(An) efficient computational method for shock hydrodynamics using particle-like discontinuities

Lee, Jae-wan Graduate School, Yonsei University 2018 국내박사

A novel computational method for shock hydrodynamics using particle-like discontinuities called “hugonions” is introduced. Hydrodynamics, the field of study concerned with the flow of fluids, is often described by the Euler equations, which tacitly assumes the continuity and smoothness of the flow field. The existence of flow discontinuities such as shocks and contact discontinuities is thus at odds with the basic assumptions of the Euler equations, and special techniques are required to deal with flow discontinuities in the computation of shock hydrodynamics. Currently, there are three major approaches to modeling flow discontinuities: artificial viscosity, linear hybridization, and Godunov’s method. Among these approaches, Godunov’s method can treat flow discontinuities as strict mathematical discontinuities, and therefore is most suited to computation of shock hydrodynamics. However, Godunov’s method suffers from the heavy computational cost associated with the solution of the Riemann problem, which must be obtained at every inter-cell boundary at each time step. Also, Godunov’s method is not immune to the artificial smearing of discontinuities, although to a lesser degree compared with other methods. Here, we propose a computational scheme that computes shock hydrodynamics more accurately and efficiently by adopting mathematical discontinuities as a numerical device. The discontinuities are called hugonions because they satisfy the Rankine-Hugoniot relations and exhibit particle-like characteristics: they travel, interact with each other, and are annihilated if certain conditions are met. Discontinuous phenomena are always represented and computed as mathematical discontinuities, and thus our scheme is free from smearing unlike the existing methods. It also has the advantage that it is able to both capture and evolve the flow field with relatively small number of elements. The feasibility and performance of the method are evaluated using well-known benchmark problems such as the Sod shock tube problem, Woodward and Colella’s two interacting blast waves problem, and blast waves. It is confirmed that our scheme improves the computational performance in terms of both accuracy and efficiency. It is shown to be particularly effective in computation of the progressive shock hydrodynamics. Lastly, an extension of the hugonion scheme to detonation is studied. The hugonion scheme is merged into the classical theories of detonation such as the Chapman-Jouguet (CJ) and Zel’dovich-von Neumann-Döring (ZND) models. The extended hugonion scheme is used to simulate detonation shocks and their interactions with boundaries. 본 논문에서는 입자성 불연속면을 이용하는 새로운 충격파 유동 계산 기법을 소개한다. 유체동역학은 일반적으로 오일러 방정식으로 기술되며, 유동장의 연속과 미분 가능을 전제로 한다. 그러나 충격파 및 접촉 불연속면과 같은 유동 내의 불연속 현상은 오일러 방정식의 기본 전제와 상충하기 때문에, 이를 다룰 수 있는 특수한 기법이 요구된다. 대표적으로 인공 점성, 선형 하이브리드화, 고두노프 기법이 있으며, 이 중 고두노프 기법은 유동 내 불연속 현상을 리만 문제를 통하여 수학적 불연속으로 다루기 때문에 충격파 유동 계산 기법에 가장 적합하다. 그러나 고두노프 기법은 매 계산 시간 간격마다 모든 요소 경계에서의 발생하는 리만 문제를 풀어야하기 때문에 오랜 계산 시간이 요구되는 단점을 갖는다. 또한, 고두노프 기법은 불연속면의 번짐 현상에서 자유롭지 못하다. 이와 같은 기존 기법들의 한계를 극복하기 위해, 수학적 불연속을 계산 요소로 채택함으로써 충격파 유동을 더욱 정확하고 효율적으로 계산할 수 있는 새로운 계산 기법을 제안한다. 본 기법에 사용된 수학적 불연속은 랭킨-휴고니오 관계식을 만족하기에 휴고니온이라고 명명되었으며, 이동, 상호작용, 소멸과 같은 입자와 같은 특성을 가진다. 본 기법에서는 불연속 현상이 항상 수학적 불연속으로 나타내어지고 계산되기 때문에 기존 기법들과 달리 불연속면의 번짐이 발생하지 않으며, 또한, 상대적으로 적은 수의 계산 요소를 이용하여 계산이 가능하다는 장점을 갖는다. 본 기법의 적용가능성과 계산 성능은 여러 가지 벤치마크 문제를 수행함으로써 검증되었다. 검증 결과, 기존 기법에 비해 정확성과 효율성이 모두 개선됨을 확인하였다. 끝으로 CJ 이론, ZND 모델과 같은 고전적인 폭굉파 이론에 본 이론을 접목하여, 폭굉파 계산이 가능하도록 기법을 확장하였다.

