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A study of relaxation phenomena via effective master equation. / 以有效主方程作弛豫現象之硏究 / Yi you xiao zhu fang cheng zuo chi yu xian xiang zhi yan jiuJanuary 2000 (has links)
Chan David. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves [73]-76). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.ii / Contents --- p.iii / List of Figures --- p.vi / List of Tables --- p.viii / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- Relaxation Phenomena --- p.8 / Chapter 2.1 --- Introduction --- p.8 / Chapter 2.2 --- Relaxation Phenomena --- p.8 / Chapter 2.3 --- Ising Model as an Example --- p.9 / Chapter 2.3.1 --- Monte Carlo Simulation --- p.10 / Chapter 2.3.2 --- Transition Matrix Method --- p.11 / Chapter 2.3.3 --- Results and Comparison --- p.13 / Chapter 2.4 --- Conclusion --- p.17 / Chapter Chapter 3. --- Stochastic Processes --- p.18 / Chapter 3.1 --- Introduction --- p.18 / Chapter 3.2 --- Stochastic Processes --- p.18 / Chapter 3.3 --- Markov Processes and Markov Chains --- p.19 / Chapter 3.4 --- Transition Matrix --- p.20 / Chapter 3.5 --- Detailed Balance Condition --- p.21 / Chapter 3.5.1 --- Weaker Balance Condition --- p.22 / Chapter 3.6 --- Ergodicity --- p.22 / Chapter 3.7 --- Conclusion --- p.23 / Chapter Chapter 4. --- Master Equation --- p.24 / Chapter 4.1 --- Introduction --- p.24 / Chapter 4.2 --- Master Equation --- p.24 / Chapter 4.3 --- Properties of the Transition Matrix W --- p.25 / Chapter 4.4 --- Eigenvalue Equation --- p.26 / Chapter 4.5 --- Relaxation Time --- p.28 / Chapter 4.6 --- Properties of Eigenvalues and Eigenvectors --- p.29 / Chapter 4.7 --- Power Method --- p.32 / Chapter 4.7.1 --- Power Method for λx --- p.33 / Chapter 4.7.2 --- Power Method for λx --- p.35 / Chapter 4.7.3 --- Power Method for λ2 of W --- p.38 / Chapter 4.8 --- Conclusion --- p.39 / Chapter Chapter 5. --- Decimation --- p.40 / Chapter 5.1 --- Introduction --- p.40 / Chapter 5.2 --- Method of Decimation --- p.40 / Chapter 5.2.1 --- Exact Formalism --- p.42 / Chapter 5.2.2 --- Iterative Formalism --- p.44 / Chapter 5.2.3 --- Approximate Formalism --- p.46 / Chapter 5.3 --- Decimation as an Effective Master Equation --- p.46 / Chapter 5.4 --- One Dimensional Energy Landscape --- p.47 / Chapter 5.5 --- Conclusion --- p.58 / Chapter Chapter 6. --- Mean Field Theory --- p.59 / Chapter 6.1 --- Introduction --- p.59 / Chapter 6.2 --- Toy Model A --- p.59 / Chapter 6.3 --- Toy Model B --- p.61 / Chapter 6.4 --- Mean Field Theory : a Lower Bound of Relaxation Time --- p.62 / Chapter 6.5 --- Mean Field Theory with the Decimation Formalism --- p.62 / Chapter 6.6 --- Mean Field Theory with Fluctuations --- p.63 / Chapter 6.6.1 --- Fluctuation Phenomena with the Decimation Formalism --- p.67 / Chapter 6.7 --- Conclusion --- p.69 / Chapter Chapter 7. --- Conclusion --- p.70 / Bibliography --- p.73
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Relaxation of confined polymer chains near glass transition temperature.January 2006 (has links)
Chau Kin Chiu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references. / Abstracts in English and Chinese. / ABSTRACT (Chinese) --- p.i / ABSTRACT --- p.Iii / ACKNOWLEDEMENT --- p.v / Chapter CHAPTER 1 --- INTRODUCTION --- p.1-9 / Chapter CHAPTER 2 --- INSTRUMENTS / Chapter 2.1 --- Laser Light Scattering (LLS) --- p.10-18 / Chapter 2.2 --- Atomic Force Microscopy (AFM) --- p.19-28 / Chapter 2.3 --- Gel Permeation Chromatography (GPC) --- p.29-31 / Chapter 2.4 --- Differential Scanning Calorimeter (DSC) --- p.32-35 / Chapter 2.5 --- Scanning Electron Microscope (SEM) --- p.36-43 / Chapter CHAPTER 3 --- EXPERIMENTAL / Chapter 3.1 --- Preparation of Neutral Polystyrene Particles --- p.45-46 / Chapter 3.2 --- Characterization of Neutral Polystyrene Particles --- p.46-47 / Chapter 3.3 --- Preparation of Carboxylated Polystyrene Particles --- p.47-48 / Chapter 3.4 --- Characterization of Carboxylated Polystyrene Particles --- p.48 / Chapter 3.5 --- Film Formation --- p.49 / Chapter 3.6 --- Investigation Polystyrene Latex Film by AFM --- p.49 / Chapter 3.7 --- Determination of Changes of Confined Polystyrene Chains --- p.50 / Chapter 3.8 --- References --- p.50-51 / Chapter CHAPTER 4 --- RESULTS AND DISCUSSIONS / Chapter 4.1 --- Basic Observations --- p.53-64 / Chapter 4.2 --- Findings from Preliminary Study --- p.65-73 / Chapter 4.3 --- Relaxation of Polymers in Neutral Polystyrene Particle --- p.74-92 / Chapter 4.4 --- Is there really on change when particles annealed below Tg? --- p.93-94 / Chapter 4.5 --- Relaxation of Polymers in CPS particles --- p.94-99 / Chapter 4.6 --- Summary --- p.100-101 / Chapter 4.7 --- Future Work --- p.101 / Chapter 4.8 --- References --- p.101-102
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Thermodynamics of polymerization, dielectric properties, and a new orientational glass /Wang, Jingsong. Johari, G. P. January 2003 (has links)
Thesis (Ph.D.)--McMaster University, 2003. / Advisor: G. P. Johari. Includes bibliographical references (leaves 191-199). Also available via World Wide Web.
