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The recently discovered ferroelectric nematic liquid crystals have been reported to exhibit very large dielectric permittivity values. Here, we report a systematic investigation of the dielectric behavior of a prototypical ferroelectric nematogen by varying the thickness of the parallel capacitor measuring cell. While in the non-polar high temperature nematic phase results show only slight differences due to slight variations of the alignment, the measured permittivity values in the ferroelectric nematic phase show a linear dependence on the cell thickness. It is also shown that the characteristic relaxation frequency decreases inversely proportionally to the thickness. The results are discussed in terms of three different available models based on different underlying mechanisms, accounting for cancellation of the probe electric fields by polarization reorientation or by ionic charges, or based on a recently proposed continuous phenomenological model.

The problem (LFP) of finding a feasible solution to a given linear semi-infinite system arises in different contexts. This paper provides an empirical comparative study of relaxation algorithms for (LFP). In this study we consider, together with the classical algorithm, imple- mented with different values of the fixed parameter (the step size), a new relaxation algorithm with random parameter which outperforms the classical one in most test problems whatever fixed parameter is taken. This new algorithm converges geometrically to a feasible so- lution under mild conditions. The relaxation algorithms under com- parison have been implemented using the Extended Cutting Angle Method (ECAM) for solving the global optimization subproblems., Peer Reviewed, Preprint

We model strong shockwave propagation, both in the ideal gas and in the dense Lennard- Jones fluid, using a refinement of earlier work, which accounts for the cold compression in the early stages of the shock rise by a nonlinear, Burnett-like, strain-rate dependence of the thermal conductivity, and relaxation of kinetic temperature components on the hot, compressed side of the shock front. The relaxation of the disequilibrium among the three components of the kinetic temperature, namely, the difference between the component in the direction of a planar shock wave and those in the transverse directions, particularly in the region near the shock front, is accomplished at a much more quantitative level by the first-ever rigorous application of the Cattaneo-Maxwell relaxation equation to a reference solution, namely, the steady shockwave solution of linear Navier- Stokes-Fourier theory, along with the nonlinear Burnett heat-flux term. Our new continuum theory is in nearly quantitative agreement with non-equilibrium molecular-dynamics simulations under strong shockwave conditions, using relaxation parameters obtained from the reference solution. © 2012 American Institute of Physics., SCOPUS: cp.p, info:eu-repo/semantics/published

We model strong shockwave propagation, both in the ideal gas and in the dense Lennard- Jones fluid, using a refinement of earlier work, which accounts for the cold compression in the early stages of the shock rise by a nonlinear, Burnett-like, strain-rate dependence of the thermal conductivity, and relaxation of kinetic temperature components on the hot, compressed side of the shock front. The relaxation of the disequilibrium among the three components of the kinetic temperature, namely, the difference between the component in the direction of a planar shock wave and those in the transverse directions, particularly in the region near the shock front, is accomplished at a much more quantitative level by the first-ever rigorous application of the Cattaneo-Maxwell relaxation equation to a reference solution, namely, the steady shockwave solution of linear Navier- Stokes-Fourier theory, along with the nonlinear Burnett heat-flux term. Our new continuum theory is in nearly quantitative agreement with non-equilibrium molecular-dynamics simulations under strong shockwave conditions, using relaxation parameters obtained from the reference solution. © 2012 American Institute of Physics., SCOPUS: cp.p, info:eu-repo/semantics/published

Chau Kin Chiu., Thesis (M.Phil.)--Chinese University of Hong Kong, 2006., Includes bibliographical references., s in English and Chinese., (Chinese) --- p.i, 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, http://library.cuhk.edu.hk/record=b5892825, Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Chau Kin Chiu., Thesis (M.Phil.)--Chinese University of Hong Kong, 2006., Includes bibliographical references., s in English and Chinese., (Chinese) --- p.i, 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, http://library.cuhk.edu.hk/record=b5892825, Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Fast relaxations of polystyrene, a significant drop of optical birefringence with order of second (~23s), below its glass temperature were studied in this thesis. Results showed that those birefringence drops are around 30x10-6 and similar results were gotten in various molecular weights of polystyrene (18.1kg/mol to 442kg/mol) and temperatures (-10°C to 20°C). However, distributions of such drops were wider at low experimental temperature. Also, saturated normalized birefringence of polystyrene is high when it is rubbed under low temperatures. In order to discover above outcomes, Reflectance Difference Spectroscopy (RDS) was employed to have real-time monitoring. Besides, double way rubbing system and low temperature plus dry experimental environment was developed to carry out experiments, which different samples were rubbed by velvet cloth under various conditions.

Fast relaxations of polystyrene, a significant drop of optical birefringence with order of second (~23s), below its glass temperature were studied in this thesis. Results showed that those birefringence drops are around 30x10-6 and similar results were gotten in various molecular weights of polystyrene (18.1kg/mol to 442kg/mol) and temperatures (-10°C to 20°C). However, distributions of such drops were wider at low experimental temperature. Also, saturated normalized birefringence of polystyrene is high when it is rubbed under low temperatures. In order to discover above outcomes, Reflectance Difference Spectroscopy (RDS) was employed to have real-time monitoring. Besides, double way rubbing system and low temperature plus dry experimental environment was developed to carry out experiments, which different samples were rubbed by velvet cloth under various conditions.

