versus unstable isotopes of iron group elements. Implications for potential progenitor systems, explosion mechanisms, and the origins and morphology of magnetic fields in SNe Ia, in addition to limitations of the method, are discussed. Observations of the latetime nearinfrared emission spectrum at multiple epochs allow for the first ever analysis of the evolution of the 1.644 μm line profile for a SNe Ia. These latetime data are really pushing the observational limits of current groundbased telescopes in terms of a dim target and low signaltonoise. The new analysis method presented in this work is used on observations of SN 2005df to constrain the initial conditions of those systems. Finally, the details and limitations of the method are presented for use with SN 2014J and future timeseries observations, which will dramatically increase in number and signaltonoise with the nextgeneration of telescopes and missions.
Show less  Date Issued
 2015
 Identifier
 FSU_migr_etd9322
 Format
 Thesis
 Title
 Measurement of the ²⁵Al(d,n) ²⁶Si(P) Reaction at RESOLUT.
 Creator

Baker, Jessica, Wiedenhöver, Ingo, Fuelberg, Henry E., Tabor, Samuel Lynn, Volya, Alexander, Höflich, Peter A., Florida State University, College of Arts and Sciences,...
Show moreBaker, Jessica, Wiedenhöver, Ingo, Fuelberg, Henry E., Tabor, Samuel Lynn, Volya, Alexander, Höflich, Peter A., Florida State University, College of Arts and Sciences, Department of Physics
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Studies of rpprocess nucleosynthesis in stellar explosions show that establishing the lowest l = 0 and l = 1 resonances is the most important step to determine reaction rates in the astrophysical rp– process path. In an experiment performed at the resolut radioactive beam facility of Florida State University, we studied the 25Al(d,n)26Si reaction in inverse kinematics to establish the spectrum of the lowest l = 0 and l = 1 resonances. We observed 4 resonances in 26 Si at 5923 keV, 6357 keV,...
Show moreStudies of rpprocess nucleosynthesis in stellar explosions show that establishing the lowest l = 0 and l = 1 resonances is the most important step to determine reaction rates in the astrophysical rp– process path. In an experiment performed at the resolut radioactive beam facility of Florida State University, we studied the 25Al(d,n)26Si reaction in inverse kinematics to establish the spectrum of the lowest l = 0 and l = 1 resonances. We observed 4 resonances in 26 Si at 5923 keV, 6357 keV, 6737 keV, and 7458 keV. We establish the lowest l = 0 resonance at 5.923 keV, 0.409 MeV above proton separation. The result is consistent with the previous experiment performed at FSU by Peplowski et al. however now with significantly larger statistics and detection of the heavy ion decay in coincidence with the proton. We determine upper and lower limits on Γ p and calculate the astrophysical reaction rate. We establish the proton density and temperature conditions in which galactic through the 25Al(d,n)26Sireaction path.
Show less  Date Issued
 2015
 Identifier
 FSU_2016SP_Baker_fsu_0071E_12983
 Format
 Thesis
 Title
 Nonlinear SchrödingerType Systems: Complex Lattices and NonParaxiality.
 Creator

