Crystals that count! Physical principles and experimental investigations of DNA tile self-assembly

Algorithmic DNA tiles systems are fascinating. From a theoretical perspective, they can result in simple systems that assemble themselves into beautiful, complex structures through fundamental interactions and logical rules. As an experimental technique, they provide a promising method for programmably assembling complex, precise crystals that can grow to considerable size while retaining nanoscale resolution. In the journey from theoretical abstractions to experimental demonstrations, however, lie numerous challenges and complications.

In this thesis, to examine these challenges, we consider the physical principles behind DNA tile self-assembly. We survey recent progress in experimental algorithmic self-assembly, and explain the simple physical models behind this progress. Using direct observation of individual tile attachments and detachments with an atomic force microscope, we test some of the fundamental assumptions of the widely-used kinetic Tile Assembly Model, obtaining results that fit the model to within error. We then depart from the simplest form of that model, examining the effects of DNA sticky end sequence energetics on tile system behavior. We develop theoretical models, sequence assignment algorithms, and a software package, StickyDesign, for sticky end sequence design.

As a demonstration of a specific tile system, we design a binary counting ribbon that can accurately count from a programmable starting value and stop growing after overflowing, resulting in a single system that can construct ribbons of precise and programmable length. In the process of designing the system, we explain numerous considerations that provide insight into more general tile system design, particularly with regards to tile concentrations, facet nucleation, the construction of finite assemblies, and design beyond the abstract Tile Assembly Model.

Finally, we present our crystals that count: experimental results with our binary counting system that represent a significant improvement in the accuracy of experimental algorithmic self-assembly, including crystals that count perfectly with 5 bits from 0 to 31. We show some preliminary experimental results on the construction of our capping system to stop growth after counters overflow, and offer some speculation on potential future directions of the field.

An experimental study of the mobility of edge dislocations in pure copper single crystals

The velocity of selectively-introduced edge dislocations in 99.999 percent pure copper crystals has been measured as a function of stress at temperatures from 66°K to 373°K by means of a torsion technique. The range of resolved shear stress was 0 to 15 megadynes/ cm^2 for seven temperatures (66°K, 74°K, 83°K, 123°K, 173°K, 296°K, 296°K, 373°K.

Dislocation mobility is characterized by two distinct features; (a) relatively high velocity at low stress (maximum velocities of about 9000 em/sec were realized at low temperatures), and (b) increasing velocity with decreasing temperature at constant stress.

The relation between dislocation velocity and resolved shear stress is:

v = v_o(τ_r/τ_o)^n

where v is the dislocation velocity at resolved shear stress τ_r, v_o is a constant velocity chosen equal to 2000 cm/ sec, τ_o is the resolved shear stress required to maintain velocity v_o, and n is the mobility coefficient. The experimental results indicate that τ_o decreases from 16.3 x 10^6 to 3.3 x 10^6 dynes/cm^2 and n increases from about 0.9 to 1.1 as the temperature is lowered from 296°K to 66°K.

The experimental dislocation behavior is consistent with an interpretation on the basis of phonon drag. However, the complete temperature dependence of dislocation mobility could not be closely approximated by the predictions of one or a combination of mechanisms.

Experimental study of the upper hybrid echo in plasmas

The two-pulse stimulated radiation of dense (10^9/cm^3 < ne ≤ 10^(11) /cm^3) nonuniform neon and argon afterglow plasma columns longitudinally immersed in a magnetic field is studied. The magnetic field is very homogeneous over the plasma volume (∆B/B~.01%). If the S-band microwave pulses' center frequency is such that they resonantly excite a narrow band of plasma upper hybrid oscillations close to the maximum upper hybrid frequency of the column, strong two pulse echoes are observed. This new echo process is called the upper hybrid echo. The echo spectrum, echo power and echo width were studied as a function of the pulse peak power P, pulse separation τ, relative density (ω_(po)/ω)^2, and relative cyclotron frequency (ω_c/ω). The complex but systematic variations of the echo properties as a function of the above-mentioned parameters arc found to be in qualitative agreement with those predicted by a theory of Gould and Blum based upon a simple nonuniform unidimensional cold plasma slab model. The possible effects of electron neutral and electron ion collisions not retained in the theoretical model are discussed.

