I. Studies on bacteriophage DNA's and minicircular DNA's in M. lysodeikticus and E. coli 15. II. Flow dichroism of DNA solutions

Part I

Chapter 1.....A physicochemical study of the DNA molecules from the three bacteriophages, N1, N5, and N6, which infect the bacterium, M. lysodeikticus, has been made. The molecular weights, as measured by both electron microscopy and sedimentation velocity, are 23 x 10⁶ for N5 DNA and 31 x 10⁶ for N1 and N6 DNA's. All three DNA's are capable of thermally reversible cyclization. N1 and N6 DNA's have identical or very similar base sequences as judged by membrane filter hybridization and by electron microscope heteroduplex studies. They have identical or similar cohesive ends. These results are in accord with the close biological relation between N1 and N6 phages. N5 DNA is not closely related to N1 or N6 DNA. The denaturation T_m of all three DNA's is the same and corresponds to a (GC) content of 70%. However, the buoyant densities in CsCl of Nl and N6 DNA's are lower than expected, corresponding to predicted GC contents of 64 and 67%. The buoyant densities in Cs₂SO₄ are also somewhat anomalous. The buoyant density anomalies are probably due to the presence of odd bases. However, direct base composition analysis of N1 DNA by anion exchange chromatography confirms a GC content of 70%, and, in the elution system used, no peaks due to odd bases are present.

Chapter 2.....A covalently closed circular DNA form has been observed as an intracellular form during both productive and abortive infection processes in M. lysodeikticus. This species has been isolated by the method of CsC1-ethidium bromide centrifugation and examined with an electron microscope.

Chapter 3.....A minute circular DNA has been discovered as a homogeneous population in M. lysodeikticus. Its length and molecular weight as determined by electron microscopy are 0.445 μ and 0.88 x 10⁶ daltons respectively. There is about one minicircle per bacterium.

Chapter 4.....Several strains of E. coli 15 harbor a prophage. Viral growth can be induced by exposing the host to mitomycin C or to uv irradiation. The coliphage 15 particles from E. coli 15 and E, coli 15 T^- appear as normal phage with head and tail structure; the particles from E. coli 15 TAU are tailless. The complete particles exert a colicinogenic activity on E.coli 15 and 15 T^-, the tailless particles do not. No host for a productive viral infection has been found and the phage may be defective. The properties of the DNA of the virus have been studied, mainly by electron microscopy. After induction but before lysis, a closed circular DNA with a contour length of about 11.9 μ is found in the bacterium; the mature phage DNA is a linear duplex and 7.5% longer than the intracellular circular form. This suggests the hypothesis that the mature phage DNA is terminally repetitious and circularly permuted. The hypothesis was confirmed by observing that denaturation and renaturation of the mature phage DNA produce circular duplexes with two single-stranded branches corresponding to the terminal repetition. The contour length of the mature phage DNA was measured relative to φX RFII DNA and λ DNA; the calculated molecular weight is 27 x 10⁶. The length of the single-stranded terminal repetition was compared to the length of φX 174 DNA under conditions where single-stranded DNA is seen in an extended form in electron micrographs. The length of the terminal repetition is found to be 7.4% of the length of the nonrepetitious part of the coliphage 15 DNA. The number of base pairs in the terminal repetition is variable in different molecules, with a fractional standard deviation of 0.18 of the average number in the terminal repetition. A new phenomenon termed "branch migration" has been discovered in renatured circular molecules; it results in forked branches, with two emerging single strands, at the position of the terminal repetition. The distribution of branch separations between the two terminal repetitions in the population of renatured circular molecules was studied. The observed distribution suggests that there is an excluded volume effect in the renaturation of a population of circularly permuted molecules such that strands with close beginning points preferentially renature with each other. This selective renaturation and the phenomenon of branch migration both affect the distribution of branch separations; the observed distribution does not contradict the hypothesis of a random distribution of beginning points around the chromosome.

Chapter 5....Some physicochemical studies on the minicircular DNA species in E. coli 15 (0.670 μ, 1.47 x 10⁶ daltons) have been made. Electron microscopic observations showed multimeric forms of the minicircle which amount to 5% of total DNA species and also showed presumably replicating forms of the minicircle. A renaturation kinetic study showed that the minicircle is a unique DNA species in its size and base sequence. A study on the minicircle replication has been made under condition in which host DNA synthesis is synchronized. Despite experimental uncertainties involved, it seems that the minicircle replication is random and the number of the minicircles increases continuously throughout a generation of the host, regardless of host DNA synchronization.

