In this thesis, molecular dynamics and dissipative particle dynamics simulation methods are adopted to investigate the effects of volume fraction (1:1; 1:4; 1:6; 1:14; 1:20), repulsive interaction parameter (aij) and chain length on the microstructure of (5,5) carbon-nanotube (CNT)/polyethylene (PE) mixture. In order to obtain the information of microstructure for different simulation conditions, we used the radius of gyration and orientational order parameter to explore the polymer conformation. It is found that micro-structures will be very different when different repulsive interaction parameters and volume fractions are used.

This thesis studies quantum coherence in macroscopic and mesoscopic dissipative electrical circuits, including LC circuits, microwave resonators, and Josephson junctions. For the LC resonator and the terminated transmission line microwave resonator, second quantization is carried out for the lossless system and dissipation in modeled as the coupling to a bath of harmonic oscillators. Stationary states of the linear and nonlinear resonator circuits as well as the associated energy levels are found, and the time evolution of uncertainty relations for the observables such as flux, charge, current, and voltage are obtained. Coherent states of both the lossless and weakly dissipative circuits are studied within a quantum optical approach based on a Fokker-Plank equation for the P-representation of the density matrix which has been utilized to obtain time-variations of the averages and uncertainties of circuit observables. Macroscopic quantum tunneling is addressed for a driven dissipative Josephson resonator from its metastable current state to the continuum of stable voltage states. The Caldeira-Leggett method and the instanton path integral technique have been used to find the tunneling rate of a driven Josephson junction from a zero-voltage state to the continuum of the voltage states in the presence of dissipation. Upper and lower bounds are obtained for the tunneling rate at the intermediate loss and approximate closed form expressions are derived for the overdamped and underdamped limits.

This thesis explores fundamental design strategies in the field of synthetic ion channel research from two different perspectives. In the first part the synthesis of complex, shape persistent and thermodynamically stable structures based on metal-ligand self-assembly is explored. The second part examines transport systems with dynamic transport behavior in response to chemical inputs which more closely mimic the dissipative assembly of Natural ion channels. In part one, two model systems, the ethylenediamine palladium(II) - 4,4’-bipyridine squares of Fujita and the trimeric bis(terpyridine) - iron(II) hexagonal macrocycles of Newkome, were targeted for structural modification towards becoming transport competent systems via improving the membrane partitioning characteristics of the final coordination compounds by increasing their lipophilicity. Modifications of the Fujita system involved the generation of two lipophilic 4,4’-bipyridines with addition of lipophilic groups of 13 and 17 carbon long alkyl chains respectively at the 3 and 3’ positions. After pursuing multiple unsuccessful synthetic routes the successful syntheses afforded the final lipophilic 4,4’-bipyridines in overall yields of 19 to 21% over two synthetic steps. Mixtures of the newly generated lipophilic 4,4’-bipyridines with a known lipophilic ethylenediamine palladium(II) “corner” exhibited evidence of self-assembly from NMR spectroscopy experiments however attempts at further characterization by ESI-MS and X-ray crystallography were unproductive. The putative self-assembled structures were inactive in HPTS vesicle assays but showed erratic conductance activity in bilayer clamp experiments. However, the magnitude of the conductance observed was not indicative of the passage of ions through the internal pore of the square complex. Modifications to the Newkome hexagons were aimed at generating overall neutral assemblies with external lipophilic groups. These modifications involved imparting a net -2 charge to the ligand via modifications to the terminal tridentate ligands so that upon coordination to octahedral metal centers in the +2 oxidation state the overall hexagonal complex would be neutrally charged. Two bis-polydentate ligands were generated; a dissymmetric molecule comprising one terpyridine and one dipicolinate tridentate ligand (TERPY-DPA) and a symmetrical molecule comprising two 2,2’-bipyridine-6-carboxylate tridentate ligands (BIPYA-BIPYA). The successful syntheses provided the desired trimethylsilylethyl ester protected compounds in yields of 9.2 and 7.5 % over 6 and 8 total synthetic steps for TERPY-DPA and BIPYA-BIPYA respectively. A new approach to metal-ligand complex formation by concomitant fluoride deprotection and assembly was demonstrated with a monomeric complex. Polymetallic complexes formed with a variety of transition metals based on colorimetric changes but the products were very intractable and resisted full structural or transport characterization. Part two develops a system potentially capable of exhibiting dissipative assembly of active transporters. A library of six thioester containing compounds structurally related to known active oligoester compounds was synthesized. The successful syntheses provided the desired compounds in overall yields of 1.0 to 17.7% over 11 to 13 total synthetic steps. The intramolecular cyclization - truncation and thioester exchange reactions central to the dissipative assembly strategy were explored using a model compound. The full length compounds showed transport activity via the HPTS vesicle assay that was significantly below that of the lead compound. Bilayer clamp experiments however, revealed significant transport activity for both the full length as well as the truncated thiol molecules. In the case of the latter the transport events had exceedingly high conductivity for such a small molecule. This unexpected activity for both the full length and truncated compounds, although different, prevented a full implementation of dissipative assembly of transport. / Graduate / 0490 / 0485 / 0494