The existence of a new type of cyclotron echo, different from that of Hill and Kaplan and not predicted by the Blum and Gould model is documented. It is believed to be also of a collective effect nature and can probably be described in terms of a theory retaining some hot plasma effects.

Experimental and theoretical developments in extended x-ray absorption fine structure (EXAFS) spectroscopy

To obtain accurate information from a structural tool it is necessary to have an understanding of the physical principles which govern the interaction between the probe and the sample under investigation. In this thesis a detailed study of the physical basis for Extended X-ray Absorption Fine Structure (EXAFS) spectroscopy is presented. A single scattering formalism of EXAFS is introduced which allows a rigorous treatment of the central atom potential. A final state interaction formalism of EXAFS is also discussed. Multiple scattering processes are shown to be significant for systems of certain geometries. The standard single scattering EXAFS analysis produces erroneous results if the data contain a large multiple scattering contribution. The effect of thermal vibrations on such multiple scattering paths is also discussed. From symmetry considerations it is shown that only certain normal modes contribute to the Debye-Waller factor for a particular scattering path. Furthermore, changes in the scattering angles induced by thermal vibrations produces additional EXAFS components called modification factors. These factors are shown to be small for most systems.

A study of the physical basis for the determination of structural information from EXAFS data is also presented. An objective method of determining the background absorption and the threshold energy is discussed and involves Gaussian functions. In addition, a scheme to determine the nature of the scattering atom in EXAFS experiments is introduced. This scheme is based on the fact that the phase intercept is a measure of the type of scattering atom. A method to determine bond distances is also discussed and does not require the use of model compounds or calculated phase shifts. The physical basis for this method is the absence of a linear term in the scattering phases. Therefore, it is possible to separate these phases from the linear term containing the distance information in the total phase.

Experimental study on inertial effects in liquid-solid flows

This thesis presents experimental measurements of the rheological behavior of liquid-solid mixtures at moderate Reynolds (defined by the shear rate and particle diameter) and Stokes numbers, ranging from 3 ≤ Re ≤ 1.6 × 10³ and 0.4 ≤ St ≤ 195. The experiments use a specifically designed Couette cylindrical rheometer that allows for probing the transition from transporting a pure liquid to transporting a dense suspension of particles. Measurements of the shear stress are presented for a wide range of particle concentration (10 to 60% in volume) and for particle to fluid density ratio between 1 and 1.05. The effective relative viscosity exhibits a strong dependence on the solid fraction for all density ratios tested. For density ratio of 1 the effective viscosity increases with Stokes number (St) for volume fractions (φ) lower than 40% and becomes constant for higher φ. When the particles are denser than the liquid, the effective viscosity shows a stronger dependance on St. An analysis of the particle resuspension for the case with a density ratio of 1.05 is presented and used to predict the local volume fraction where the shear stress measurements take place. When the local volume fraction is considered, the effective viscosity for settling and no settling particles is consistent, indicating that the effective viscosity is independent of differences in density between the solid and liquid phase. Shear stress measurements of pure fluids (no particles) were performed using the same rheometer, and a deviation from laminar behavior is observed for gap Reynolds numbers above 4× 10³, indicating the presence of hydrodynamic instabilities associated with the rotation of the outer cylinder. The increase on the effective viscosity with Stokes numbers observed for mixtures with φ ≤ 30% appears to be affected by such hydrodynamic instabilities. The effective viscosity for the current experiments is considerably higher than the one reported in non-inertial suspensions.

