Some problems of edge waves and standing waves on beaches

Some problems of edge waves and standing waves on beaches are examined.

The nonlinear interaction of a wave normally incident on a sloping beach with a subharmonic edge wave is studied. A two-timing expansion is used in the full nonlinear theory to obtain the modulation equations which describe the evolution of the waves. It is shown how large amplitude edge waves are produced; and the results of the theory are compared with some recent laboratory experiments.

Traveling edge waves are considered in two situations. First, the full linear theory is examined to find the finite depth effect on the edge waves produced by a moving pressure disturbance. In the second situation, a Stokes' expansion is used to discuss the nonlinear effects in shallow water edge waves traveling over a bottom of arbitrary shape. The results are compared with the ones of the full theory for a uniformly sloping bottom.

The finite amplitude effects for waves incident on a sloping beach, with perfect reflection, are considered. A Stokes' expansion is used in the full nonlinear theory to find the corrections to the dispersion relation for the cases of normal and oblique incidence.

Finally, an abstract formulation of the linear water waves problem is given in terms of a self adjoint but nonlocal operator. The appropriate spectral representations are developed for two particular cases.

On the settling speed of dilute arrays of spheres

A method is developed to calculate the settling speed of dilute arrays of spheres for the three cases of: I, a random array of freely moving particles; II, a random array of rigidly held particles; and III, a cubic array of particles. The basic idea of the technique is to give a formal representation for the solution and then manipulate this representation in a straightforward manner to obtain the result. For infinite arrays of spheres, our results agree with the results previously found by other authors, and the analysis here appears to be simpler. This method is able to obtain more terms in the answer than was possible by Saffman's unified treatment for point particles. Some results for arbitrary two sphere distributions are presented, and an analysis of the wall effect for particles settling in a tube is given. It is expected that the method presented here can be generalized to solve other types of problems.

Biotechnologies for cancer diagnostics : cell sorting, protein analysis and imaging of cellular metabolism

This thesis presents the development of chip-based technology for informative in vitro cancer diagnostics. In the first part of this thesis, I will present my contribution in the development of a technology called “Nucleic Acid Cell Sorting (NACS)”, based on microarrays composed of nucleic acid encoded peptide major histocompatibility complexes (p/MHC), and the experimental and theoretical methods to detect and analyze secreted proteins from single or few cells.

Secondly, a novel portable platform for imaging of cellular metabolism with radio probes is presented. A microfluidic chip, so called “Radiopharmaceutical Imaging Chip” (RIMChip), combined with a beta-particle imaging camera, is developed to visualize the uptake of radio probes in a small number of cells. Due to its sophisticated design, RIMChip allows robust and user-friendly execution of sensitive and quantitative radio assays. The performance of this platform is validated with adherent and suspension cancer cell lines. This platform is then applied to study the metabolic response of cancer cells under the treatment of drugs. Both cases of mouse lymphoma and human glioblastoma cell lines, the metabolic responses to the drug exposures are observed within a short time (~ 1 hour), and are correlated with the arrest of cell-cycle, or with changes in receptor tyrosine kinase signaling.

The last parts of this thesis present summaries of ongoing projects: development of a new agent as an in vivo imaging probe for c-MET, and quantitative monitoring of glycolytic metabolism of primary glioblastoma cells. To develop a new agent for c-MET imaging, the one-bead-one-compound combinatorial library method is used, coupled with iterative screening. The performance of the agent is quantitatively validated with cell-based fluorescent assays. In the case of monitoring the metabolism of primary glioblastoma cell, by RIMChip, cells were sorting according to their expression levels of oncoprotein, or were treated with different kinds of drugs to study the metabolic heterogeneity of cancer cells or metabolic response of glioblastoma cells to drug treatments, respectively.

Model studies of Ziegler-Natta olefin polymerization using group 3 and group 4 metallocenes

Evidence for the stereochemical isomerization of a variety of ansa metallocene compounds is presented. For the scandocene allyl derivatives described here, we have established that the process is promoted by a variety of salts in both ether and hydrocarbon solvents and is not accelerated by light. A plausible mechanism based on an earlier proposal by Marks, et al., is offered as an explanation of this process. It involves coordination of anions and/or donor solvents to the metal center with cation assistance to encourage metalcyclopentadienyl bond heterolysis, rotation about the Si-Cp bond of the detached cyclopentadienide and recoordination of the opposite face. Our observations in some cases of thermodynamic racemic:meso ratios under the reaction conditions commonly used for the synthesis of the metallocene chlorides suggests that the interchange is faster than metallation, such that the composition of the reaction mixture is determined by thermodynamic, not kinetic, control in these cases.

