The interplay of localization and interactions in quantum many-body systems

Disorder and interactions both play crucial roles in quantum transport. Decades ago, Mott showed that electron-electron interactions can lead to insulating behavior in materials that conventional band theory predicts to be conducting. Soon thereafter, Anderson demonstrated that disorder can localize a quantum particle through the wave interference phenomenon of Anderson localization. Although interactions and disorder both separately induce insulating behavior, the interplay of these two ingredients is subtle and often leads to surprising behavior at the periphery of our current understanding. Modern experiments probe these phenomena in a variety of contexts (e.g. disordered superconductors, cold atoms, photonic waveguides, etc.); thus, theoretical and numerical advancements are urgently needed. In this thesis, we report progress on understanding two contexts in which the interplay of disorder and interactions is especially important.

The first is the so-called “dirty” or random boson problem. In the past decade, a strong-disorder renormalization group (SDRG) treatment by Altman, Kafri, Polkovnikov, and Refael has raised the possibility of a new unstable fixed point governing the superfluid-insulator transition in the one-dimensional dirty boson problem. This new critical behavior may take over from the weak-disorder criticality of Giamarchi and Schulz when disorder is sufficiently strong. We analytically determine the scaling of the superfluid susceptibility at the strong-disorder fixed point and connect our analysis to recent Monte Carlo simulations by Hrahsheh and Vojta. We then shift our attention to two dimensions and use a numerical implementation of the SDRG to locate the fixed point governing the superfluid-insulator transition there. We identify several universal properties of this transition, which are fully independent of the microscopic features of the disorder.

The second focus of this thesis is the interplay of localization and interactions in systems with high energy density (i.e., far from the usual low energy limit of condensed matter physics). Recent theoretical and numerical work indicates that localization can survive in this regime, provided that interactions are sufficiently weak. Stronger interactions can destroy localization, leading to a so-called many-body localization transition. This dynamical phase transition is relevant to questions of thermalization in isolated quantum systems: it separates a many-body localized phase, in which localization prevents transport and thermalization, from a conducting (“ergodic”) phase in which the usual assumptions of quantum statistical mechanics hold. Here, we present evidence that many-body localization also occurs in quasiperiodic systems that lack true disorder.

Beyond Watson and Crick : programming the self-assembly and reconfiguration of DNA nanostructures based on stacking interactions

Life is the result of the execution of molecular programs: like how an embryo is fated to become a human or a whale, or how a person’s appearance is inherited from their parents, many biological phenomena are governed by genetic programs written in DNA molecules. At the core of such programs is the highly reliable base pairing interaction between nucleic acids. DNA nanotechnology exploits the programming power of DNA to build artificial nanostructures, molecular computers, and nanomachines. In particular, DNA origami—which is a simple yet versatile technique that allows one to create various nanoscale shapes and patterns—is at the heart of the technology. In this thesis, I describe the development of programmable self-assembly and reconfiguration of DNA origami nanostructures based on a unique strategy: rather than relying on Watson-Crick base pairing, we developed programmable bonds via the geometric arrangement of stacking interactions, which we termed stacking bonds. We further demonstrated that such bonds can be dynamically reconfigurable.

The first part of this thesis describes the design and implementation of stacking bonds. Our work addresses the fundamental question of whether one can create diverse bond types out of a single kind of attractive interaction—a question first posed implicitly by Francis Crick while seeking a deeper understanding of the origin of life and primitive genetic code. For the creation of multiple specific bonds, we used two different approaches: binary coding and shape coding of geometric arrangement of stacking interaction units, which are called blunt ends. To construct a bond space for each approach, we performed a systematic search using a computer algorithm. We used orthogonal bonds to experimentally implement the connection of five distinct DNA origami nanostructures. We also programmed the bonds to control cis/trans configuration between asymmetric nanostructures.

The second part of this thesis describes the large-scale self-assembly of DNA origami into two-dimensional checkerboard-pattern crystals via surface diffusion. We developed a protocol where the diffusion of DNA origami occurs on a substrate and is dynamically controlled by changing the cationic condition of the system. We used stacking interactions to mediate connections between the origami, because of their potential for reconfiguring during the assembly process. Assembling DNA nanostructures directly on substrate surfaces can benefit nano/microfabrication processes by eliminating a pattern transfer step. At the same time, the use of DNA origami allows high complexity and unique addressability with six-nanometer resolution within each structural unit.