Relativistic approaches to compact stars and their applications

김진호 서울대학교 대학원 2012 국내박사

이 학위 논문의 주된 내용은 물질을 포함하는 아인슈타인 방정식의 수치적인 풀이이다. 물질의 운동은 상대론적인 유체역학으로 기술하였는데 여기서 우리는 다음과 같은 두 가지 방법을 이용하였다. 첫째 아인슈타인 방정식을 어떠한 근사 없이 완전히 푸는 방법이다. 두 번째 방법은 ``pseudo-Newtonain'' 방법인데, 시공간을 중력 퍼텐셜의 1차 항까지만 기술하여, 간단히 뉴턴 중력으로 기술하지만 다른 특수 상대론적인 효과를 모두 고려할 수 있는 방법이다. 여기서 중력 포텐셜은 Poisson 방정식으로 풀 수 있는데 여기에서 뉴턴 방정식의 질량 밀도만 포함한 것과는 다르게 모든 에너지의 소스를 모두 포함한다. 이 에너지는 ``active mass density‘’로 불리는데 유체의 운동에너지, 내부 에너지, 압력에 의한 에너지, 질량에 의한 에너지가 포함된다. 따라서 이 방법은 상대론적인 운동을 하거나 상대론적인 상태방정식을 써야하는 중성자별에 응용할 수 있다. 먼저 위 두 가지 방법의 식을 이용하여 중성자별과 같이 정역학적 평형 상태에 있고 회전하는 별에 대한 해를 찾았다. 정역학적 평형 상태란 압력과 중력이 평형 상태를 이루는 것으로 유체역학 방정식 중 운동량 방정식을 이용하여 구할 수 있다. 일반상대론에서 평형상태의 회전하지 않는 별에 대한 식을 Tolmann-Oppenheimer-Volkoff (TOV) 방정식이라 하는데 이 방정식을 풀고 중심 밀도의 변화에 대한 여러 해의 변화를 보며 안정성(stability)에 대하여 기술하였다. 또한 pseudo-Newtonian 방법에서 회전하는 정역학적 평형 상태에 있는 해를 Hachisu의 self-consistent field (SCF) 방법을 사용하여 구하였다. 회전 타원체(spheroid)와 환상면체(toroid)의 해를 구하였으며 이 두 가지 위상의 해의 시퀀스(sequence)도 구하였다. 그리고 여기서 구한 해와 일반상대론 적인 해와 비교를 해보았는데 그 차이는 5\% 내로 일치함을 알 수 있었다. 그 다음으로 두 가지 방법에 대한 유체역학 코드를 개발 하였는데 이 코드는 고밀도 천체가 포함된 여러 천체물리학적 현상을 기술 하는데 사용할 수 있다. 유체역학 방정식은 유한체적법(finite volume method)을 이용하여 기술하였고 유체역학 방정식을 풀 때 생기는 여러 불연속적인 해를 다루기 위하여 high resolution shock capturing (HRSC) 기술을 이용하였다. HRSC에서 플럭스를 찾기 위해서는 그리드 사이사이의 값들을 찾아내야 하는데 이 방법을 reconstruction이라고 한다. 여러 2차 정확도를 가지는 법 그리고 그것보다 높은 차수를 이용한 방법(PPM, ENO, WENO)이 코드에 구현되어 있다. 유체의 방정식은 시간과 공간에 대한 편미분 방정식 형태인데 method of line (MoL)을 이용하면 전미분 방정식 형태로 전환할 수 있고 이것은 2차 또는 3차 Runge-Kutta 방법으로 풀 수 있다. 3차 Runge-Kutta 방법 까지는 total variation diminishing (TVD) 방법으로 알려져 있다. 시공간을 기술하는 metric의 진화는 ADM 방법 보다 훨씬 안정적인 BSSN방법을 이용하여 구현하였다. 이것은 유체방정식을 푸는 방식과는 다르게 유한차분법(finite difference method)을 이용하였고 시간 미분은 iterative Crank-Nicholson방법 또는 Runge-Kutta방법을 이용하였다. pseudo-Newtonian방법의 중력 퍼텐셜은 타원형 편미분 방정식(elliptic equation)으로 멀티그리드(multigrid)방법을 이용하였다. 경계 값을 간단히 하기 위하여 축을 콤팩트화(coordinate compactification) 하여 무한대까지 확장하였다. 코드의 유효성을 확인하기 위하여 여러 가지 테스트를 진행하였다. 첫 번째, shock tube 실험에서는 여러 가지 불연속적인 해에서 해석적 해와 잘 맞는 결과를 보여주었다. 두 번째, 앞에서 구한 회전하는 또는 회전 하지 않는 정역학적 평형 상태의 별의 진화에서는 중심밀도와 질량, 각운동량이 잘 보존 되는지 검사 하였고 이 실험에서 1 역학적 시간동안 중심밀도의 상대적인 변화량은 $4\times 10^{-6}$, 전체 질량과 각운동량은 $5\times 10^{-7}$과 $2\times 10^{-6}$ 정도를 보여주었다. 이 학위 논문의 천체물리학적으로 중요한 목표 중 하나는 펄서 글리치(pulsar glitch)에서 나오는 중력파이다. 이 중력파는 다음 세대의 중력파 검출기에서 관측될 수 있는 하나의 후보 중에 하나이다. 중력파의 세기와 주파수를 알기 위하여 앞에서 구한 회전하는 중성자별에 펄서 글리치를 잘 모방할 수 있는 섭동을 넣어 pseudo-Newtonian방법으로 진화를 시켰고 이 수치 실험에서 4극자 모멘트(quadrupole moment)의 시간에 따른 변화를 보았다. 이전 ${}^2 f$ 모드만 고려한 이전 연구와는 다르게, 우리 연구는 여러 모드들이 섭동의 방법에 따라 그리고 중성자별 모델에 따라 다르게 다양하게 나타났다. 대부분의 경우에서 가장 강한 중력파를 내는 모드는 ${}^2 p_1$, $H_1$모드로 났고 그 크기는 약 $\sim\times 10^{-25}$ 정도이다. 이것은 지구에서 1 kpc 떨어진 펄서에서 $\Delta\Omega/\Omega=10^{-5}$의 크기를 가지는 글리치가 나타났을 때를 가정한 크기이다. 또한 한 가지 흥미로운 현상 중 하나는, 초유동체 모델의 경우 관성모드(inertial mode)가 잘 나타나는데 주파수가 크지 않아 중력파가 크게 나오지는 않았지만 이 모드는 많은 에너지를 가지고 있어 모드의 크기가 줄어드는 시간이 다른 모드들에 비해 상대적으로 매우 길다. 또한 주파수의 위치가 LIGO 중력파 검출기의 가장 감도가 좋은 밴드에 위치해 있어 중력파 관측을 기대 할 수 있다 This dissertation is primarily concerned with the numerical solution of the Einstein equation having non-vacuum space time. In order to solve study hydrodynamics, we used the approximate approach called ``pseudo-Newtonian'' method as well as full relativistic approach. The pseudo-Newtonian method takes care of the special relativistic effects while the gravitational field is assumed to be Newtonian, but we used the active mass density, which takes into account all forms of energies ingredients such as motions of the fluids, internal energy, pressure energy in addition to the rest mass energy, in the source term of the Poisson's equation. In this approach, the metric is correct up to the first order in the Newtonian potential. Such a treatment could be applicable to the neutron stars with relativistic motions or relativistic equation of state. We present computational method and procedures in both approximate and fully relativistic methods to obtain stationary solutions for rapidly rotating compact stars such as neutron stars. The hydrostatic equation comes from the momentum equation in hydrodynamics. We obtained the solutions of the Tolmann-Oppenheimer-Volkoff (TOV) equation and their sequences of the equilibrium stars