A study of flow conditions near the substratum in an experimental channel [Translation from: Verhandlungen der Internationalen Vereinigung fur Theoretische und Angewandte Limnologie 18, 718-725, 1972]

In a slow flow, on a smooth uniform substratum, a limited bed allows the existence of currents slow enough for benthic invertebrates. These conditions rarely occur naturally. The investigations carried out in this work aimed, on an intermediary scale, to define the influence of irregularities in the substratum on flow near the bottom. The substrata used were made of glass marbles. The investigations were carried out in a transparent channel of 70 cm in length and a rectangular section 10 x 5 cm. The data was analysed to study the general evolution of flow in terms of average speeds and the appearance of the turbulence near the bottom.

Experimental, Numerical and Analytical Studies of the MHD-driven plasma jet, instabilities and waves

This thesis describes a series of experimental, numerical, and analytical studies involving the Caltech magnetohydrodynamically (MHD)-driven plasma jet experiment. The plasma jet is created via a capacitor discharge that powers a magnetized coaxial planar electrodes system. The jet is collimated and accelerated by the MHD forces.

We present three-dimensional ideal MHD finite-volume simulations of the plasma jet experiment using an astrophysical magnetic tower as the baseline model. A compact magnetic energy/helicity injection is exploited in the simulation analogous to both the experiment and to astrophysical situations. Detailed analysis provides a comprehensive description of the interplay of magnetic force, pressure, and flow effects. We delineate both the jet structure and the transition process that converts the injected magnetic energy to other forms.

When the experimental jet is sufficiently long, it undergoes a global kink instability and then a secondary local Rayleigh-Taylor instability caused by lateral acceleration of the kink instability. We present an MHD theory of the Rayleigh-Taylor instability on the cylindrical surface of a plasma flux rope in the presence of a lateral external gravity. The Rayleigh-Taylor instability is found to couple to the classic current-driven instability, resulting in a new type of hybrid instability. The coupled instability, produced by combination of helical magnetic field, curvature of the cylindrical geometry, and lateral gravity, is fundamentally different from the classic magnetic Rayleigh-Taylor instability occurring at a two-dimensional planar interface.

In the experiment, this instability cascade from macro-scale to micro-scale eventually leads to the failure of MHD. When the Rayleigh-Taylor instability becomes nonlinear, it compresses and pinches the plasma jet to a scale smaller than the ion skin depth and triggers a fast magnetic reconnection. We built a specially designed high-speed 3D magnetic probe and successfully detected the high frequency magnetic fluctuations of broadband whistler waves associated with the fast reconnection. The magnetic fluctuations exhibit power-law spectra. The magnetic components of single-frequency whistler waves are found to be circularly polarized regardless of the angle between the wave propagation direction and the background magnetic field.

Experimental research on dormancy in Cyclops vicinus [Translation from: Naturwissenschaften 56 93-94, 1969]

Dormancy has been observed in several species of Cyclops. Animals in dormancy are characterised by almost complete inactivity of the main appendages and sluggish intestinal peristalsis. In Cyclops vicinus dormancy can take place in copepod stages III (19%), IV (78%) and V (3%) but one and the same animal only in one developmental stage. The author gives his own results between frequency of dormancy and photoperiod (20 C, 1000 lux). He concludes that dormancy in C. vicinus can be influenced by day length and can be ended prematurely by short day length.

Experimental study of the Talbot effect under femtosecond laser illumination

Experimental results of the Talbot effect of an amplitude grating under femtosecond laser illumination are reported. Compared with Talbot image under continuous wave (CW) illumination, Talbot images under femtosecond laser illumination are different due to the wide spectral bandwidth and the Talbot images are more distorted at longer Talbot distances. The spectrums and the pulsewidths of femtosecond laser pulses are measured with the frequency-resolved optical gating (FROG) apparatus. Experimental results are in good agreement with the theoretical analysis. (c) 2005 Elsevier B.V. All rights reserved.