This thesis describes the development of an ion channel system exhibiting dissipative assembly characteristics. In this system an active transporter based on an oligoester fragment terminated in a thioester of 6-aminohexanoic acid (HO2C-Hex-Adip-OctS-Hex-NH2) undergoes thioester cleavage to form a thiol terminated oligoester (HO2C-Hex-ADip-Oct-SH). This fragment was expected to be inactive for ion transport but previous work showed high activity in planar bilayer experiments. In this work, the high activity was shown to be due to the oxidized form of the thiol, the disulfide HO2C-ADip-Oct-SS-Oct-ADip-Hex-CO2H. Air oxidation was found to be quite rapid for the thiol based on ESI-MS (negative ion) and HPLC analysis. Under anaerobic conditions, the thiol fragment was an inactive species for ion transport. In situ air oxidation initiated transport activity associated with the disulfide. The transporter HO2C-Hex-Adip-Oct-Hex-NH2 was active in planar bilayer experiments and was compared to the disulfide via activity grids. The activity of these two compounds was shown to be distinct from each other by conductance and channel duration differences. The activity of HO2C-Hex-Adip-Oct-Hex-NH2 was shown to die off in a period of 30 minutes at pH 8.2. Techniques were developed to stimulate and monitor activity and bilayer quality so that an inactive condition could be confirmed. The addition of Pr-S-Hex-NH3+-Cl as a fuel was shown to extend the activity of HO2C-Hex-Adip-Oct-Hex-NH2 by eight-fold in 1M CsCl electrolyte. Previous work had established the capability of thioester exchange reactions by a reaction between Pr-S-Hex-NH3+-Cl and benzyl thiol in a homogenous solution. The extended activity indicated that the same process may occur in a heterogeneous bilayer system. An inactive system created by the die-off in activity of HO2C-Hex-Adip-Oct-S-Hex-NH2 was treated with Pr-S-Hex-NH3+-Cl to regenerate activity. This cycle could be repeated once the activity died off again. All these findings are consistent with the dissipative assembly of a membrane transport system. / Graduate / 0490

Research Doctorate - Doctor of Philosophy (PhD) / This thesis addresses the problem of robustness in model predictive control (MPC) of discrete-time systems. In contrast with most previous work on robust MPC, our main focus is on robustness in the face of both imperfect state information and dynamic model uncertainty. For linear discrete-time systems with model uncertainty described by sum quadratic constraints, we propose output-feedback MPC policies that: (i) treat soft constraints using quadratic penalty functions; (ii) respect hard constraints using 'tighter' constraints; and (iii) achieve robust closed-loop stability and non-zero setpoint tracking. Our two main tools are: (1) a new linear matrix inequality condition which parameterizes a class of quadratic MPC cost functions that all lead to robust closed-loop stability; and (2) a new parameterization of soft constraints which has the advantage of leading to optimization problems of prescribable size. The stability test we use for MPC design builds on well-known results from dissipativity theory which we tailor to the case of constrained discrete-time systems. The proposed robust MPC designs are shown to converge to well-known nominal MPC designs as the model uncertainty (description) goes to zero. Furthermore, the present approach to cost function selection is independently motivated by a novel result linking MPC and minimax optimal control theory. Specifically, we show that the considered class of MPC policies are the closed-loop optimal solutions of a particular class of minimax optimal control problems. In addition, for a class of nonlinear discrete-time systems with constraints and bounded disturbance inputs, we propose state-feedback MPC policies that input-to-state stabilize the system. Our two main tools in this last part of the thesis are: (1) a class of N-step affine state-feedback policies; and (2) a result that establishes equivalence between the latter class and an associated class of N-step affine disturbance-feedback policies. Our equivalence result generalizes a recent result in the literature for linear systems to the case when N is chosen to be less than the nonlinear system's 'input-state linear horizon'.