changing the central densties. We also describe the stability of the TOV stars from the sequences. In the pseudo-Newtonian approach, we applied the Hachisu's self-consistent field (SCF) method to find spheroidal as well as toroidal sequences of equilibrium solutions. Our approximated solutions show better agreement than Newtonian relativistic hydrodynamic approach that does not take into account the active mass, with general relativistic solutions. The physical quantities such as the peak density, equatorial radii of our solutions agree with general relativistic ones within 5\%. We also develop new computational codes for the evolution of both approaches which can cover various topics in astrophysics involving compact stars. The hydrodynamics equations are solved using finite volume method with High Resolution Shock Capturing(HRSC) technique. We implement several different slope limiters for the 2nd order reconstruction schemes as well as the higher order ones such as PPM, ENO and WENO. We use the method of line (MoL) to convert the mixed spatial-time partial differential equations into the ordinary differential equations with respect to the time only. For the time integration, the 2nd and 3rd order Runge-Kutta methods, which are total variation diminishing (TVD) ones, are applied to our code. The metric field equations are solved by using Baumgrate-Shapiro-Shibata-Nakamura (BSSN) formalism which turned out to give stable solutions, while the ADM has unstable modes. Using the finite difference scheme, we can solve the evolution equation from BSSN method. As for the time integration, we use the iterative Crank-Nicholson method as well as the Runge-Kutta method with MoL. The Newtonian gravitational potential in pseudo-Newtonian approach, which is an elliptic equation, is solved by the multigrid method. To simplify the boundary conditions, we use the compactified coordinate which covers spatial infinity using a tangent function. In order to confirm the validity of our codes, we carried out the various tests such as shock tube tests, stationary star tests of both non-rotating and rotating stars, and the radial oscillation mode tests of spherical stars. In the shock tube tests, the code shows good agreement with the analytic solution which include shocks, rarefaction waves and contact discontinuities. The code also can keep the maximum rest mass density of the non-rotating and rotating stars constants. Its relative change of the maximum rest mass in a dynamical time is $4\times10^{-6}$ in the stationary star tests while the ones for their total baryonic mass and angular momentum are around $5\times10^{-7}$ and $2\times10^{-6}$ respectively. As an application of our code, we investigate the pulsar glitches which could be a possible source of gravtitational wave detection. We investigate the characteristic strains and their frequencies of gravitational wave by introducing two kinds of perturbations which satisfy conservation of total rest mass and angular momentum in order to mimic the glitch induced pulsar oscillations. We carry out numerical hydrodynamic evolution using pseudo-Newtonian method and obtained the characteristic strain of gravitational wave ($h_c$) from the time series of quadrupole moment. Unlike previous studies, we find out that various modes are excited by the perturbations. The strongest mode depends on the perturbations as well as the models of the neutron stars. In most cases, the first and second strongest mode that give gravitational wave are ${}^{2}p_1$ and $H_1$ rather than ${}^{2}f$. Their characteristic strains ($h_c$) are expected to be $\sim9\times10^{-25}$ for the ${}^{2}p_1$ mode and $\sim3\times10^{-25}$ for the $H_1$ mode respectively when the perturbation follows vortex unpinning theory with $\Delta\Omega/\Omega\sim 10^{-5}$ and at a distace of $1\kpc$ from the {1.4\solarmass} pulsar. It is a little bit higher for the star quake model. One of the interesting feature is the vortex unpinning model excites the inertial mode in quadrupole moment quite effectively. Although $h_c$ is not very strong due to its fairly low frequency, its frequency is located at the most sensitive region in LIGO band and its damping time is regarded as longer than other modes.