The third part of this thesis describes the use of stacking bonds as dynamically breakable bonds. To break the bonds, we used biological machinery called the ParMRC system extracted from bacteria. The system ensures that, when a cell divides, each daughter cell gets one copy of the cell’s DNA by actively pushing each copy to the opposite poles of the cell. We demonstrate dynamically expandable nanostructures, which makes stacking bonds a promising candidate for reconfigurable connectors for nanoscale machine parts.

Generation of strong quasistatic magnetic fields in interactions of ultraintense and short laser pulses with overdense plasma targets

An analytical fluid model is proposed for the generation of strong quasistatic magnetic fields during normal incidence of a short ultraintense Gaussian laser pulse with a finite spot size on an overdense plasma. The steepening of the electron density profile in the originally homogeneous overdense plasma and the formation of electron cavitation as the electrons are pushed inward by the laser are included self-consistently. It is shown that the appearance of the cavitation plays an important role in the generation of quasistatic magnetic fields: the strong plasma inhomogeneities caused by the formation of the electron cavitation lead to the generation of a strong axial quasistatic magnetic field B-z. In the overdense regime, the generated quasistatic magnetic field increases with increasing laser intensity, while it decreases with increasing plasma density. It is also found that, in a moderately overdense plasma, highly intense laser pulses can generate magnetic fields similar to 100 MG and greater due to the transverse linear mode conversion process.

The interactions of basic proteins and DNA

I. ELECTROPHORESIS OF THE NUCLEIC ACIDS

A zone electrophoresis apparatus using ultraviolet optics has been constructed to study nucleic acids at concentrations less than 0.004%. Native DNA has a mobility about 15% higher than denatured DNA over a range of conditions. Otherwise, the electrophoretic mobility is independent of molecular weight, base composition or source. DNA mobilities change in the expected way with pH but the fractional change in mobility is less than the calculated change in charge. A small decrease in mobility accompanies an increase in ionic strength. RNA’s from various sources have mobilities slightly lower than denatured DNA except for s-RNA which travels slightly faster. The important considerations governing the mobility of nucleic acids appear to be the nature of the hydrodynamic segment, and the binding of counterions. The differences between electrophoresis and sedimentation stem from the fact that all random coil polyelectrolytes are fundamentally free draining in electrophoresis.

II. THE CYTOCHROME C/DNA COMPLEX

The basic protein, cytochrome c, has been complexed to DNA. Up to a cytochrome:DNA mass ratio of 2, a single type of complex is formed. Dissociation of this complex occurs between 0.05F and 0.1F NaCl. The complexing of cytochrome to DNA causes a slight increase in the melting temperature of the DNA, and a reduction of the electrophoretic mobility proportional to the decrease in net charge. Above a cytochrome:DNA mass ratio of 2.5, a different type of complex is formed. The results suggest that complexes such as are formed in the Kleinschmidt technique of electron microscopy would not exist in bulk solution and are exclusively film phenomena.

III. STUDIES OF THE ELECTROPHORESIS AND MELTING BEHAVIOUR OF NUCLEOHISTONES

Electrophoresis studies on reconstituted nucleohistones indicate that the electrophoretic mobility for these complexes is a function of the net charge of the complex. The mobility is therefore dependent on the charge density of the histone complexing the DNA, as well as on the histone/DNA ratio. It is found that the different histones affect the transition from native to denatured DNA in different ways. It appears that histone I is exchanging quite rapidly between DNA molecules in 0.01 F salt, while histone II is irreversibly bound. Histone III-IV enhances the capacity of non-strand separated denatured DNA to reanneal. Studies on native nucleoproteins indicate that there are no gene-sized uncomplexed DNA regions in any preparations studied.

IV. THE DISSOCIATION OF HISTONE FROM CALF THYMUS CROMATIN

Calf thymus nucleoprotein was treated with varying concentrations of NaCl. The identity of the histones associated and dissociated from the DNA at each salt concentration was determined by gel electrophoresis. It was found that there is no appreciable histone dissociation below 0.4 F NaCl. The lysine rich histones dissociate between 0.4 and 0.5 F NaCl. Their dissociation is accompanies by a marked increase in the solubility of the chromatin. The moderately lysine rich histones dissociate mainly between 0.8 and 1.1 F NaCl. There are two arginine rich histone components: the first dissociates between 0.8 F and 1.1 F NaCl, but the second class is the very last to be dissociated from the DNA (dissociation beginning at 1.0 F NaCl). By 2.0 F NaCl, essentially all the histones are dissociated.

