This work explores the physics of micro and nano-scale systems immersed in a fluid. Previous literature has established an understanding of the fluid-solid interaction for systems including cantilevers and doubly clamped beams. Building on these advances, this work extends the theory of doubly clamped beams with an arbitrary amount of tension. Both the driven and stochastic dynamics of a doubly clamped beam are explored. The driven dynamics are investigated for a spatially applied harmonic driving force, and demonstrates quantitative agreement with an experimental beam that is driven electrothermally, in both air and in water. For the stochastic dynamics, the noise spectrum describes the thermal fluctuations at a given frequency. The theoretical model provides an analytical expression for the noise spectrum from an arbitrary number of modes. The noise spectrum of the first eleven modes are computed, and show excellent agreement with the noise spectrum from finite element simulations, which is computed from the deterministic ring down. This agreement is shown across different fluids (air and water), and for multiple measuring points including at the beam midpoint and the quarter point. In addition to exploring the linear dynamics of these systems, the case of large perturbations, resulting in nonlinear dynamics, is explored. This regime is motivated by exploring the theoretical dynamics of a uniformly shrinking doubly clamped beam. The challenges of modeling such a beam using finite element simulations are discussed. As a simpler and more direct alternative to access the nonlinear regime, a virtual beam is defined. The virtual beam controls the nonlinearity of the restoring force by modifying the Young's modulus. This work defines the Young's modulus such that the restoring force is like a Duffing oscillator. Then, the dynamics of this virtual beam are explored in air and water, and it is demonstrated that the Duffing oscillator serves as an appropriate reduced order model for this virtual beam. To understand the stochastic dynamics of the virtual beam, the stochastic Duffing oscillator is solved numerically. The ensemble autocorrelation of the beam dynamics are investigated for nonlinearities varying from linear to strongly nonlinear. The numeric autocorrelation is used to quantify the range of nonlinear strength where a deterministic approach, the ring down, can yield a good approximation. In the strongly nonlinear regime, the stochastic numerical approach is used to determine the autocorrelation. This research was supported by the National Science Foundation, grant number CMMI-2001559, and portions of the computations were conducted using the resources of Virginia Tech's Advanced Research Computing center. / Doctor of Philosophy / This work explores the physics of small systems immersed in a fluid, such as air or water. Previous literature has established an understanding of the force from a fluid acting on solids such as cantilevers and doubly clamped beams. Building on these advances, this work extends theory to doubly clamped beams with any amount of tension. Both the driven and stochastic, or randomly driven, dynamics of a doubly clamped beam are explored. The driven dynamics are developed for a driving force applied over part of the beam, and demonstrates quantitative agreement with an experimental beam, in both air and in water. For the stochastic dynamics, the noise spectrum describes the random thermal fluctuations of the beam at a given frequency. These thermal fluctuations are small, but measureable deviations of the system from equilibrium and are significant for these small scale systems. The noise spectrum can be estimated by computing the statistics from many randomly forced simulations. However, previous literature provides a direct computation of the noise spectrum with a single deterministic ring down. This work provides an analytical expression for the noise spectrum of a doubly clamped beam in tension in fluid for multiple modes. The theoretical noise spectrum shows excellent quantitative agreement with the ring down from finite element simulations. The agreement between theory and simulation is demonstrated in air and water, for a measurement of the noise spectrum at the beam midpoint and at the beam quarter point. In addition to exploring the linear dynamics of these systems, the case of large perturbations, resulting in nonlinear dynamics, is explored. This regime is motivated by exploring the theoretical dynamics of a uniformly shrinking doubly clamped beam. The challenges of modeling such a beam using finite element simulations are discussed. As a simpler and more direct alternative to access the nonlinear regime, a virtual beam is defined. The virtual beam controls the nonlinearity of the restoring force such that the system becomes increasingly stiff as the displacements become larger. This definition results in the restoring force following a Duffing oscillator. Then, the dynamics of this virtual beam are explored in air and water, and it is demonstrated that the Duffing oscillator serves as an appropriate reduced order model for this virtual beam. For varying nonlinear strengths, the stochastic numerical approach is used to quantify the dynamics, and the range of usefulness for the deterministic ring down is investigated. This research was supported by the National Science Foundation, grant number CMMI-2001559, and portions of the computations were conducted using the resources of Virginia Tech's Advanced Research Computing center.