The properties of plasma turbulence in the outer region of the Reversed Field Pinch experiments RFX and EXTRAP-T2R are reviewed. The statistical properties of fluctuations in the range of scales relevant for transport are presented. The observation of coherent structures emerging from the background turbulence and their interpretation in terms of vortices is reported. The interplay between these structures and the mean ExB flow of the plasma is demonstrated with emphasis to the action on the preferential rotation direction. The effect on the particle transport induced by the background turbulence and by the structures is discussed. Finally the methods tested to control turbulence and to mitigate the related transport are illustrated and discussed., QC 20100525 QC 20111025

The relaxation times distribution of molecular alignments in polymers induced by mechanically rubbing with velvet cloth was found to be different from those induced by other means of mechanical deformation, e.g. hot drawing. Several attempts have been made but failed to achieve a complete model in describing the relaxation times distribution. In this thesis, we are going to introduce a new mathematical model to determine the distribution. The model is supported by experimental results. The relaxation was also found independent of its thermal history which is e.g., raising and lowering the temperature of the sample several times, and independent of the rubbing history.

The relaxation times distribution of molecular alignments in polymers induced by mechanically rubbing with velvet cloth was found to be different from those induced by other means of mechanical deformation, e.g. hot drawing. Several attempts have been made but failed to achieve a complete model in describing the relaxation times distribution. In this thesis, we are going to introduce a new mathematical model to determine the distribution. The model is supported by experimental results. The relaxation was also found independent of its thermal history which is e.g., raising and lowering the temperature of the sample several times, and independent of the rubbing history.

The relaxation times distribution of molecular alignments in polymers induced by mechanically rubbing with velvet cloth was found to be different from those induced by other means of mechanical deformation, e.g. hot drawing. Several attempts have been made but failed to achieve a complete model in describing the relaxation times distribution. In this thesis, we are going to introduce a new mathematical model to determine the distribution. The model is supported by experimental results. The relaxation was also found independent of its thermal history which is e.g., raising and lowering the temperature of the sample several times, and independent of the rubbing history.

Chan David., Thesis (M.Phil.)--Chinese University of Hong Kong, 2000., Includes bibliographical references (leaves [73]-76)., s in English and Chinese., 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, http://library.cuhk.edu.hk/record=b5890500, Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Two types of relaxation processes in amorphous alloys have been investigated in metal-metalloid systems. One of them has been studied by measuring the static structure factor S(Q) in cobalt boron glass samples that have been previously isothermally treated on temperatures close to crystallization temperature. Furthermore, nonisothermal measurements have been done by using the well-known DSC method for the above-mentioned glasses, as well as for Al-87 Y-8 Ni-5 and Fe40Ni40B20 under similar conditions. The processes of relaxation transformations were analyzed under the Kolmogorov-Johanson-Mehl-Avrami (KJMA) kinetic model, from which the coefficient n was determined and the scaling parameter tau estimated. The parameter tau has been also determined using the Vogel-Tammann-Fulcher (VTF) relation in the vicinity of T-g. Besides that, the static properties of amorphous alloys have been studied by measurement of resistivity while heating the samples up to the crystallization temperature and cooling down to liquid nitrogen temperature.

Very inherent metastable character of amorphous metal alloys, induces structure phase transformations which manifest themselves in thermally activated relaxation processes. The kinetics of these processes can be interpreted with the aid of two models: two equilibrium states and spectrum of activation energies. Structure relaxation of amorphous Fe40Ni40B20 metallic glass has been observed by measuring changes in electrical resistivity at corresponding isothermal treatments. Electrical resistance changes have been measured at liquid nitrogen temperature (78 K) using the d.c. method and a fixed probe. By measuring the resistivity change during isothermal treatment, logarithmic kinetics has been observed. Also, Q(E) function has been derived having a symmetric distribution around the value of activation energy of 2.1 eV, determined by some other methods too.

Two types of relaxation processes in amorphous alloys have been investigated in metal-metalloid systems. One of them has been studied by measuring the static structure factor S(Q) in cobalt boron glass samples that have been previously isothermally treated on temperatures close to crystallization temperature. Furthermore, nonisothermal measurements have been done by using the well-known DSC method for the above-mentioned glasses, as well as for Al-87 Y-8 Ni-5 and Fe40Ni40B20 under similar conditions. The processes of relaxation transformations were analyzed under the Kolmogorov-Johanson-Mehl-Avrami (KJMA) kinetic model, from which the coefficient n was determined and the scaling parameter tau estimated. The parameter tau has been also determined using the Vogel-Tammann-Fulcher (VTF) relation in the vicinity of T-g. Besides that, the static properties of amorphous alloys have been studied by measurement of resistivity while heating the samples up to the crystallization temperature and cooling down to liquid nitrogen temperature.

The derivation of the closed-form solution to the generalized Langevin equation (Mori formula) is reviewed. We derive rigorous constraints for transport coefficients in the limit of low frequency and those obtained in the memory functional approach to the closed-form solution. We calculate the closed-form solution for the relaxation functions of the fluctuating force in a free two-band model to find a long-time tail of t^<-1> and the strongly colored quantum noise at T = 0.