The properties of the extracted nucleoprotein were studied. The electrophoretic mobility increases and the melting temperature decreases as more histones are dissociated from the DNA. A comparison with the dissociation of histones from DNA in NaClO₄ shows that to dissociate the same class of histones, the concentration of NaCl required is twice that of NaClO₄.

Fluid-structure Interactions of Inverted Leaves and Flags

Interactions between fluid flows and elastic bodies are ubiquitous in nature. One such phenomena that is encountered on a daily basis is the flapping and fluttering of leaves in the wind. The fluid-structure interaction that governs the physics of a leaf in the wind is poorly understood at best and has potential applications in biomechanics, vehicle design, and energy conversion. We build upon previous work on the flapping dynamics of inverted flags, which are cantilevered elastic sheets with free leading edge and fixed trailing edge that display unique large amplitude oscillatory behaviors. We model a leaf in the laboratory using modified inverted flags, experimentally probing the governing parameters behind leaf fluttering as well as shedding light on the physics behind the inverted flag phenomena. The behavior of these "inverted leaves" studied here display sensitive dependence on two biomechanically relevant parameters, stem-to-leaf rigidity and stem-to-leaf length. In addition, leaves on a tree are not often found alone. We seek to understand the complex interactions of multiple fluttering and flapping leaves by way of examining the interactions between pairs of inverted flags. Coupling through their flow fields, pairs of inverted flags exhibit striking emergent phenomena. We report these observed dynamical behaviors and the conditions upon which they arise.

Fish pass design - criteria for the design and approval of fish passes and other structures to facilitate the passage of migratory fish in rivers

Many of British rivers hold stocks of salmon (Salmo salar L.) and sea trout (Salmo trutta L.) and during most of the year some of the adult fish migrate upstream to the head waters where, with the advent of winter, they will eventually spawn. For a variety of reasons, including the generation of power for milling, improving navigation and measuring water flow, man has put obstacles in the way of migratory fish which have added to those already provided by nature in the shape of rapids and waterfalls. While both salmon and sea trout, particularly the former, are capable of spectacular leaps the movement of fish over man-made and natural obstacles can be helped, or even made possible, by the judicious use of fish passes. These are designed to give the fish an easier route over or round an obstacle by allowing it to overcome the water head difference in a series of stages ('pool and traverse' fish pass) or by reducing the water velocity in a sloping channel (Denil fish pass). Salmon and sea trout make their spawning runs at different flow conditions, salmon preferring much higher water flows than sea trout. Hence the design of fish passes requires an understanding of the swimming ability of fish (speed and endurance) and the effect of water temperature on this ability. Also the unique features of each site must be appreciated to enable the pass to be positioned so that its entrance is readily located. As well as salmon and sea trout, rivers often have stocks of coarse fish and eels. Coarse fish migrations are generally local in character and although some obstructions such as weirs may allow downstream passages only, they do not cause a significant problem. Eels, like salmon and sea trout, travel both up and down river during the course of their life histories. However, the climbing power of elvers is legendary and it is not normally necessary to offer them help, while adult silver eels migrate at times of high water flow when downstream movement is comparatively easy: for these reasons neither coarse fish nor eels are considered further. The provision of fish passes is, in many instances, mandatory under the Salmon and Freshwater Fisheries Act 1975. This report is intended for those involved in the planning, siting, construction and operation of fish passes and is written to clarify the hydraulic problems for the biologist and the biological problems for the engineer. It is also intended to explain the criteria by which the design of an individual pass is assessed for Ministerial Approval.

Interactions of age-dependent mortality and selectivity functions in age-based stock assessment models

The natural mortality rate (M) of fish varies with size and age, although it is often assumed to be constant in stock assessments. Misspecification of M may bias important assessment quantities. We simulated fishery data, using an age-based population model, and then conducted stock assessments on the simulated data. Results were compared to known values. Misspecification of M had a negligible effect on the estimation of relative stock depletion; however, misspecification of M had a large effect on the estimation of parameters describing the stock recruitment relationship, age-specific selectivity, and catchability. If high M occurs in juvenile and old fish, but is misspecified in the assessment model, virgin biomass and catchability are often poorly estimated. In addition, stock recruitment relationships are often very difficult to estimate, and steepness values are commonly estimated at the upper bound (1.0) and overfishing limits tend to be biased low. Natural mortality can be estimated in assessment models if M is constant across ages or if selectivity is asymptotic. However if M is higher in old fish and selectivity is dome-shaped, M and the selectivity cannot both be adequately estimated because of strong interactions between M and selectivity.