Fluid mixing that is induced by hydrodynamic instability is ubiquitous in nature; the material interface between two fluids when perturbed even slightly, changes shape under the influence of hydrodynamic forces, and an additional zone called the mixing layer where the two fluids mix, develops and grows in size. This dissertation reports a study on the role of thermal fluctuations in fluid mixing at the interface separating two perfectly miscible fluids of different densities. Mixing under the influence of two types of instabilities is studied; the Rayleigh-Taylor (RTI) and Richtmyer-Meshkov (RMI) instabilities. The study was conducted using numerical simulations after verification of the simulation methodology. Specifically, fluctuating hydrodynamic simulations were used; the fluctuating compressible Navier-Stokes equations were the physical model of the system, and they were solved using numerical methods that were developed and implemented in-house. Our results indicate that thermal fluctuations can trigger the onset of RTI at an initially unperturbed fluid-fluid interface, which subsequently leads to mixing of multi-mode character. In addition we find that for both RMI and RTI, whether or not thermal fluctuations quantitatively affect the mixing behavior, depends on the magnitude of the dimensionless Boltzmann number of the hydrodynamic system in question, and not solely on its size. When the Boltzmann number is much smaller than unity, the quantitative effect of thermal fluctuations on the mixing behavior is negligible. Under this circumstance, we show that mixing behavior is the average of the outcome from several stochastic instances, with the ensemble of stochastic instances providing the bounds on mixing-related metrics such as the mixing width. Most macroscopic hydrodynamic systems fall in this category. However, when the system is such that the Boltzmann number is of order unity, we show that thermal fluctuations can significantly affect the mixing behavior; the ensemble-averaged solution shows a departure from the deterministic solution. We conclude that for such systems, it is important to account for thermal fluctuations in order to correctly capture their physical behavior.