Part II

The flow dichroism of dilute DNA solutions (A₂₆₀≈0.1) has been studied in a Couette-type apparatus with the outer cylinder rotating and with the light path parallel to the cylinder axis. Shear gradients in the range of 5-160 sec.^-1 were studied. The DNA samples were whole, "half," and "quarter" molecules of T4 bacteriophage DNA, and linear and circular λb₂b₅c DNA. For the linear molecules, the fractional flow dichroism is a linear function of molecular weight. The dichroism for linear A DNA is about 1.8 that of the circular molecule. For a given DNA, the dichroism is an approximately linear function of shear gradient, but with a slight upward curvature at low values of G, and some trend toward saturation at larger values of G. The fractional dichroism increases as the supporting electrolyte concentration decreases.

Stationary random response of multidegree-of-freedom systems

An approximate approach is presented for determining the stationary random response of a general multidegree-of-freedom nonlinear system under stationary Gaussian excitation. This approach relies on defining an equivalent linear system for the nonlinear system. Two particular systems which possess exact solutions have been solved by this approach, and it is concluded that this approach can generate reasonable solutions even for systems with fairly large nonlinearities. The approximate approach has also been applied to two examples for which no exact or approximate solutions were previously available.

Also presented is a matrix algebra approach for determining the stationary random response of a general multidegree-of-freedom linear system. Its derivation involves only matrix algebra and some properties of the instantaneous correlation matricies of a stationary process. It is therefore very direct and straightforward. The application of this matrix algebra approach is in general simpler than that of commonly used approaches.

Advancements in jet turbulence and noise modeling: accurate one-way solutions and empirical evaluation of the nonlinear forcing of wavepackets

Jet noise reduction is an important goal within both commercial and military aviation. Although large-scale numerical simulations are now able to simultaneously compute turbulent jets and their radiated sound, lost-cost, physically-motivated models are needed to guide noise-reduction efforts. A particularly promising modeling approach centers around certain large-scale coherent structures, called wavepackets, that are observed in jets and their radiated sound. The typical approach to modeling wavepackets is to approximate them as linear modal solutions of the Euler or Navier-Stokes equations linearized about the long-time mean of the turbulent flow field. The near-field wavepackets obtained from these models show compelling agreement with those educed from experimental and simulation data for both subsonic and supersonic jets, but the acoustic radiation is severely under-predicted in the subsonic case. This thesis contributes to two aspects of these models. First, two new solution methods are developed that can be used to efficiently compute wavepackets and their acoustic radiation, reducing the computational cost of the model by more than an order of magnitude. The new techniques are spatial integration methods and constitute a well-posed, convergent alternative to the frequently used parabolized stability equations. Using concepts related to well-posed boundary conditions, the methods are formulated for general hyperbolic equations and thus have potential applications in many fields of physics and engineering. Second, the nonlinear and stochastic forcing of wavepackets is investigated with the goal of identifying and characterizing the missing dynamics responsible for the under-prediction of acoustic radiation by linear wavepacket models for subsonic jets. Specifically, we use ensembles of large-eddy-simulation flow and force data along with two data decomposition techniques to educe the actual nonlinear forcing experienced by wavepackets in a Mach 0.9 turbulent jet. Modes with high energy are extracted using proper orthogonal decomposition, while high gain modes are identified using a novel technique called empirical resolvent-mode decomposition. In contrast to the flow and acoustic fields, the forcing field is characterized by a lack of energetic coherent structures. Furthermore, the structures that do exist are largely uncorrelated with the acoustic field. Instead, the forces that most efficiently excite an acoustic response appear to take the form of random turbulent fluctuations, implying that direct feedback from nonlinear interactions amongst wavepackets is not an essential noise source mechanism. This suggests that the essential ingredients of sound generation in high Reynolds number jets are contained within the linearized Navier-Stokes operator rather than in the nonlinear forcing terms, a conclusion that has important implications for jet noise modeling.