Trends and Potential Interactions Between Pinnipeds and Fisheries of New England and the U.S. West Coast

Long-term trends in the abundance and distribution of several pinniped species and commercially important fisheries of New England and the contiguous U.S. west coast are reviewed, and their actual and potential interactions discussed. Emphasis is on biological interactions or competition. The pinnipeds include the western North Atlantic stock of harbor seals, Phoca vitulina concolor; western North Atlantic gray seals, Halochoerus grypus; the U.S. stock of California sea lions, Zalophus californianus californianus; the eastern stock of Steller sea lions, Eumetopias jubatus; and Pacific harbor seals, Phoca vitulina richardii. Fisheries included are those for Atlantic cod, Gadus morhua; silver hake, Merluccius bilinearis; Atlantic herring, Clupea harengus; the coastal stock of Pacific whiting, Merluccius productus; market squid, Loligo opalescens; northern anchovy, Engraulis mordax; Pacific her-ring, Clupea pallasi; and Pacific sardine, Sardinops sagax. Most of these pinniped populations have grown exponentially since passage of the U.S. Marine Mammal Protection Act in 1972. They exploit a broad prey assemblage that includes several commercially valuable species. Direct competition with fisheries is therefore possible, as is competition for the prey of commercially valuable fish. The expanding pinniped populations, fluctuations in commercial fish biomass, and level of exploitation by the fisheries may affect this potential for competition. Concerns over pinnipeds impacting fisheries (especially those with localized spawning stocks or at low biomass levels) are more prevalent than concerns over fisheries’ impacts on pinnipeds. This review provides a framework to further evaluate potential biological interactions between these pinniped populations and the commercial fisheries with which they occur.

Wake, shock and potential field interactions in a 1.5 stage turbine: Part II: Vane-vane interaction and discussion of results

The composition of the time-resolved surface pressure field around a high-pressure rotor blade caused by the presence of neighboring blade rows was studied, with the individual effects of wake, shock and potential field interaction being determined. Two test geometries were considered: first, a high-pressure turbine stage coupled with a swan-necked diffuser exit duct; secondly, the same high-pressure stage but with a vane located in the downstream duct. Both tests were carried out at engine-representative Mach and Reynolds numbers. By comparing the results to time-resolved computational predictions of the flowfield, the accuracy with which the computation predicts blade interaction was determined. Evidence was obtained that for a large downstream vane, the flow conditions in the rotor passage, at any instant in time, are close to being steady state.

Interactions of dietary levels of protein and energy on rainbow trout (Oncorhynchus mykiss) in desert brackish water

A 3x3 factorial experiment was conducted to determine the optimum protein to energy (P/E) ratio for rainbow trout in brackish water. Three crud protein levels and three energy levels at each protein level were utilized. Diets were made in semi-purified that in all of them fish meal, casein and gelatin as the sources of protein and dextrin, starch and oil as the sources of energy were used. Each of experimental diets was fed to triplicate groups of 20 fish with an average individual weight of 81.5 g in 9 2000-1 flow trough fiberglass tanks. During this experiment water temperature, dissolved oxygen, PH and EC were 15±2°C, 6.5-8.1 mg/1, 7.7-8.6 and 25400 grills respectively. The diets were fed at a rate between 1.6-2 wet body weight% per day depended to water temperature in three equal rations and adjusted two weekly for 84 days. At each of protein levels, weight gain percent (%WG), average daily growth percent (%ADG), protein efficiency ratio (PER), apparent net protein utilization percent (%ANPU), or percent of protein deposited, specific growth rate (SGR) and condition factor (CF) were found to increase and food conversion ratio (FCR) was found to decrease with an increasing energy levels from 370 to 430 Kcal/100g. Fish fed a 35% protein, 430 Kcal/100g energy diet with a P/E ratio of 81.4 mg protein/ Kcal PFV energy, attained the best growth performance. Fat and moisture of carcass were affected by protein and energy levels of test diets while protein and ash of carcass were relatively constant in different treatments.