Investigating the body shape drag coefficient of beetles (Coleoptera) with different foraging strategies using 3D scanned models

Suelen Saggiorato Seidler 이화여자대학교 대학원 2024 국내석사

In many beetle species, foraging typically involves movements of the whole body, and successful foraging may be related to body shape, velocity, and hydrodynamic/aerodynamic efficiency. Insects with lower drag coefficients are likely to have more efficient flight or swimming capabilities. This confers advantages in terms of energy, maneuverability, and overall performance. Predatory beetles require fast-forward acceleration and strikes to chase their prey, and hence their drag coefficient is expected to be lower compared to species with more stationary foraging styles. Natural selection may favor insects with streamlined body shapes that minimize drag. Here, we aim to estimate the body shape drag coefficient of different foraging styles in aquatic and terrestrial beetles: the carnivorous Cybister chinensis (Dystiscidae), the herbivorous Hydrophilus acuminatus (Hydrophilidae), the herbivorous Pseudotorynorrhina japonica (scarabaeidae) for comparison. We took a series of 2D pictures of the specimen from multiple angles using a 3D scanner. Utilizing Zephyr 3DF software, we were able to generate a 3D model to produce more detailed representations of the beetle geometry. Using computational fluid dynamics (CFD), a software used to simulate complex fluid flow and assess the hydrodynamics and aerodynamics around a body., we were able to calculate the drag coefficient of these three species for hydrodynamic efficiency. The results for the CFD simulation were consistent with the drag coefficient number found in the literature, the results were considerably different among three species. When a 3D model was set to face the flow at a velocity of 0.1 m/s, the drag coefficient number was 0.430 for Cybister chinensis, 0.477 for Hydrophilus acuminatus, 0.376 for Pseudotorynorrhina japonica. These findings highlight the significance of body shape and drag coefficient in determining the hydrodynamic efficiency of beetles, providing valuable insights into their evolutionary adaptations and ecological performance. 많은 딱정벌레 종에서 채집은 일반적으로 몸 전체의 움직임을 포함하며, 성공적인 채집은 몸 모양, 속도 및 유체 역학/공기 역학 효율성과 관련이 있을 수 있습니다. 항력 계수가 낮은 곤충은 더 효율적인 비행이나 수영 능력을 가질 가능성이 높습니다. 이는 에너지, 기동성 및 전반적인 성능 측면에서 이점을 제공합니다. 포식성 딱정벌레는 먹이를 쫓기 위해 빠른 가속과 공격이 필요하므로 항력 계수는 고정된 채집 스타일을 가진 종에 비해 낮을 것으로 예상됩니다. 자연 선택은 항력을 최소화하는 유선형 몸체를 가진 곤충을 선호할 수 있습니다. 우리는 비교를 위해 육식성 Cybister chinensis (Dystiscidae), 초식성 Hydrophilus acuminatus (Hy-drophilidae), 초식성 Pseudotorynorrhina japonica (scarabaeidae) 등 수생 및 육상 딱정벌레의 다양한 채집 스타일의 체형 항력 계수를 추정하는 것을 목표로 합니다. 우리는 3D 스캐너를 사용하여 여러 각도에서 표본의 일련의 2D 사진을 찍었습니다. Zephyr 3DF 소프트웨어를 활용하여 3D 모델을 생성하여 딱정벌레 형상을 보다 자세히 표현할 수 있었습니다. 복잡한 유체 흐름을 시뮬레이션하고 신체 주변의 유체역학과 공기역학을 평가하는 데 사용되는 소프트웨어인 전산유체역학 (CFD)을 사용하여 유체역학적 효율성에 대한 이 세 종의 항력 계수를 계산할 수 있었습니다. CFD 시뮬레이션 결과는 문헌에서 발견된 항력 계수 수치와 일치했으며 결과는 세 가지 종 사이에서 상당히 달랐습니다. 3D 모델이 0.1m/s의 속도로 흐름을 향하도록 설정한 경우 항력계수는 Cybister chinensis의 경우 0.430, Hydrophilus acuminatus의 경우 0.477, Pseudotory-norrhina japonica의 경우 0.376이었습니다. 이러한 발견은 딱정벌레의 유체역학적 효율성을 결정하는 데 있어 체형과 항력 계수의 중요성을 강조하여 진화적 적응과 생태학적 성능에 대한 귀중한 통찰력을 제공합니다.