Two new ansa-scandocene alkenyl compounds react with olefins resulting in the formation of η³-allyl complexes. Kinetics and labeling experiments indicate a tuck-in intermediate on the reaction pathway; in this intermediate the metal is bound to the carbon adjacent to the silyllinker in the rear of the metallocene wedge. In contrast, reaction of permethylscandocene alkenyl compounds with olefins results, almost exclusively, in vinylic C-H bond activation. It is proposed that relieving transition state steric interactions between the cyclopentadienyl rings and the olefin by either linking the rings together or using a larger lanthanide metal may allow for olefin coordination, stabilizing the transition state for allylic σ-bond metathesis.

A selectively isotopically labeled propylene, CH₂CD(¹³CH₃), was synthesized and its polymerization was carried out at low concentration in toluene solution using isospecific metallocene catalysts. Analysis of the NMR spectra (¹³C, ¹H, and ²H) of the resultant polymers revealed that the production of stereoerrors through chain epimerization proceeds exclusively by the tertiaryalkyl mechanism. Additionally, enantiofacial inversion of the terminally unsaturated polymer chain occurs by a non-dissociative process. The implications of these results on the mechanism of olefin polymerization with these catalysts is discussed.

Suspension mechanics: I. Inertial and non-Newtonian migration of neutrally buoyant rigid spheres in two-dimensional unidirectional flows; II. The effect of viscoelasticity on the creeping motion of a train of neutrally buoyant Newtonian drops through a circular tube

The lateral migration of neutrally buoyant rigid spheres in two-dimensional unidirectional flows was studied theoretically. The cases of both inertia-induced migration in a Newtonian fluid and normal stress-induced migration in a second-order fluid were considered. Analytical results for the lateral velocities were obtained, and the equilibrium positions and trajectories of the spheres compared favorably with the experimental data available in the literature. The effective viscosity was obtained for a dilute suspension of spheres which were simultaneously undergoing inertia-induced migration and translational Brownian motion in a plane Poiseuille flow. The migration of spheres suspended in a second-order fluid inside a screw extruder was also considered.

The creeping motion of neutrally buoyant concentrically located Newtonian drops through a circular tube was studied experimentally for drops which have an undeformed radius comparable to that of the tube. Both a Newtonian and a viscoelastic suspending fluid were used in order to determine the influence of viscoelasticity. The extra pressure drop due to the presence of the suspended drops, the shape and velocity of the drops, and the streamlines of the flow were obtained for various viscosity ratios, total flow rates, and drop sizes. The results were compared with existing theoretical and experimental data.

Generalizations and extensions of the Fokker-Planck-Kolmogorov equations

The problem of determining probability density functions of general transformations of random processes is considered in this thesis. A method of solution is developed in which partial differential equations satisfied by the unknown density function are derived. These partial differential equations are interpreted as generalized forms of the classical Fokker-Planck-Kolmogorov equations and are shown to imply the classical equations for certain classes of Markov processes. Extensions of the generalized equations which overcome degeneracy occurring in the steady-state case are also obtained.

The equations of Darling and Siegert are derived as special cases of the generalized equations thereby providing unity to two previously existing theories. A technique for treating non-Markov processes by studying closely related Markov processes is proposed and is seen to yield the Darling and Siegert equations directly from the classical Fokker-Planck-Kolmogorov equations.

As illustrations of their applicability, the generalized Fokker-Planck-Kolmogorov equations are presented for certain joint probability density functions associated with the linear filter. These equations are solved for the density of the output of an arbitrary linear filter excited by Markov Gaussian noise and for the density of the output of an RC filter excited by the Poisson square wave. This latter density is also found by using the extensions of the generalized equations mentioned above. Finally, some new approaches for finding the output probability density function of an RC filter-limiter-RC filter system driven by white Gaussian noise are included. The results in this case exhibit the data required for complete solution and clearly illustrate some of the mathematical difficulties inherent to the use of the generalized equations.

Photochemical cis-trans isomerization of β-styrylferrocene

The effect of metal atoms on photochemical transformations has been investigated by studies of the cis-trans isomerization of β-styrylferrocene.

The photostationary state lies entirely on the side of the trans isomer in the cases of direct irradiation at 3130 Å or at 3660 Å. The quantum yield at 3130 Å is 0.00650 and does not vary with concentration. In the presence of benzophenon as sensitizer the quantum yield is 0.00540. On the other hand, the quantum yield for direct irradiation at 3660 Å decreases with increasing concentration of cis β- styrylferrocene varying from 0.00365 to 0.00198.