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Relaxation of polystyrene rubbed at low temperature /Chan, Ngo-Hin. January 2005 (has links)
Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2005. / Includes bibliographical references (leaves 84-85). Also available in electronic version.
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Study of relaxation time of mechanically aligned polystyrene thin films /Shiu, Kai Pong. January 2003 (has links)
Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2003. / Includes bibliographical references (leaves 23). Also available in electronic version. Access restricted to campus users.
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Experimental investigation and theoretical analysis of the structural relaxation in amorphous Fe40Ni40B20.Valanathan, Munsami. January 1998 (has links)
Amorphous metallic alloys are produced by a variety of techniques some of which involve rapid solidification of the alloying constituents. In these methods the solidification occurs so rapidly that the atoms are frozen-in and partially retain their liquid configuration. There are clear structural and other indications from their various properties that amorphous metallic alloys possess short range order but lack long range order. In general, amorphous alloys are not in a thermodynamic equilibrium state and, therefore, relax structurally whenever atoms attain an appreciable mobility. Associated with structural relaxation, many physical properties change; some significantly and others only slightly. Relaxation experiments in amorphous metallic alloys often display approximate In(t) kinetics which can be understood in terms of various models. In the present work the model by Primak (1955), for which the kinetic behaviour of a system depends on processes that are distributed over a range of activation energies, is used as a basis for further development. The Primak model allows, in principle, for the identification of the order of
the relaxation reaction and for the determination of an initial activation energy spectrum Po(Єo), where Єo is a characteristic activation energy. Although the model provides for a qualitative explanation of the In(t) law, it has no predictive power as to the quantitative
changes accompanying the various relaxing properties. Furthermore, an estimation of Po( Єo), inferred from various isothermal annealing procedures, reveals the approximate shape but does not fix its location on the activation energy axis. These shortfalls are attributed to complications in the frequency factor v, inherent to the Primak model. Also, the Primak model does not include consideration of the entropy involved in a 'configurational jump' of any particular atom during the relaxation process. Inclusion of the configurational entropy through the frequency factor v, in the present treatment, leads to a 'relaxation equation'. Structural relaxation measurements of density (in practice length - from which density can be approximately inferred) and electrical resistivity, in an Fe4oNi40B20 alloy, have been obtained and fitted to this relaxation equation. The fitting parameters are
found, within experimental error, to be the same for both length and resistivity relaxation. The initial activation energy spectrum Po(Єo), as inferred from the fits, over the energy range 1.4 to 2.0 eV, reveals roughly three regimes, namely below 1.5 eV, from 1.5 to 1.8 eV, and above 1.8 eV, respectively, over which the initial activation energy spectrum Po( Єo) assumes different approximately constant values. Previous treatments have, however, implicitly assumed that Po( Єo) is constant throughout a temperature range over which In(t) kinetics is observed. The behaviour observed in this work is associated with
the intrinsic relaxation mechanism involving consecutive diffusion of the metallic and metalloid atoms, respectively. A configurational entropy change inferred from this work is found to be negative as a consequence of contraction of the spread-out free volume resulting from thermal fluctuations. Within the framework of the 'present model', other related behaviour of amorphous metallic alloys, including the glass transition, crystallization and diffusion, are discussed. Where direct comparison between theory and experiment is possible for the various observed phenomena, the agreement is good and shows an overall consistency in our approach. Finally, the analysis considered here gives an expression which can be easily
used to make quantitative predictions about the experimental relaxation behaviour. An immediate understanding of some of the main features of experimental data on relaxation can, therefore, be obtained through application of the present model. / Thesis (Ph.D.)-University of Natal, Durban, 1998.
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Simulation of thermal decay and dynamic relaxation in ferromagnetic materials /Boerner, Eric D. January 2000 (has links)
Thesis (Ph. D.)--University of California, San Diego, 2000. / Vita. Includes bibliographical references.