Modeling of air burst phenomena within complex environments after high-energy explosion

송승호 Graduate School, Yonsei University 2020 국내박사

본 연구에서는 고에너지 폭발 후 복잡 지형에서의 유동을 효율적으로 해석하기 위해 복사수 력방정식의 개발 연구를 수행하였다. 고에너지 폭발 후 충격파의 전파과정 및 발달과정을 해 석하기 위해서는 매우 짧은 시간 내에 형성되는 고온/고압의 화구의 정밀한 해석모델링이 요 구된다. 고온/고압의 화구 모델을 정확히 모사하기 위하여 이상기체 상태방정식을 알맞지 않 으므로 실제 기체 상태방정식을 고려한 유한 체적 기반의 3차원 압축성 유동 해석 모델을 개 발했다. 또한, 고에너지폭발 후 발생되는 복사 열전달을 효과를 반영하여 복사수력방정식을 개발하였다. 복사 수력방정식은 폭발 량 및 폭발고도를 고려하여, 지표면에서 발생되는 폭풍 충격파의 첨두과압력, 도달시간, 지속 시간 등을 해석하고 기존 문헌들과 검증을 했다. 기존에 제시된 이상기체 상태방정식을 고려한 3차원 압축성 유동해석 모델과 비교했을 때, 상대적으 로 지표면이 받게 되는 압력 및 온도를 더 잘 모사 하는 것을 볼 수 있었다. 수치 계산의 효 율성을 고려하여 직교 좌표계 (cartesian coordinate)을 사용했으며, 개발된 정밀 분석 모델 에서 임의형상 지형/지물영향을 효과적으로 반영하고 충격파의 반사/회절, 굴절등의 전파과정 특성을 분석하였다. 또한, 지표면에 대한 충격파 전파과정을 보기 위해 실제 지형 데이터를 사용하여 폭발 후에 나타나는 전반적인 전파과정에 대해 발생되는 폭풍충격파의 특성을 분석 했다. 가상경계기법은 폭풍 충격파에 의한 지형/지물 영향에 대한 해석에 대해, 기존의 맞춤 형 격자계 기반 해석자에서 요구되었던 격자생성의 난해성을 완화시켜, 수치모사 과정이 보다 용이한 계산환경을 제공하였다. 복잡한 지형에서 발생하는 입사파와 반사파가 중첩이 형성되 어 충격파의 첨두 과압력이 높아지는 것을 볼 수 있었으며 충격하중 또한 오래 지속되어 지표 구조물에 더 심각한 타격을 미치게 된다는 결과를 도출했다. In this study, to efficiently analyze the flow in complex terrain after a high-energy explosion, a research on the development of the radiation hydrodynamics equation is conducted. In order to analyze the propagation and development process of blast wave after a high-energy explosion, precise analysis modeling of high-temperature/high-pressure fireball formed in a very short time is required. In order to accurately simulate the high temperature/high pressure fireball model, we develop a finite volume-based three-dimensional compressible flow analysis model considering the real gas EOS because the ideal gas EOS is not suitable. In addition, a radiation hydrodynamics equation is developed by reflecting the effect of radiation heat transfer after high-energy explosion. The radiation hydrodynamics equation is analyzed for the peakoverpressure, the arrival time and the duration of the blast wave generated on the surface in consideration of the amount of explosion , the altitude and verified with existing reference. Compared to the three-dimensional compressible flow analysis model considering the existing ideal gas EOS, it can be seen that the pressure and temperature of the surface are relatively better simulated. Cartesian coordinates were used in consideration of the efficiency of numerical calculations, and the developed terrain analysis model effectively reflected random terrain/geologic effects. In addition, the propagation process characteristics such as reflection/diffraction and refraction of blast wave are analyzed. It can be seen that the peakoverpressure of the shock wave is increased due to the overlap of the incident wave and the reflected wave generate in the complex terrain. The result is that the impact load also lasted longer, causing more severe damage to the surface structure. Key