Recruitment as an evolving random process of aggregation and mortality

The dynamics of the survival of recruiting fish are analyzed as evolving random processes of aggregation and mortality. The analyses draw on recent advances in the physics of complex networks and, in particular, the scale-free degree distribution arising from growing random networks with preferential attachment of links to nodes. In this study simulations were conducted in which recruiting fish 1) were subjected to mortality by using alternative mortality encounter models and 2) aggregated according to random encounters (two schools randomly encountering one another join into a single school) or preferential attachment (the probability of a successful aggregation of two schools is proportional to the school sizes). The simulations started from either a “disaggregated” (all schools comprised a single fish) or an aggregated initial condition. Results showed the transition of the school-size distribution with preferential attachment evolving toward a scale-free school size distribution, whereas random attachment evolved toward an exponential distribution. Preferential attachment strategies performed better than random attachment strategies in terms of recruitment survival at time when mortality encounters were weighted toward schools rather than to individual fish. Mathematical models were developed whose solutions (either analytic or numerical) mimicked the simulation results. The resulting models included both Beverton-Holt and Ricker-like recruitment, which predict recruitment as a function of initial mean school size as well as initial stock size. Results suggest that school-size distributions during recruitment may provide information on recruitment processes. The models also provide a template for expanding both theoretical and empirical recruitment research.

Isoscalar Giant Monopole Resonance in Relativistic Continuum Random Phase Approximation

The isoscalar giant monopole resonance (ISGMR) in nuclei is studied in the framework of a fully consistent relativistic continuum random phase approximation (RCRPA). In this method the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single particle Green's function technique. The negative energy states in the Dirac sea are also included in the single particle Green's function in the no-sea approximation. The single particle Green's function is calculated numerically by a proper product of the regular and irregular solutions of the Dirac equation. The strength distributions in the RCRPA calculations, the inverse energy-weighted sum rule m(-1) and the centroid energy of the ISGMR in Sn-120 and Pb-208 are analysed. Numerical results of the RCRPA are checked with the constrained relativistic mean field model and relativistic random phase approximation with a discretized spectrum in the continuum. Good agreement between them is achieved.

Relativistic Continuum Random Phase Approximation and Applications I. Formalism

A fully consistent relativistic continuum random phase approximation (RCRPA) is constructed in terms of the Green's function technique. In this method the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single particle Green's function, which includes also the negative states in the Dirac sea in the nose aapproximation. The theoretical formalism of RCRPA and numerical details are presented. The single particle Green's function is calculated numerically by a proper product of regular and irregular solutions of the Dirac equation. The numerical details and the formalism of RCRPA in the momentum representation are presented.

Effects of polar group saturation on physical gelation of Amphiphilic polymer solutions

Monte Carlo simulation on the basis of the comblike coarse grained nonpolar/polar (NP) model has been carried out to study the polar group saturation effect on physical gelation of amphiphilic polymer solutions. The effects of polar group saturation due to hydrogen bonding or ion bridging on the sol-gel phase diagram, microstructure of aggregates, and chain conformation of amphiphilic polymer solutions under four different solvent conditions to either the nonpolar backbone or the polar side chain in amphiphilic polymer chains have been investigated. It is found that an increase of polar group saturation results in a monotonically decreased critical concentration of gelation point, which can be qualitatively supported by the dynamic theological measurements on pectin aqueous solutions. Furthermore, various solvent conditions to either the backbone or the side chain have significant impact on both chain conformation and microstructure of aggregates. When the solvent is repulsive to the nonpolar backbone but attractive to the polar side chain, the polymer chains are collapsed, and the gelation follows the mechanism of colloidal packing; at the other solvent conditions, the gelation follows the mechanism of random aggregation.

Statistical distribution of depth-integrated local horizontal momentum for second-order random ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, statistical distributions of the depth- integrated local horizontal momentum components are derived by use of the characteristic function expansion method. The parameters involved in the distributions can be all determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, a fully developed wind-generated sea is considered and the parameters are calculated for typical wind speeds and water depths by means of the Donelan and Pierson spectrum. The effects of nonlinearity and water depth on the distributions are also investigated.