With the extreme miniaturization of NEMS, the role of nonlinear dynamics has become increasingly important -- even when the dynamics are driven by the Brownian force. This nonlinearity has imposed a mechanical noise floor on the linear frequency measurements made in sensing applications. Given that NEMS also become more sensitive as they become smaller, this floor has resulted in a complex interplay between the nonlinear regime and the linear sensitivity required to make continued advancements in exercising ultra-sensitive measurements. Recently, this has led to efforts to more accurately characterize the edge of the linear regime. Inside of the nonlinear regime, there are also ongoing fundamental studies in theory and experiment to partially characterize the nonlinear behavior of NEMS. Theoretically, these systems are frequently studied by decomposing the nonlinear continuous system into one or more nonlinear oscillators. However, in many of these works, the nonlinear spring constants are estimated at the lowest order. As such, there is a clear need to more accurately characterize and scale the nonlinear coefficients for NEMS. This work considers a long and slender NEMS resonator in the form of a doubly-clamped beam in tension. Using nonlinear Euler-Bernoulli beam theory, the geometric nonlinearity due to the stretching of the neutral axis is considered. We extensively explore simplifications in using a Galerkin discretization of the continuous system, where a single mode's dynamics are described as a damped, Duffing oscillator. We examine limitations of current approaches and find that using a tensioned and doubly-clamped mode shape for the trial function more accurately predicts experiment. Additionally, we find that doubly-clamped beams of finite tension may have their boundary conditions modified to that of a hinged-hinged beam in tension with little to no loss of generality. This modification allows for closed-form scaling of the critical amplitude and dynamic range at arbitrary mode number and tension. We extend this approach to scale the relative influence of bending, tension, and nonlinearity with increasing mode number n, finding that bending and nonlinear influences quickly outgrow the contributions of the intrinsic tension. Where applicable, these results are compared with experiment, and we obtain good agreement. To validate the approximate Galerkin formulations, we develop a finite element method to calculate the nonlinear coefficients of symmetric NEMS resonators. Unlike previous works, the present formulation may include all nonlinearity due to geometry, and the nonlinear amplitude-frequency backbone described by the Duffing oscillator is found as an excellent approximation for large amplitude beams. For beams of zero intrinsic tension, the finite element method obtains excellent agreement with the literature. For beams of finite tension and varying mode number, we find the error from the Galerkin discretization is small (≈5%). In addition, we theoretically explore the stochastic dynamics of a Duffing oscillator driven nonlinearly by the Brownian force. To access this regime experimentally with current nanomechanical systems, we motivate an experimental "synthetic noise" to approximate the Brownian force in the proximity of a single mode. As a measure of drive magnitude, we vary an effective temperature to explore the linear and nonlinear stochastic dynamics of a doubly-clamped nanoresonator. Using similitude and the Fluctuation-Dissipation theorem, we show that varying the effective temperature of the synthetic noise offers a window into the fundamental limits of thermally-driven nonlinearities. We compare theory, numerics, and experiment where applicable, obtaining good agreement for both limits of frequency shifts in the weakly nonlinear case. This research was supported by the National Science Foundation, grant number CMMI-2001559, and portions of the computations were conducted using the resources of Virginia Tech's Advanced Research Computing (ARC) center. / Master of Science / Nanoelectromechanical systems (NEMS) are nanoscale mechanical structures that convert physical stimuli (force, mass, acceleration, charge, etc.) to measurable electrical signals. Due to the extremely small size of NEMS, they offer an unprecedented level of sensitivity in a variety of measurement applications. However, as NEMS become smaller, the response of these mechanical structures begin to exhibit nonlinear behaviors. Said otherwise, proportional inputs (such as drive strength) do not result in proportional outputs. These nonlinear behaviors include a variety of undesired effects, such as multi-valued unstable/stable solutions and a noisy resonant frequency. In this work, we study a NEMS resonator in the form of a doubly-clamped beam, and we consider the stretching of the mid-plane as the nonlinearity. Here, the stretching of the mid-plane (an axial strain) is nonlinearly dependent on the amplitude of vibration, inducing a nonlinear tension force. With this model, it is typical to represent a singular nonlinear vibrational mode as a simple harmonic oscillator with an additional cubic term. In order to better characterize the edge of the nonlinear regime, the relative strength of the cubic term must be known. We thoroughly explore existing and new simplifications to obtain the nonlinear coefficient for the cubic term, demonstrating two possible approaches for better accuracy in beams of varying tension and mode number. These simplifications are validated by comparing with the present finite element method to determine the nonlinearity in symmetric NEMS resonators. Using these new insights, theory and numerics are used to explore the behavior of a doubly-clamped beam in a stochastic (random) force field. This force field is tailored to represent the collisions of surrounding molecules at the nanoscale, allowing exploration of nonlinear behavior at its fundamental limits. Where applicable, theory and numerics are compared to experiment, and we obtain good agreement. This research was supported by the National Science Foundation, grant number CMMI-2001559, and portions of the computations were conducted using the resources of Virginia Tech's Advanced Research Computing (ARC) center.