Receptivity of Chemically-Reacting Hypersonic Boundary Layers to Kinetic Fluctuations

Luna, Kevin ProQuest Dissertations & Theses The University of 2023 해외박사(DDOD)

We examine the receptivity of high-speed chemically-reacting boundary layers in two-component fluids to kinetic fluctuations within the framework of fluctuating hydrodynamics. To solve the receptivity problem, we systematically extend a number of boundary layer stability and receptivity results to the case of a two-component chemically-reacting mixture. To that end, we formulate and solve a spatial initial-boundary value problem for three-dimensional perturbations in a chemically-reacting boundary layer within a two-component fluid. We show that the solution can be presented as a sum of modes consisting of continuous and discrete spectra of the corresponding quasi-parallel flow eigenvalue problem. We also perform a comprehensive numerical investigation of the spectrum to understand the effect of chemical reactions on features of the spectrum. We give special attention to an unreported compositional branch of the continuous spectrum that arises from modeling chemical reactions. We then explore implications of the corresponding compositional freestream waves to boundary layer stability and receptivity through methods developed herein. We then use the developed methods to construct an algorithm for decomposing experimental and numerical data in terms of the highly interpretable stability modes. With these foundational results in hand, we solve the kinetic fluctuation receptivity problem using asymptotic methods for a variety of conditions relevant to hypersonic flight. Through the solution to the receptivity problem, we find an estimate for the upper bound of the laminar-turbulent transition Reynolds number, and quantify the impact of chemical reactions.

Transport and Spectral Functions in Low-Dimensional Quantum Spin Systems

Sherman, Nicholas E University of California, Berkeley ProQuest Disser 2023 해외박사(DDOD)

Non-equilibrium properties of quantum materials are examined in low-dimensional systems using matrix product state (MPS) simulations. The spectral function known as the dynamical structure factor, which is directly observed in neutron scattering experiments, is studied for two classes of novel quantum systems. First, recent work has demonstrated that the Heisenberg spin chain exhibits anomalous super-diffusive transport at infinite temperature called Kardar-Parisi-Zhang (KPZ) hydrodynamics. Here, it is demonstrated that signatures of KPZ physics are present in the low-energy spectrum at experimentally relevant temperatures, and this has been detected in KCuF3 with neutron scattering. The crossover from the ground state physics described by the Tomonaga-Luttinger liquid theory to KPZ hydrodynamics at high temperatures is explored.Second, the spectral function of the \uD835\uDC3D1 − \uD835\uDC3D2 Heisenberg model is studied using MPS simulations. Signatures for the three primary classes of quantum spin liquid (QSL) states in the spectral function are discussed. Our findings point to a U(1) Dirac spin liquid ground state in this model. The calculated spectrum is then compared with the triangluar lattice compounds KYbSe2 and YbZn2GaO5. We find that KYbSe2 is well modelled by the \uD835\uDC3D1 − \uD835\uDC3D2 Heisenberg model in close proximity to the QSL phase. Additionally, we find that the QSL phase of the \uD835\uDC3D1 − \uD835\uDC3D2 Heisenberg model captures the essential features of the YbZn2GaO5, suggesting a realization of a Dirac spin liquid in this material.Lastly, the effect of using an MPS to study quantum dynamics is explored. Using an MPS places a restriction on the entanglement in the system, and we study how this modifies time dynamics in a Kibble-Zurek process. We derive that the effect of finite entanglement on a Kibble-Zurek process is captured by a dimensionless scaling function of the ratio of two length scales, one determined dynamically and one by the entanglement restriction. This result is verified numerically in the transverse field Ising model and the 3-state Potts model.