Statistical distribution of wave-surface elevation for second-order random directional ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, a statistical distribution of the wave-surface elevation is derived by using the characteristic function expansion method. It is found that the distribution, after normalization of the wave-surface elevation, depends only on two parameters. One parameter describes the small mean bias of the surface produced by the second-order wave-wave interactions. Another one is approximately proportional to the skewness of the distribution. Both of these two parameters can be determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, we consider a fully developed wind-generated sea and the parameters are calculated for various wind speeds and water depths by using Donelan and Pierson spectrum. It is also found that, for deep water, the dimensionless distribution reduces to the third-order Gram-Charlier series obtained by Longuet-Higgins [J. Fluid Mech. 17 (1963) 459]. The newly proposed distribution is compared with the data of Bitner [Appl. Ocean Res. 2 (1980) 63], Gaussian distribution and the fourth-order Gram-Charlier series, and found our distribution gives a more reasonable fit to the data. (C) 2002 Elsevier Science B.V. All rights reserved.

Probability distribution of random wave-current forces

Based on the second-order solutions obtained for the three-dimensional weakly nonlinear random waves propagating over a steady uniform current in finite water depth, the joint statistical distribution of the velocity and acceleration of the fluid particle in the current direction is derived using the characteristic function expansion method. From the joint distribution and the Morison equation, the theoretical distributions of drag forces, inertia forces and total random forces caused by waves propagating over a steady uniform current are determined. The distribution of inertia forces is Gaussian as that derived using the linear wave model, whereas the distributions of drag forces and total random forces deviate slightly from those derived utilizing the linear wave model. The distributions presented can be determined by the wave number spectrum of ocean waves, current speed and the second order wave-wave and wave-current interactions. As an illustrative example, for fully developed deep ocean waves, the parameters appeared in the distributions near still water level are calculated for various wind speeds and current speeds by using Donelan-Pierson-Banner spectrum and the effects of the current and the nonlinearity of ocean waves on the distribution are studied. (c) 2006 Elsevier Ltd. All rights reserved.

Seeing 'Ghost' Solutions in Stereo Vision

A unique matching is a stated objective of most computational theories of stereo vision. This report describes situations where humans perceive a small number of surfaces carried by non-unique matching of random dot patterns, although a unique solution exists and is observed unambiguously in the perception of isolated features. We find both cases where non-unique matchings compete and suppress each other and cases where they are all perceived as transparent surfaces. The circumstances under which each behavior occurs are discussed and a possible explanation is sketched. It appears that matching reduces many false targets to a few, but may still yield multiple solutions in some cases through a (possibly different) process of surface interpolation.

A biased random-key genetic algorithm with forward-backward improvement for the resource constrained project scheduling problem

This paper presents a biased random-key genetic algorithm for the resource constrained project scheduling problem. The chromosome representation of the problem is based on random keys. Active schedules are constructed using a priority-rule heuristic in which the priorities of the activities are defined by the genetic algorithm. A forward-backward improvement procedure is applied to all solutions. The chromosomes supplied by the genetic algorithm are adjusted to reflect the solutions obtained by the improvement procedure. The heuristic is tested on a set of standard problems taken from the literature and compared with other approaches. The computational results validate the effectiveness of the proposed algorithm.

Poly(ethylene-co-acrylic acid) random copolymers : amphiphilic properties and self-assembly in aqueous medium

Les travaux de recherche présentés ici avaient pour objectif principal la synthèse de copolymères statistiques à base d’éthylène et d’acide acrylique (AA). Pour cela, la déprotection des groupements esters d’un copolymère statistique précurseur, le poly(éthylène-co-(tert-butyl)acrylate), a été effectuée par hydrolyse à l’aide d’iodure de triméthylsilyle. La synthèse de ce précurseur est réalisée par polymérisation catalytique en présence d’un système à base de Palladium (Pd). Le deuxième objectif a été d’étudier et de caractériser des polymères synthétisés à l’état solide et en suspension colloïdale. Plusieurs copolymères précurseurs comprenant différents pourcentages molaires en tert-butyl acrylate (4 à 12% molaires) ont été synthétisés avec succès, puis déprotégés par hydrolyse pour obtenir des poly(éthylène-coacide acrylique) (pE-co-AA) avec différentes compositions. Seuls les copolymères comprenant 10% molaire ou plus de AA sont solubles dans le Tétrahydrofurane (THF) et uniquement dans ce solvant. De telles solutions peuvent être dialysées dans l’eau, ce qui conduit à un échange lent entre cette dernière et le THF, et l’autoassemblage du copolymère dans l’eau peut ensuite être étudié. C’est ainsi qu’ont pu être observées des nanoparticules stables dans le temps dont le comportement est sensible au pH et à la température. Les polymères synthétisés ont été caractérisés par Résonance Magnétique Nucléaire (RMN) ainsi que par spectroscopie Infra-Rouge (IR), avant et après déprotection. Les pourcentages molaires d’AA ont été déterminés par combinaison des résultats de RMN et ii de titrages conductimètriques. A l’état solide, les échantillons ont été analysés par Calorimétrie différentielle à balayage (DSC) et par Diffraction des rayons X. Les solutions colloïdales des polymères pE-co-AA ont été caractérisées par Diffusion dynamique de la lumière et par la DSC-haute sensibilité. De la microscopie électronique à transmission (TEM) a permis de visualiser la forme et la taille des nanoparticules.