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Defects in amorphous SiO₂ reactions, dynamics and optical properties /Bakos, Tamás, January 2003 (has links)
Thesis (Ph. D. in Physics)--Vanderbilt University, 2003. / Title from PDF title screen. Includes bibliographical references.
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Spin resonance excitation of Gd-based contrast agents for thermal energy depositionDinger, Steven Conrad January 2016 (has links)
A thesis submitted to the Faculty of Engineering and the Built
Environment, University of the Witwatersrand, Johannesburg, in
fulfilment of the requirements for the degree of Doctor of Philosophy.
Johannesburg, 2016 / The theoretical and experimental investigation of electron spin-resonance relaxation to
deposit thermal energy into liquid gadolinium-based contrast agents for cancer hyperthermia
treatment is presented. Previous works suggest that using protons in water are
inadequate, with a thermal deposition rate of approximately 1 ◦C per two years. A novel
component of this research relies on the use of gadolinium-chelated molecules, which are
currently used as contrast agents in clinical MRI scans. The chelating agents, or ligands,
investigated are Gadobenate (MultiHance R
), Gadopentetate (Magnevist R
), Gadoterate
(DotaremR
) and Gadoteridol (ProHance R
). The gadolinium atom has seven unpaired
electrons in its inner f shell orbital and as a result has a 660 times stronger paramagnetic
response when placed in an external magnetic field. The research tests the hypothesis
that by using an appropriate external homogeneous DC magnetic field, together with a radiofrequency
excited resonator, that a measurable amount of thermal energy is deposited
into a liquid gadolinium-based contrast agent. The aim of this research is to ultimately
discover a new cancer hyperthermia treatment. The research theory suggests that a temperature
rate of 13.4 ◦C · s−1 can be achieved using the gadolinium-based contrast agents
under certain experimental conditions, and a maximum of 29.4 ◦C · s−1 under more optimal
conditions. The temperature rates are calculated using parameter values commonly
found in literature and practice. The simulation and design of the DC magnetic field coil
system is discussed, together with the simulation results and design parameters of the radiofrequency
loop-gap resonator. The experimental results and analysis indicate that the
selected contrast agents have varied responses based on their chemical nature and that
only two out of the four contrast agents, Dotarem and ProHance, show a measurable
effect albeit sufficiently small that statistical techniques were necessary to distinguish
the effect from background. A model fit to the data is performed in order to determine
the spin-lattice relaxation time of the contrast agents under the specified experimental
conditions. The model estimate is significantly smaller than the values found in literature
under similar conditions, with a spin-lattice relaxation time τ1e of approximately 0.2 ps
compared to the literature value of 0.1 ns. Although the observed electron spin resonance
heating rate is in the milli-Watt range it is still notably larger (167 000 times) compared
to the heating rate obtained using protons. The low temperature rates suggest that a
more suitable agent or molecule with a larger spin-relaxation time be used, in order to
achieve clinical useful temperature rates in the range of 14 ◦C · s−1. / MT2017
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Magnetization Dynamics and Interparticle Interactions in Ferrofluids and NanostructuresMorales, Marienette B. 09 June 2009 (has links)
Nanoparticle assemblies are of current interest as they are used in a wide variety of industrial
and biomedical applications. This work presents two studies aimed at understanding
the magnetization dynamics and interparticle interactions in nanoparticle assemblies
and various types of ferrofluids.
First, we studied the influence of varying strengths of dipolar interaction on the static
and dynamic magnetic properties of surfactant-coated monodispersed manganese-zinc ferrite
nanoparticles using reversible transverse susceptibility. We tracked the evolution of
the anisotropy peaks with varying magnetic field, temperature, and interaction strength.
The anisotropy peaks of weakly interacting particles appears as non-symmetric peaks and
at lower fields in a unipolar transverse susceptibility scan. On the other hand, a strongly
interacting particle system exhibits symmetric anisotropy peaks situated at higher field
values.
In the second study, we successfully synthesized stable ferrofluids out of high quality
Fe
3O4 and CoFe2O4
nanoparticles. Such ferrofluids are excellent systems for the investigation
of physics of relaxation phenomena in magnetic nanoparticles. Motivated by the
need to understand their peculiar magnetic response, a comparative study on Fe
3O4
- and
CoFe
2O4
-based ferrofluids was performed. We investigated cases in which particle blocking
and carrier fluid freezing temperatures were close and far apart from each other. Our
experimental results reveal the true origin of the glass-like relaxation peaks that have been
widely observed in ferrofluids by many groups but remained largely unexplained. Contrary
to the speculation of previous literature, we argue that the formation of the magnetic
anomaly is due not only to the particle blocking but also to its correlation with the the
carrier fluid freezing effects. It is also shown that the nature of these peaks is strongly
affected by varying particle size and carrier fluid medium. Quantitative fits of the frequency
dependent AC susceptibility to the Vogel-Fulcher scaling law clearly indicate that
the blocking of magnetic nanoparticles in the frozen state significantly affects the interparticle
dipole-dipole interaction, causing characteristic spin-glass-like dynamics. A clear
correlation between the blocking and freezing temperatures emerges from our studies for
the first time.
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