Cole, Justin, Musslimani, Ziad H., Höflich, Peter A., Wang, Xiaoming, Moore, M. Nicholas J. (Matthew Nicholas J.), Florida State University, College of Arts and Sciences,...
Show moreCole, Justin, Musslimani, Ziad H., Höflich, Peter A., Wang, Xiaoming, Moore, M. Nicholas J. (Matthew Nicholas J.), Florida State University, College of Arts and Sciences, Department of Mathematics
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This thesis investigates nonlinear systems that are dispersive and conservative in nature and wellapproximated by the nonlinear Schrödinger (NLS) equation. The NLS equation is the prototypical equation for describing such phenomena and it has been utilized in a large number of physical systems. This work considers novel applications and exotic parameter regimes that fall inside the class of solutions well described by nonlinear Schrödingertype systems. A brief historical, physical, and...
Show moreThis thesis investigates nonlinear systems that are dispersive and conservative in nature and wellapproximated by the nonlinear Schrödinger (NLS) equation. The NLS equation is the prototypical equation for describing such phenomena and it has been utilized in a large number of physical systems. This work considers novel applications and exotic parameter regimes that fall inside the class of solutions well described by nonlinear Schrödingertype systems. A brief historical, physical, and mathematical introduction to deriving the NLS equation and its variants is presented. The topics considered in detail cover optical systems in various media and are naturally divided into two parts: nonparaxiality through the inclusion of higherorder dispersion/diffraction and beam propagation in the presence of complex lattices. The higherorder dispersion/diffraction effects on soliton solutions are considered in detail. The propagation of a short soliton pulse as it travels down a fiber optic in the presence of a linear timeperiodic potential is considered. Due to the short duration of the pulse fourthorder dispersive effects are relevant. The band gap structure is determined using FloquetBloch theory and the shape of its dispersion curves as a function of the fourthorder dispersion coupling constant β is discussed. Several features not observed in the absence of highorder dispersion (β=0) are highlighted, such as a nonzero threshold value of potential strength below which there is no band gap and the formation of novel localized modes at large potential amplitudes. A higher order two band tight binding model is introduced that captures and intuitively explains most of the numerical results related to the spectral bands. Lattice solitons corresponding to spectral eigenvalues lying in the semiinfinite and first band gaps are constructed. Stability of various localized lattice modes is studied via linear stability analysis and direct numerical simulation. Next the spectral transverse instabilities of onedimensional solitary wave solutions to the twodimensional NLS equation with biharmoinc diffraction and subject to higherdimensional perturbations are studied. Physically, the inclusion of the biharmonic term corresponds to spatial beams with a narrow width in comparison to their wavelength. A linear boundary value problem governing the evolution of the transverse perturbations is derived. The eigenvalues of the perturbations are numerically computed and a finite band of unstable transverse modes is found to exist. In the long wavelength limit an asymptotic formula for the perturbation growth rate that agrees well with the numerical findings. Using a variational formulation based on Lagrangian model reduction, an approximate expression for the perturbation eigenvalues is obtained and its validity is compared with both the asymptotic and numerical results. The dynamics of a onedimensional soliton stripe in the presence of a transverse perturbation is studied using direct numerical simulations. The second half of the dissertation is concerned with beam propagation in the presence of complex lattices, in particular lattices that possess paritytime (PT) symmetries. A new family of nonhermitian optical potentials given in terms of double exponential periodic functions is introduced. The center of PTsymmetry is not around zero and the potential satisfies a shifted PTsymmetry relation at two distinct locations. These novel refractive index modulations are examined from the perspective of optical lattices that are homogeneous along the propagation direction. The diffraction dynamics, abrupt phase transitions in the eigenvalue spectrum and exceptional points in the band structure are studied in detail. In addition, the nonlinear properties of coherent structures in Kerr media is probed. The spatial symmetries of such lattice solitons follow the shifted PTsymmetric relations. Furthermore, such lattice solitons have a power threshold and their linear and nonlinear stability is critically dependent on their spatial symmetry point. In the final chapter a class of exact multicomponent constant energy solutions to a Manakov system in the presence of an external PTsymmetric complex potential is constructed. This type of uniform wave pattern displays a nontrivial phase whose spatial dependence is induced from the lattice structure. In this regard, light can propagate without scattering while retaining its original form despite the presence of inhomogenous gain and loss. The constantintensity continuous waves are then used to perform a modulational instability analysis in the presence of both nonhermitian media and cubic nonlinearity. A linear stability eigenvalue problem is formulated that governs the dynamical evolution of the periodic perturbation and its spectrum is numerically determined using FourierFloquetBloch theory. The stability of the selffocusing and defocusing cases is considered and compared to the zeropotential results. Our linear stability results are supplemented with direct (nonlinear) numerical simulations.
Show less  Date Issued
 2016
 Identifier
 FSU_2016SP_Cole_fsu_0071E_13102
 Format
 Thesis
 Title
 Mapping Circumstellar Matter With Polarized Light: The Case Of Supernova 2014j In M82.
 Creator

Yang, Yi, Wang, Lifan, Baade, Dietrich, Brown, Peter J., Cikota, Aleksandar, Cracraft, Misty, Hoflich, Peter A., Maund, Justyn R., Patat, Ferdinando, Sparks, William B.,...
Show moreYang, Yi, Wang, Lifan, Baade, Dietrich, Brown, Peter J., Cikota, Aleksandar, Cracraft, Misty, Hoflich, Peter A., Maund, Justyn R., Patat, Ferdinando, Sparks, William B., Spyromilio, Jason, Stevance, Heloise F., Wang, Xiaofeng, Wheeler, J. Craig
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Optical polarimetry is an effective way of probing the environment of a supernova for dust. We acquired linear HST ACS/WFC polarimetry in bandsF475W, F606W, and F775W of the supernova (SN) 2014J in M82 at six epochs from similar to 277 days to similar to 1181 days after the Bband maximum. The polarization measured at day 277 shows conspicuous deviations from other epochs. These differences can be attributed to at least similar to 10(6) Mcircle dot of circumstellar dust located at a...
Show moreOptical polarimetry is an effective way of probing the environment of a supernova for dust. We acquired linear HST ACS/WFC polarimetry in bandsF475W, F606W, and F775W of the supernova (SN) 2014J in M82 at six epochs from similar to 277 days to similar to 1181 days after the Bband maximum. The polarization measured at day 277 shows conspicuous deviations from other epochs. These differences can be attributed to at least similar to 10(6) Mcircle dot of circumstellar dust located at a distance of similar to 5 x 10(17) cm from the SN. The scattering dust grains revealed by these observations seem to be aligned with the dust in the interstellar medium that is responsible for the large reddening toward the supernova. The presence of this circumstellar dust sets strong constraints on the progenitor system that led to the explosion of SN 2014J; however, it cannot discriminate between singleand doubledegenerate models.
Show less  Date Issued
 20180210
 Identifier
 FSU_libsubv1_wos_000424897400005, 10.3847/15384357/aaa76a
 Format
 Citation
 Title
 Latetime Flattening Of Type Ia Supernova Light Curves: Constraints From.
 Creator