The aim of this thesis is to study the energy fluctuations (leading to thermal fluctuations) during thermal and enzymatic denaturation of biological molecules and to study the variation in fluctuations between simple molecules like the DNA (which have only a secondary structure) to molecules with higher order structures and packaging. We have developed a new technique - Thermal Fluctuation Spectroscopy (TFS) to study these fluctuations. The technique of Thermal Fluctuation Spectroscopy (TFS) is a combination of microcalorimetry and noise measurement techniques. The combination of these two powerful techniques has never been exploited before. In this technique any energy exchange between sample and the substrate is reflected as a thermal fluctuation of the substrate. The system resolution is few parts per billion (ppb) and fluctuations in energy ~ 100nJ (which correspond to temperature fluctuations ~ K) can be measured. Chromatin is the basic building block of chromosome and this thesis focuses on the constituents this fundamental building block - DNA, histones and nucleosomes. Heteropolymeric dsDNA shows extremely large non-Gaussian fluctuation around its melting temperature. For homopolymeric DNA the fluctuations during denaturation are smaller. The thermal fluctuation during denaturation of a heteropolymer in buffer is several orders larger than when the DNA is on a substrate while that for a homopolymer is comparable in both cases. Our measurements established that heteropolymeric dsDNA denaturation occurs in two stages. Initially, at around 330 K, bubbles are formed in the AT rich regions. At higher temperatures, the GC rich regions binding them denature in a cooperative transition causing extremely large fluctuations. TFS on histone monomers showed that H1 monomer shows an increase in thermal fluctuation in the temperature range studied, while the core histones did not. We infer that this is due to the fact that the core histones may not be properly folded when they exist as monomers. It was seen that H1 crosses an energy barrier of 17 kcal/mol to go from its native to denatured state. The transition was kinetically driven with a fixed barrier till 352 K. At 352K, the barrier softened by ~ 1 kcal/mol leading to faster denaturation. The core histones when assembled as dimers/oligomers showed an increase in fluctuation at temperatures below 350 K. The assembling of these histones and DNA into a mononucleosome causes a very large increase in fluctuation over the entire temperature range studied. TFS showed that the fluctuation during mononucleosome denaturation was much larger than a simple sum of the fluctuations of its constituents. From the data we were able to identify that the denaturation starts with dissociation and unfolding of the core histones and the denaturation of AT rich regions of the DNA which leads to the breaking of some of the histone-DNA contacts. At higher temperatures the linker histone H1 and the GC rich regions of the DNA denature, leading to a collapse of the entire nucleosome structure. The broadness of the transition region (the fact that the fluctuation is large over the entire temperature range) was attributed to the presence of different types of contacts and interactions (with different energies) stabilizing the nucleosome structure. The nucleosome was found to favour large energy jumps over smaller ones indicating that the denaturation has an element of cooperativity involved. Using TFS we have been able to determine the fluctuations involved in the denaturation of biomolecules like DNA, histones and nucleosomes. The energy barriers to denaturation have been determined. We have also been able to give models for the denaturation of these biomolecules. We have also shown that it is possible to study enzymatic digestion using TFS. Thus, the technique of TFS is a viable tool for the study of fluctuations in reactions, in biomolecules, during transitions and in any process where there is an energy exchange involved.

We present predictions for the statistical error due to finite sampling in the presence of thermal fluctuations in molecular simulation algorithms. Expressions for the fluid velocity, density and temperature are derived using equilibrium statistical mechanics. The results show that the number of samples needed to adequately resolve the flow-field scales as the inverse square of the Mach number. The theoretical results are verified for a dilute gas using direct Monte Carlo simulations. The agreement between theory and simulation verifies that the use of equilibrium theory is justified. / Singapore-MIT Alliance (SMA)

Dry adhesion systems adhere via physical bonds without any significant contribution from a liquid medium. In nature, these systems are found among the footpads of spiders, lizards and many other small animals, with high adhesion force, low detachment force and elfcleaning properties. These features are highly interesting for biomimetic man-made adhesives. Heavy animals have an adhesion force much higher than its muscle force, and to enable detachment, they have evolved a functional surface with hair-like structures called setae. Each seta branches into numerous microcontact elements that interact with the contacting area. This thesis continue on previous work, analyzing the functional surface in terms of contact geometries and stress distribution, and considers, for the first time, the effect of thermal fluctuations. Numerical and analytical results show how the muscle force is concentrated to a small fraction of the adhesion area, where each microcontact element is trapped in a potential well. The rate of detachment depends on the maximal concentration of stress across the crocontacts. When a seta is axially loaded, the concentration of stress is minimized, whereas radial loading amplifies the concentration of stress by a factor of maximum 68 and enable detachment with the animal’s limited muscle force. The results give theoretical insight in the adhesion and detachment of a functional surface. This knowledge is valuable and can be considered when constructing man-made adhesives with inspiration from nature’s dry adhesion solutions.

Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第14589号 / 工博第3057号 / 新制||工||1455(附属図書館) / 26941 / UT51-2009-D301 / 京都大学大学院工学研究科化学工学専攻 / (主査)教授 山本 量一, 教授 宮原 稔, 教授 大嶋 正裕 / 学位規則第4条第1項該当

Nous avons déterminé par diffusion de rayons X le potentiel d’interaction entre deux bicouches, une première adsorbée sur un substrat solide et une deuxième flottant à proximité. Nous montrons que les interactions dans ces systèmes fortement hydratés sont deux ordres de grandeur plus faibles que dans les travaux précédents menés sur des phases multilamellaires. Cette caractéristique est attribuée à la répulsion électrostatique due à la faible fraction de lipides ionisés. Nous avons de plus accès aux potentiels de répulsion entropique, et testons les différents modèles théoriques existants.Les effets d’un champ électrique sur les membranes ont également été étudiés. Nous montrons que le champ induit une tension négative et une rigidité positive, et mène à la déstabilisation d’une bicouche supportée sous certaines conditions.Finalement, nous mesurons les propriétés de membranes chargées par diffusion de rayons X, nous permettant d’accéder aux limites de la théorie de Poisson-Boltzmann. / We have determined by grazing incidence X-ray scattering the interaction potential between two lipid bilayers, one adsorbed on a solid surface and the other floating close by. We find that interactions in this highly hydrated system are two orders of magnitude softer than in previously reported work on multilayer stacks. This is attributed to the weak electrostatic repulsion due to the small fraction of ionized lipids in defectless supported bilayers. We also access the entropic repulsion potentials, allowing us to discriminate between the different existing models.The effects of an electric field on the properties of membranes have also been studied. We show that the field induces a negative tension and an increase of the rigidity. We also show that it is possible to destabilize a supported bilayer by an electric field under certain conditions.Finally, we measure the properties of charged membranes using X-ray scattering, giving access to the limits of the Poisson-Boltzmann theory.

No description available.

The utilization of thermal fluctuations or Johnson/Nyquist noise as a spectroscopic method to determine transport properties in conductors or semiconductors is developed in this paper. The autocorrelation function is obtained from power spectral density measurements thus enabling electronic transport property calculation through the Green-Kubo formalism. This experimental approach is distinct from traditional numerical methods such as molecular dynamics simulations, which have been used to extract the autocorrelation function and directly related physics only. This work reports multi-transport property measurements consisting of the electronic relaxation time, resistivity, mobility, diffusion coefficient, electronic contribution to thermal conductivity and Lorenz number from experimental data. Double validation of the experiment was accomplished through the use of a standard reference material and a standard measurement method, i.e. four-probe collinear resistivity technique. The advantages to this new experimental technique include the elimination of any required thermal or potential gradients, multi-transport property measurements within one experiment, very low error and the ability to apply controlled boundary conditions while gathering data. This research has experimentally assessed the gas pressure and flow effects of helium and argon on 30 nm Au and Cu thin films. The results show a reduction in Au and Cu electronic thermal conductivity and electrical resistivity when subjected to helium and argon pressure and flow. The perturbed electronic transport coefficients, attributed to increased electron scattering at the surface, were so dominant that further data was collected through straight-forward resistance measurements. The resistance data confirmed the thermal noise measurements thus lending considerable evidence to the presence of thin film surface scattering due to elastic and inelastic gas particle scattering effects with the electron ensemble.