Analytical and Computational Techniques for Fluid Flows Interacting with Intense Radiation Fields

Cearley, Griffin S ProQuest Dissertations & Theses University of Mich 2022 해외박사(DDOD)

The field of high-energy-density (HED) physics features many problems of importance to society, including stellar formation in astrophysics as well as next-generation energy technologies. Often, these systems involve complex fluid flows, such as mixing between different fluids, that are influenced by radiation fields. Predicting the evolution of these systems requires understanding the role of the two-way coupling between radiation and the fluid flow. The development of experimental techniques for creating and diagnosing HED systems has greatly expanded our understanding of their evolution. However, these experiments are challenging, and the state of HED plasmas often cannot be completely constrained by available diagnostics. Analytical and computational tools provide valuable insight in predicting quantities that may be difficult to glean from experiments.Intense sources of radiation drive ablative flow in many applications, generating impulse and driving a compression wave into the bulk material. Analytical models exist to predict the impulse generated in materials exposed to radiation, but they depend on the energy of the blown-off material, which in general is not known due to the complex partitioning of energy that occurs in the system. The uncertainty associated with measurements of x-ray spectra poses another difficulty in predicting the impulse generated in an irradiated material. We address these issues via a data-driven approach to modeling the impulse generated in materials exposed to a given x-ray source spectrum. We use data from high-fidelity simulations to inform an analytical model for the impulse generated in a given material by an arbitrary radiation source. This model also provides an analytical form for the impulse-spectrum sensitivity, a quantity that is important for constraining the uncertainty in impulse resulting from uncertainty in the source spectrum. The model for the impulse-spectrum sensitivity agrees well with the sensitivity evaluated directly from simulations, requires significantly less computation time, and can also be evaluated using data from experiments. This work enables low-cost prediction of important quantities in the radiation-generated impulse in materials. The modeling approach we propose greatly simplifies the study of such systems, as well as the design of robust experiments.Numerical simulation of HED systems poses a challenge, as the problems tend to be multi-scale and involve fundamentally different, often competing, physical processes. The discontinuous Galerkin (DG) method offers many advantages, particularly as computing architectures evolve to offer exascale capabilities. In particular, DG offers arbitrarily high-order accuracy with a compact stencil, making it well-suited for parallel scaling. However, high-order methods have seen limited application to the study of HED systems. As we are primarily interested in the study of multimaterial flows in intense radiation fields, we extend interface capturing techniques used for classical fluid flows to radiation hydrodynamics in the framework of the DG discretization. Our approach uses a careful, physically consistent treatment of material interfaces, including a limiting procedure designed to prevent unphysical errors that occur from other approaches. This development results in an approach that is high-order accurate, conservative, physically consistent, and well-suited for parallel computation of radiation hydrodynamics. We demonstrate these properties of the method using one- dimensional verification problems, as well as a two-dimensional problem relevant to HED science. This work demonstrates the promising application of high-order numerical methods to practical problems in HED science, a field that has seen limited application of such methods.

Numerical Simulations of Plasmas in Galaxy Clusters

Glines, Forrest Wolfgang Michigan State University ProQuest Dissertations & 2022 해외박사(DDOD)