Yang, Yi, Wang, Lifan, Baade, Dietrich, Brown, Peter J., Cikota, Aleksandar, Cracraft, Misty, Hoflich, Peter A., Maund, Justyn R., Patat, Ferdinando, Sparks, William B.,...
Show moreYang, Yi, Wang, Lifan, Baade, Dietrich, Brown, Peter J., Cikota, Aleksandar, Cracraft, Misty, Hoflich, Peter A., Maund, Justyn R., Patat, Ferdinando, Sparks, William B., Spyromilio, Jason, Stevance, Heloise F., Wang, Xiaofeng, Wheeler, J. Craig
Show less  Abstract/Description

The very nearby Type Ia supernova 2014J in M82 offers a rare opportunity to study the physics of thermonuclear supernovae at extremely late phases (greater than or similar to 800 days). Using the Hubble Space Telescope, we obtained 6 epochs of highprecision photometry for SN 2014J from 277 days to 1181 days past the Bband maximum light. The reprocessing of electrons and Xrays emitted by the radioactive decay chain Co57 > Fe57 is needed to explain the significant flattening of both the...
Show moreThe very nearby Type Ia supernova 2014J in M82 offers a rare opportunity to study the physics of thermonuclear supernovae at extremely late phases (greater than or similar to 800 days). Using the Hubble Space Telescope, we obtained 6 epochs of highprecision photometry for SN 2014J from 277 days to 1181 days past the Bband maximum light. The reprocessing of electrons and Xrays emitted by the radioactive decay chain Co57 > Fe57 is needed to explain the significant flattening of both the F606Wband and the pseudobolometric light curves. The flattening confirms previous predictions that the latetime evolution of type Ia supernova luminosities requires additional energy input from the decay of Co57. By assuming the F606Wband luminosity scales with the bolometric luminosity at similar to 500 days after the Bband maximum light, a mass ratio Ni57/Ni56 similar to 0.065(0.005)(+0.004) is required. This mass ratio is roughly similar to 3 times the solar ratio and favors a progenitor white dwarf with a mass near the Chandrasekhar limit. A similar fit using the constructed pseudobolometric luminosity gives a mass ratio Ni57/Ni56 similar to 0.066(0.009)(+0.008) . Astrometric tests based on the multiepoch HST ACS/WFC images reveal no significant circumstellar light echoes in between 0.3 and 100 pc from the supernova.
Show less  Date Issued
 20180110
 Identifier
 FSU_libsubv1_wos_000419798700006, 10.3847/15384357/aa9e4c
 Format
 Citation
 Title
 Scale Setting and Topological Observables in Pure SU(2) LGT.
 Creator

Clarke, David A. (David Anthony), Berg, Bernd A., Reina, Laura, AlbrechtSchmitt, Thomas E., Yohay, Rachel, Höflich, Peter, Florida State University, College of Arts and...
Show moreClarke, David A. (David Anthony), Berg, Bernd A., Reina, Laura, AlbrechtSchmitt, Thomas E., Yohay, Rachel, Höflich, Peter, Florida State University, College of Arts and Sciences, Department of Physics
Show less  Abstract/Description

In this dissertation, we investigate the approach of pure SU(2) lattice gauge theory to its continuum limit using the deconfinement temperature, six gradient scales, and six cooling scales. We find that cooling scales exhibit similarly good scaling behavior as gradient scales, while being computationally more efficient. In addition, we estimate systematic error in continuum limit extrapolations of scale ratios by comparing standard scaling to asymptotic scaling. Finally we study topological...
Show moreIn this dissertation, we investigate the approach of pure SU(2) lattice gauge theory to its continuum limit using the deconfinement temperature, six gradient scales, and six cooling scales. We find that cooling scales exhibit similarly good scaling behavior as gradient scales, while being computationally more efficient. In addition, we estimate systematic error in continuum limit extrapolations of scale ratios by comparing standard scaling to asymptotic scaling. Finally we study topological observables in pure SU(2) using cooling to smooth the gauge fields, and investigate the sensitivity of cooling scales to topological charge. We find that large numbers of cooling sweeps lead to metastable charge sectors, without destroying physical instantons, provided the lattice spacing is fine enough and the volume is large enough. Continuum limit estimates of the topological susceptibility are obtained, of which we favor χ 1/4 /T c = 0.643(12). Differences between cooling scales in different topological sectors turn out to be too small to be detectable within our statistical error.
Show less  Date Issued
 2018
 Identifier
 2018_Fall_Clarke_fsu_0071E_14832
 Format
 Thesis