These results lead to the suggestion that the isomerization takes place from a triplet state of β-styrylferrocene which probably has higher energy than the lowest triplet; reaction from the third triplet seems most likely.

Photosensitized CIS-TRANS isomerization of 2,3-diphenylbutene-2 investigation of anomalous sensitizers for substituted Stilbene isometrization

The behavior of the photosensitized cis-trans isomerization of 2,3-diphenylbutene-2 was studied as a function of sensitizer energy by previously established methods. In addition, certain sensitizers for which parameters other than energy transfer are operative in inducting isomerizations, were studied in more detail. Sensitization of various stilbenes and substituted stilbenes by triphenylene is discussed in terms of excited state complex formation with stilbene. Sensitization by quinones, halogen-containing aromatics and 1,2-diketones is discussed in terms of attack by photolytically produced free radicals, either by addition to and elimination from the double bond, or in the cases of 1,2-diphenylpropene and 2,3-diphenylbutene-2, by hydrogen abstraction from one of the methyl groups and reversible abstraction by the allylic radical to produce cis-trans isomerized substrate and the structurally isomerized products, 2,3-diphenylpropene and 2,3-diphenylbutene-1.

Large plane deformations of thin elastic sheets of neo-hookean material

Large plane deformations of thin elastic sheets of neo-Hookean material are considered and a method of successive substitutions is developed to solve problems within the two-dimensional theory of finite plane stress. The first approximation is determined by linear boundary value problems on two harmonic functions, and it is approached asymptotically at very large extensions in the plane of the sheet. The second and higher approximations are obtained by solving Poisson equations. The method requires modification when the membrane has a traction-free edge.

Several problems are treated involving infinite sheets under uniform biaxial stretching at infinity. First approximations are obtained when a circular or elliptic inclusion is present and when the sheet has a circular or elliptic hole, including the limiting cases of a line inclusion and a straight crack or slit. Good agreement with exact solutions is found for circularly symmetric deformations. Other examples discuss the stretching of a short wide strip, the deformation near a boundary corner which is traction-free, and the application of a concentrated load to a boundary point.

I. The structure and properties of closed circular duplex DNA. II. Chemically interacting systems at equilibrium in a buoyant density gradient

I. The binding of the intercalating dye ethidium bromide to closed circular SV 40 DNA causes an unwinding of the duplex structure and a simultaneous and quantitatively equivalent unwinding of the superhelices. The buoyant densities and sedimentation velocities of both intact (I) and singly nicked (II) SV 40 DNAs were measured as a function of free dye concentration. The buoyant density data were used to determine the binding isotherms over a dye concentration range extending from 0 to 600 µg/m1 in 5.8 M CsCl. At high dye concentrations all of the binding sites in II, but not in I, are saturated. At free dye concentrations less than 5.4 µg/ml, I has a greater affinity for dye than II. At a critical amount of dye bound I and II have equal affinities, and at higher dye concentration I has a lower affinity than II. The number of superhelical turns, τ, present in I is calculated at each dye concentration using Fuller and Waring's (1964) estimate of the angle of duplex unwinding per intercalation. The results reveal that SV 40 DNA I contains about -13 superhelical turns in concentrated salt solutions.

The free energy of superhelix formation is calculated as a function of τ from a consideration of the effect of the superhelical turns upon the binding isotherm of ethidium bromide to SV 40 DNA I. The value of the free energy is about 100 kcal/mole DNA in the native molecule. The free energy estimates are used to calculate the pitch and radius of the superhelix as a function of the number of superhelical turns. The pitch and radius of the native I superhelix are 430 Å and 135 Å, respectively.

A buoyant density method for the isolation and detection of closed circular DNA is described. The method is based upon the reduced binding of the intercalating dye, ethidium bromide, by closed circular DNA. In an application of this method it is found that HeLa cells contain in addition to closed circular mitochondrial DNA of mean length 4.81 microns, a heterogeneous group of smaller DNA molecules which vary in size from 0.2 to 3.5 microns and a paucidisperse group of multiples of the mitochondrial length.

II. The general theory is presented for the sedimentation equilibrium of a macromolecule in a concentrated binary solvent in the presence of an additional reacting small molecule. Equations are derived for the calculation of the buoyant density of the complex and for the determination of the binding isotherm of the reagent to the macrospecies. The standard buoyant density, a thermodynamic function, is defined and the density gradients which characterize the four component system are derived. The theory is applied to the specific cases of the binding of ethidium bromide to SV 40 DNA and of the binding of mercury and silver to DNA.