As the largest gravitationally bound objects in the universe, galaxy clusters are a unique probe of large scale cosmological structure. Determining the distribution of galaxy clusters and their virial masses may be key to constraining properties of dark energy and dark matter. Since 84%of a typical galaxy cluster’s mass is comprised of non-radiating dark matter, however, determining the virial mass of galaxy clusters depends on inference from the radiating baryonic matter. 84%of this baryonic matter is contained in the intracluster medium (ICM)—a hot, diffuse, magnetized plasma permeating the galaxy cluster. While the baryonic matter is the only emitter of observable electromagnetic emissions from galaxy clusters, the complex behavior of the ICM as a turbulent magnetized plasma makes constraining the virial mass of the cluster with observable signatures difficult. Numerical simulations are essential tools for advancing understanding of the ICM and for tying galaxy cluster observables to virial masses. The goal of this dissertation is to explore and enable simulations of galaxy clusters and magnetized plasmas via a number of different avenues.I first explore self-regulation of feedback from active galactic nuclei (AGN) preventing over-cooling in cool-core (CC) clusters—galaxy clusters with anomalously high central thermal emission which should cool on shorter timescales than they persist. In the idealized galaxy cluster simulations with a thermal abstraction of AGN feedback, we find that the thermal-only heating kernels we test are unable to offset cooling while maintaining a realistic structure, suggesting exploration of more complex AGN feedback mechanisms such as those including magnetic fields and turbulence.We then explore how kinetic and magnetic energy thermalizes in the ICM by studying decaying magnetized turbulence with simulations of the magnetized compressible Taylor-Green vortex. Using a shell-to-shell energy transfer analysis, we find that the magnetic fields facilitate a significant amount of the energy flux that is not seen in hydrodynamic turbulence. Although the full cascade will not be directly captured in ICM simulations for the foreseeable future, higher resolution simulations enabled by larger computational resources can diminish such effects.Different novel many-core architectures have emerged in recent years on the way toward larger supercomputers in the exascale era. Performance portability is required to prevent repeated nontrivial refactoring of a code for different architectures. To address the need for a performance portable magnetohydrodynamics (MHD) code, we combined Athena++, an existing MHD CPU code, with Kokkos, a performance portable framework, into K-Athena to allow efficient simulations on multiple architectures using a single codebase. K-Athena has also inspired the Parthenon performance portable adaptive mesh refinement (AMR) framework. Using this framework, we developed the performance portable AMR MHD code AthenaPK.Galaxy clusters contain significant magnetic fields, although their origin and role is still under investigation. Numerical modeling is essential for the inference of their properties. One aspect is whether magnetic AGN feedback models can self-regulate. I present work-in-progress simulations with AthenaPK of magnetized galaxy clusters slated for exascale supercomputers later this year.With the higher resolutions enabled by exascale systems, galaxy cluster simulations with relativistic jet velocities will be possible. Robust methods for relativistic plasmas will be needed. With this goal, I present a discontinuous-Galerkin (DG) method for relativistic hydrodynamics. We include an exploration of different methods to recover the primitive variables from conserved variables, a new operator for enforcing a physically permissible conserved state, and numerous tests of the method. This method has been used at Sandia National Laboratories to study terrestrial plasmas and will inform relativistic MHD methods for AthenaPK.Finally, I cover the future directions of the work in this dissertation, including the many codes enabled by Parthenon, additions to the magnetized galaxy cluster simulations with AthenaPK, and the large body of projects at Los Alamos National Laboratory to explore binary black hole mergers embedded within AGN accretion disks as a possible formation channel of the massive black holes observed by LIGO. The work in this dissertation to develop performance portable plasma simulations will enable ground-breaking simulations for years to come.

Targeted gene delivery to human colon carcinoma by anti-TAG-72 immunoliposomes

김근식 Graduate School, Yonsei University 2004 국내박사

Mapping of the surface profile of an asymmetric dielectric microcavity and identification of shape-sensitive internal modes

문송기 서울대학교 대학원 2014 국내박사

In this thesis, I first present a non-destructive and non-contact highresolution optical technique for profiling soft or fluidic boundary of an opaque object. This technique utilizes the fact that the angle width, the angular separation between two adjacent intensity minima in the forward shadow diffraction, is inversely proportional to the projected width of the object in the same direction. An analytic formula for reconstructing the boundary shape is obtained for an object with two-fold symmetry in terms of the angle widths measured for various rotational angles of the object. The typical error in determining the object shape parameter is less than 0.2%, which corresponds to 20 nm of radial accuracy when applied to an object with a mean radius of 10 μm. I then apply the profiling technique to asymmetric liquid micro jet cavity and determine its surface profile in the accuracy enough to analyze the experimental results with theoretical concepts based on the one-to-one comparison between the experiments and with the numerical simulations. I found that the most dominant oscillation mode of our jet is the combination of quadrupolar and octapolar waves. The amplitudes of these two components are related by a certain quadratic relation, η2≃Bη1 2 ( η1 and η2 are amplitudes of quadrupolar and octapolar oscillation, respectively). The coefficient B is obtained as 0.42±0.08. I also survey the surface vibration of a microjet analytically by modifying Niels Bohr’s non-linear hydrodynamical i treatment of the same problem, and find out that the expected value of B from this theory is nearly 0.41. The measured result and the theoretical prediction agree experimental error. With this information, fundamental intra quasi-mode positions can be predicted by simulation within experimental error. Moreover, I also confirm that numerical simulations show good agreement with spectroscopic experimental results for non-trivial features of quasi-mode dynamics such as avoided crossing gaps.