Nesta tese analisamos o comportamento dinâmico, no espaço elos parâmetros, ele duas versões elo circuito eletrônico Double Scroll, descritas por sistemas, não integráveis, de equações diferenciais lineares por partes. A diferença entre esses circuitos reside na curva característica ela resistência negativa, uma contínua e a outra descontínua. O circuito Double Scroll é conhecido por apresentar comportamento caótico associado à existência ele órbitas homoclínicas. Desenvolvemos métodos numéricos para identificar distintos atratores periódicos e caóticos nesses circuitos. Realizamos um estudo completo elas variedades que esses sistemas apresentam, onde demonstramos que o circuito descontínuo não pode formar órbitas homoclínicas. Desenvolvemos um método geral para obter órbitas homoclínicas e heteroclínicas em sistemas lineares por partes. Esse método foi utilizado no circuito contínuo para identificar famílias ele órbitas homoclínicas no espaço elos parâmetros. Fazemos um estudo teórico sobre as órbitas homoclínicas, baseado no teorema ele Shilnikov, e determinamos a lei ele escala geral que descreve as acumulações elas infinitas órbitas homoclínicas no espaço elos parâmetros. Utilizando o método ele detecção ele órbitas homoclínicas, comprovamos, em distintos tipos ele órbitas homoclínicas, a validade dessa lei para o circuito Double Scroll contínuo. Além do mais, através da geometria apresentada pelas famílias ele órbitas homoclínicas que identificamos e ela teoria que permitiu demonstrar a lei ele escala, mostramos a existência ele estruturas ele órbitas homoclínicas que explicam o cenário homoclínico do espaço elos parâmetros. Essas estruturas estão presentes em todos os sistemas para os quais o teorema ele Shilnikov se aplica. Finalmente, sugerimos três experimentos para verificar a existência dessas órbitas e a relação delas com a dinâmica elo sistema. / In this thesis we study the dynamic behavior, in the parameter space, of two versions of the Double Scroll electronic circuit, whose flows are represented by piecewise non integrable systems. The difference between these circuits is the characteristic curves of the negative resistance, one continuous and the other discontinuous. The Double Scroll circuit is known to present chaotic behavior associated to the existence of homoclinic orbits. We develop numerical methods to identify periodic and chaotic attractors in these circuits. We present a complete study of these systems manifolds and demonstrate that the discontinuous circuit cannot form homoclinic orbits. We develop a general method to obtain homoclinic and heteroclinic orbits in piecewise linear systems. This method was used in the continuous circuit to identify homoclinic orbit families in the parameter space. We develop a theoretical study about the homoclinic orbits based on the Shilnikov theorem, determining a general scaling law that describes the accumulations of the infinity homoclinic orbits in the parameter space. Using the detecting homoclinic orbits method, we show the validity of this law for the continuous Double Scroll circuit. Moreover, combining the geometry of the homoclinic or bit families with the scaling law, we show the existence of homoclinic orbits structures of the homoclinic orbits that explain the homoclinic scenario in the parameter space. These structures are present in all systems for which we can apply the Shilnikov theorem. Finally, we suggest three experiments to verify the existence of these orbits and their relation with the system dynamics.

The main objective of the thesis is to understand the parameters that contribute in limiting the pulse energy and spectral bandwidth of the mode-locked femtosecond fiber lasers. I have focused on studying the impact of the parameters of the saturable absorber and the bandwidth of the lumped spectral filter on the temporal and spectral profiles of the pulse. Therefore, I developed two models that can help us to optimize the pulse characteristics such as the pulse energy, spectral bandwidth and de-chirped pulse width. I also introduce two techniques that result in increasing the pulse peak power and spectral bandwidth. The nonlinear transmission coefficient of the saturable absorber is one of the main limitations to achieving high-energy pulses. Throughout my research, I have used two types of saturable absorbers. The first is a lumped semiconductor saturable absorber mirror (SESAM) and the second is based on the nonlinear polarization rotation (NPR) that is considered an artificial saturable absorber with distributed effect. The first model introduced in this thesis is an analytical model, which provides closed form relations for the pulse characteristics of all-normal dispersion fiber laser. It shows how the spectral bandwidth of the lumped filter inserted inside the cavity affects the pulse characteristics. Also, it illustrates the influence of the saturable absorber parameters on the pulse characteristics. I show that increasing the small signal saturable absorber loss and decreasing the saturation power leads to the increase in pulse energy and spectral bandwidth. Numerical simulation and experimental results are in agreement with the results of the analytical models. The second model, which is called the semi-vector model, is applicable to all-normal dispersion mode-locked fiber laser with high output coupling ratio. Nonlinear polarization rotation is employed for mode-locking. The model shows the relationship between the location of the overdriving point of the saturable absorber and the output pulse energy. The results of this model are in agreement with those of the full-vector model, but with a much reduced simulation time. In addition, the experimental results show the accuracy of the proposed model. In this thesis, I mitigate the peak power limitation, caused by the accumulated nonlinear phase shift, by replacing the short high-doped Yb3+ fiber with a long low-doped one. This results in an increase of the peak power by a factor that depends on the ratio between the gain coefficient of the high- and low-doped Yb3+ fiber. The length of the nonlinear section is kept unchanged by reducing the length of the single mode fiber after the long low-doped Yb3+ fiber. Numerical simulation and experimental results validate the idea. The location of narrow bandwidth lumped spectral filter, in an active Similariton laser, has proved to have a distinct effect on the pulse energy, spectral bandwidth and de-chirped pulse width and peak power. The proximity of the spectral filter to the input of the Yb3+-doped fiber leads to increasing the pulse spectral bandwidth and peak power of the de-chirped pulse as well as shortening the de-chirped pulse, but at the expense of reducing the pulse energy.