New stimuli-responsive block random copolymers and their aggregation

Les polymères sensibles à des stimuli ont été largement étudiés ces dernières années notamment en vue d’applications biomédicales. Ceux-ci ont la capacité de changer leurs propriétés de solubilité face à des variations de pH ou de température. Le but de cette thèse concerne la synthèse et l’étude de nouveaux diblocs composés de deux copolymères aléatoires. Les polymères ont été obtenus par polymérisation radicalaire contrôlée du type RAFT (reversible addition-fragmentation chain-transfer). Les polymères à bloc sont formés de monomères de méthacrylates et/ou d’acrylamides dont les polymères sont reconnus comme thermosensibles et sensible au pH. Premièrement, les copolymères à bloc aléatoires du type AnBm-b-ApBq ont été synthétisés à partir de N-n-propylacrylamide (nPA) et de N-ethylacrylamide (EA), respectivement A et B, par polymérisation RAFT. La cinétique de copolymérisation des poly(nPAx-co-EA1-x)-block-poly(nPAy-co-EA1-y) et leur composition ont été étudiées afin de caractériser et évaluer les propriétés physico-chimiques des copolymères à bloc aléatoires avec un faible indice de polydispersité . Leurs caractères thermosensibles ont été étudiés en solution aqueuse par spectroscopie UV-Vis, turbidimétrie et analyse de la diffusion dynamique de la lumière (DLS). Les points de trouble (CP) observés des blocs individuels et des copolymères formés démontrent des phases de transitions bien définies lors de la chauffe. Un grand nombre de macromolécules naturels démontrent des réponses aux stimuli externes tels que le pH et la température. Aussi, un troisième monomère, 2-diethylaminoethyl methacrylate (DEAEMA), a été ajouté à la synthèse pour former des copolymères à bloc , sous la forme AnBm-b-ApCq , et qui offre une double réponse (pH et température), modulable en solution. Ce type de polymère, aux multiples stimuli, de la forme poly(nPAx-co-DEAEMA1-x)-block-poly(nPAy-co-EA1-y), a lui aussi été synthétisé par polymérisation RAFT. Les résultats indiquent des copolymères à bloc aléatoires aux propriétés physico-chimiques différentes des premiers diblocs, notamment leur solubilité face aux variations de pH et de température. Enfin, le changement d’hydrophobie des copolymères a été étudié en faisant varier la longueur des séquences des blocs. Il est reconnu que la longueur relative des blocs affecte les mécanismes d’agrégation d’un copolymère amphiphile. Ainsi avec différents stimuli de pH et/ou de température, les expériences effectuées sur des copolymères à blocaléatoires de différentes longueurs montrent des comportements d’agrégation intéressants, évoluant sous différentes formes micellaires, d’agrégats et de vésicules.

Branching random motions, nonlinear hyperbolic systems and traveling waves

A branching random motion on a line, with abrupt changes of direction, is studied. The branching mechanism, being independient of random motion, and intensities of reverses are defined by a particle's current direction. A soluton of a certain hyperbolic system of coupled non-linear equations (Kolmogorov type backward equation) have a so-called McKean representation via such processes. Commonly this system possesses traveling-wave solutions. The convergence of solutions with Heaviside terminal data to the travelling waves is discussed.This Paper realizes the McKean programme for the Kolmogorov-Petrovskii-Piskunov equation in this case. The Feynman-Kac formula plays a key role.