Estimation of catalyst activity profiles and deactivation parameters from reactor operating data with applications to naphtha reforming

Techniques are developed for estimating activity profiles in fixed bed reactors and catalyst deactivation parameters from operating reactor data. These techniques are applicable, in general, to most industrial catalytic processes. The catalytic reforming of naphthas is taken as a broad example to illustrate the estimation schemes and to signify the physical meaning of the kinetic parameters of the estimation equations. The work is described in two parts. Part I deals with the modeling of kinetic rate expressions and the derivation of the working equations for estimation. Part II concentrates on developing various estimation techniques.

Part I: The reactions used to describe naphtha reforming are dehydrogenation and dehydroisomerization of cycloparaffins; isomerization, dehydrocyclization and hydrocracking of paraffins; and the catalyst deactivation reactions, namely coking on alumina sites and sintering of platinum crystallites. The rate expressions for the above reactions are formulated, and the effects of transport limitations on the overall reaction rates are discussed in the appendices. Moreover, various types of interaction between the metallic and acidic active centers of reforming catalysts are discussed as characterizing the different types of reforming reactions.

Part II: In catalytic reactor operation, the activity distribution along the reactor determines the kinetics of the main reaction and is needed for predicting the effect of changes in the feed state and the operating conditions on the reactor output. In the case of a monofunctional catalyst and of bifunctional catalysts in limiting conditions, the cumulative activity is sufficient for predicting steady reactor output. The estimation of this cumulative activity can be carried out easily from measurements at the reactor exit. For a general bifunctional catalytic system, the detailed activity distribution is needed for describing the reactor operation, and some approximation must be made to obtain practicable estimation schemes. This is accomplished by parametrization techniques using measurements at a few points along the reactor. Such parametrization techniques are illustrated numerically with a simplified model of naphtha reforming.

To determine long term catalyst utilization and regeneration policies, it is necessary to estimate catalyst deactivation parameters from the the current operating data. For a first order deactivation model with a monofunctional catalyst or with a bifunctional catalyst in special limiting circumstances, analytical techniques are presented to transform the partial differential equations to ordinary differential equations which admit more feasible estimation schemes. Numerical examples include the catalytic oxidation of butene to butadiene and a simplified model of naphtha reforming. For a general bifunctional system or in the case of a monofunctional catalyst subject to general power law deactivation, the estimation can only be accomplished approximately. The basic feature of an appropriate estimation scheme involves approximating the activity profile by certain polynomials and then estimating the deactivation parameters from the integrated form of the deactivation equation by regression techniques. Different bifunctional systems must be treated by different estimation algorithms, which are illustrated by several cases of naphtha reforming with different feed or catalyst composition.

Chemical and electrochemical investigations of cobalt cyanide and ruthenium ammine complexes

Part I.

The stoichiometry and kinetics of the reaction between Co(CN₅H^3- and HgX₂ (X = CN, OH) have been investigated. The products of the reaction are two new complexes, [(NC)₅Co-HgX]^3- and [(NC)₅Co-Hg-Co(CN)₅]^6-, whose spectra are reported. The kinetic measurements produced a value for the forward rate constant of the reaction Co(CN)₅H^3- + OH^- k₁/k_-1 Co(CN)₅^4- +H₂O, k1 = (9.7 ± 0.8) x 10^-2 M^-1 sec^-1 at 24°C, and an equilibrium constant for the reaction K = 10^-6 M^-1.

Part II.

Unusually large and sharp "adsorption waves" appear in cyclic voltammograms of Co(CN)₅^3- and several cobalt(III) pentacyano complexes at stationary mercury electrodes. The nature of the adsorbed species and the reasons for the absence of the adsorption waves in polarograms taken with a d.m.e. have been examined. The data are compatible with the adsorption, in all cases, of a coordinatively unsaturated cobalt(II) complex, Co(CN)₄^2-, by means of a cobalt-mercury bond. When the resulting adsorbed complex is reduced, a series of subsequent chemical and electrode reactions is initiated in which three faradays of charge are consumed for each mole of adsorbed complex. The adsorption of the anionic complex strongly retards the reduction of other negatively charged complexes.

Part III.

A number of formal redox potentials for Ru^III (NH₃)₅L + e = Ru^II (NH₃)₅L and Ru^III(NH₃)₄L₂ + e = Ru^II (NH₃)₄L₂ (where L is various ligands) has been measured by cyclic voltammetry, potentiometry, and polarography and are discussed in terms of the properties of the ligands, such as π-accepting capability. Reduction of coordinated pyrazine in the complexes, Ru(NH₃)₅ Pz²⁺, cis- and trans-Ru(NH₃)₄Pz₂²⁺, on a mercury electrode has been observed. The behavior of this reduction in various acidity of the solution as well as the reoxidation of the reduction products are discussed.