An aqueous solution of electrolytes can be modelled simplistically as charged hard spheresdispersed in a dielectric continuum. We review various classical theories for hard sphere systems including the Percus-Yevick theory, the mean spherical approximation, the Debye-Hückel theory and the hyper-netted chain theory, and we compare the predictions of the theories with simulation results. The statistical associating fluid theory (SAFT) has proved to be accurate for neutral polymers. It is modified to cope with charged polyelectrolyte systems. A chain term for the charged reference fluid is introduced into the theory. Some well-established results are reproduced in this study and we also introduce new terms and discuss their effects. The results show that the SAFT is semi-quantitatively correct in predicting the phase behaviour of polyelectrolytes. The electrostatic attraction between unlike charged particles at low temperature is very strong. The short-range attractions between unlike pairs are treated via an association theory while the remaining interactions are handled by hypernetted chain theory. This method works quite well with multiple associating sites. The phase prediction for the size and charge symmetric restricted primitive model is quantitatively correct as compared with simulation results. Furthermore, it also gives semi-quantitatively correct predictions for the phase behaviour of size- and charge-asymmetric cases. Dissipative particle dynamics (DPD) is a powerful simulation technique for mesoscopic systems. Molecules with specific shapes (rods and spheres) are simulated using this technique.By tuning the density of the system, some liquid crystal phase transitions can be observed.The properties of spider silk fibroin are also modelled by DPD, indicating a possible route offorming spider silk.

Isoporous membranes manufactured from diblock copolymer are successfully produced at laboratory scale under controlled conditions. Because of the complex phenomena involved, membrane preparation requires trial and error methodologies to find the optimal conditions, leading to a considerable demand of resources. Experimental insights demonstrate that the self-assembly of the block copolymers in solution has an effect on the final membrane structure. Nevertheless, the complete understanding of these multi-scale phenomena is elusive. Herein we use the coarse-grained method Dissipative Particle Dynamics to study the self-assembly of block copolymers that are used for the preparation of the membranes. To simulate representative time and length scales, we introduce a framework for model reduction of polymer chain representations for dissipative particle dynamics, which preserves the properties governing the phase equilibria. We reduce the number of degrees of freedom by accounting for the correlation between beads in fine-grained models via power laws and the consistent scaling of the simulation parameters. The coarse-graining models are consistent with the experimental evidence, showing a morphological transition of the aggregates as the polymer concentration and solvent affinity change. We show that hexagonal packing of the micelles can occur in solution within different windows of polymer concentration depending on the solvent affinity. However, the shape and size dispersion of the micelles determine the characteristic arrangement. We describe the order of crew-cut micelles using a rigid-sphere approximation and propose different phase parameters that characterize the emergence of monodisperse-spherical micelles in solution. Additionally, we investigate the effect of blending asymmetric diblock copolymers (AB/AC) over the properties of the membranes. We observe that the co-assembly mechanism localizes the AC molecules at the interface of A and B domains, and induces the swelling of the B-rich domains. The B-C interactions control the curvature of the assemblies in these blends. Finally, we study the self-assembly triblock copolymers used for membranes fabrication. We show that the polymer concentration, the block-copolymer composition, and the swelling of the micelle are responsible for the formation of elongated micelles in the casting solution. The formation of nanoporous membranes arises from the network-like packing of those micelles.

A spatial soliton is a shape invariant self guided beam of light or a self induced waveguide. Spatial solitons appear as a result of the balance of diffraction and nonlinear focusing in a system. They have been observed in many different conservative media in the last couple of years. Solitons are ubiquitous, because of the probability of using their interactions in optical data processing, communications etc. Up to now due to the power required to generate the solitons, and the response times of the soliton supporting media, these special waves of nature could not penetrate the applications arena. Semiconductors, with their resonant nonlinearities, are thought to be ideal candidates for fast switching, low power spatial solitons. In this dissertation it is shown theoretically and experimentally that it is possible to observe stable spatial solitons in a periodically patterned semiconductor optical amplifier (PPSOA). The solitons have unique beam profiles that change only with system parameters, like pumping current, etc. Their coherent and incoherent interactions which could lead to all optical devices have been investigated experimentally and theoretically. The formation of filaments or modulational instability has been studied theoretically and yielded analytical formulae for evaluating the filament gain and the maximum spatial frequencies in PPSOA devices. Furthermore, discrete array amplifiers have been analyzed numerically for discrete solitons, and the prospect of using multi peak discrete solitons as laser amplifiers is discussed.