Statistical Fluctuations of Two Dimensional Turbulence

The statistics of two-dimensional (2D) turbulence driven by electro-magneticforce are investigated in freely-suspended soap film. The turbulentflow is analyzed using the particle imaging velocimetry (PIV) method.In this thesis, three important features of 2D turbulence are mainlystudied. First, the effects of addition of small amounts of polymers on 2Dturbulent flows are carefully investigated. As the polymer concentration$phi$ increases, large scale velocity fluctuations are suddenlysuppressed at a certain $phi$. This suppression is believed to happendue to the redistribution of saddle points of the flow. It impliesthat the saddle structures may play a role in energy-transfer to largescales. The thesis also presents 2D intermittency in inverse energy cascaderegime. In this subrange, the energy transfers from injection scale$l_{inj}$ to large scales. Intermittency is recognized and analyzedby the structure function $S_{p}(l)$ of the velocity difference betweentwo points, and log-normal model of the energy dissipation rate $varepsilon$.The analyses show signs of intermittency even though its intensityis weaker than that in three-dimensional (3D) turbulence. Finally, single-point(SP) velocity statistics are investigated, inspiredby the theory proposed by Falkovich and Lebedev (FL). This theoryreveals the connection between SP statistics and forcing statistics.For forced 2D turbulence, the SP velocity probability distribution function (PDF) deviates from Gaussian when turbulence intensity issufficiently strong, which can be explained using FL theory. In thecase of decaying turbulence, SP velocity PDF gradually evolves fromsuper-Gaussian to sub-Gaussian as time increases

Elastic turbulence in a curvilinear channel flow

We report detailed quantitative studies of elastic turbulence in a curvilinear channel flow in a dilute polymer solution of high molecular weight polyacrylamide in a high viscosity water-sugar solvent. Detailed studies of the average and rms velocity and velocity gradients profiles reveal an emergence of the boundary layer associated with the nonuniform distribution of the elastic stresses across the channel. The characteristic boundary width is independent of the Weissenberg number Wi and proportional to the channel width that follows from our early investigations of the boundary layer in elastic turbulence of different flow geometries. The appearance of the characteristic spatial scales of the order of the boundary layer width of both velocity and velocity gradient in the correlation functions of the velocity and velocity gradient fields in a bulk flow suggests that rare and strong parcels of excessive elastic stresses, concentrated in the boundary layer, are ejected into the bulk flow similar to jets observed in passive scalar mixing. And finally, the experimental results show that one of the main predictions of the theory of elastic turbulence, namely the saturation of the normalized rms velocity gradient in the bulk flow of elastic turbulence contradicts to the experimental observations both qualitatively and quantitatively in spite of the fact that the theory explains well the observed sharp decay of the velocity power spectrum. The experimental findings call for further development of theory of elastic turbulence in a bounded container, similar to what was done for a passive scalar problem.Comment: 14 pages, 36 figure

Virtual potentials for feedback traps

The recently developed feedback trap can be used to create arbitrary virtual potentials, to explore the dynamics of small particles or large molecules in complex situations. Experimentally, feedback traps introduce several finite time scales: There is a delay between the measurement of a particle's position and the feedback response, the feedback response is applied for a finite update time, and a finite camera exposure integrates motion. We show how to incorporate such timing effects into the description of particle motion. For the test case of a virtual quadratic potential, we give the first accurate description of particle dynamics, calculating the power spectrum and variance of fluctuations as a function of feedback gain, testing against simulations. We show that for small feedback gains, the motion approximates that of a particle in an ordinary harmonic potential. Moreover, if the potential is varied in time, for example by varying its stiffness, the work that is calculated approximates that done in an ordinary changing potential. The quality of the approximation is set by the ratio of the update time of the feedback loop to the relaxation time of motion in the virtual potential

Optical tweezers as a mathematically driven spatio-temporal potential generator

The ability to create and manipulate spatio-temporal potentials is essential in the diverse fields of science and technology. Here, we introduce an optical feedback trap system based on high precision position detection and ultrafast feedback control of a Brownian particle in the optical tweezers to generate spatio-temporal virtual potentials of the desired shape in a controlled manner. As an application, we study the nonequilibrium fluctuation dynamics of the particle in a time-varying virtual harmonic potential and validate the Crooks fluctuation theorem in the highly nonequilibrium condition

Shift a laser beam back and forth to exchange heat and work in thermodynamics

Abstract Although the equivalence of heat and work has been unveiled since Joule’s ingenious experiment in 1845, they rarely originate from the same source in experiments. In this study, we theoretically and experimentally demonstrated how to use a high-precision optical feedback trap to combine the generation of virtual temperature and potential to simultaneously manipulate the heat and work of a small system. This idea was applied to a microscopic Stirling engine consisting of a Brownian particle under a time-varying confining potential and temperature. The experimental results justified the position and the velocity equipartition theorem, confirmed several theoretically predicted energetics, and revealed the engine efficiency as well as its trade-off relation with the output power. The small theory–experiment discrepancy and high flexibility of the swift change of the particle condition highlight the advantage of this optical technique and prove it to be an efficient way for exploring heat and work-related issues in the modern thermodynamics for small systems

Near-Infrared Spectroscopic Analysis for Classification of Water Molecules in Wood by a Theory of Water Mixtures

This study was conducted to analyze the mechanism of moisture adsorption-desorption in wood using near-IR (NIR) spectroscopy. NIR spectra reflected from moist wood were acquired, and spectra in the range from 1800-2100 nm, which were sensitive to water variation, were decomposed into three different components according to the Buijs and Choppin theory. It is assumed that the three components represent three types of bound water: water molecules without -OH groups engaged in hydrogen bonds (S0), water molecules with one -OH group engaged in a hydrogen bond (S1), and water molecules with two -OH groups engaged in hydrogen bonds (S2). Ratios of the decomposed spectra of NIR absorbed by each type of water molecule were analyzed during changes in water adsorption-desorption states. Through this analysis, a sorption model for predicting the structural state of each water component in wood was constructed. This model may be used to explain the effect of each water component on the occurrence of hysteresis as well as the transient state between bound water and free water. Based on the model, it was concluded that the monomolecular water layer in yellow poplar wood formed below approximately 8% MC during adsorption. Additionally, the phenomenon of hysteresis was demonstrated by the difference between the ratios of the S2 components in desorption and adsorption

Comprehensive structural model of the mechanochemical cycle of a mitotic motor highlights molecular adaptations in the kinesin family.

Kinesins are responsible for a wide variety of microtubule-based, ATP-dependent functions. Their motor domain drives these activities, but the molecular adaptations that specify these diverse and essential cellular activities are poorly understood. It has been assumed that the first identified kinesin--the transport motor kinesin-1--is the mechanistic paradigm for the entire superfamily, but accumulating evidence suggests otherwise. To address the deficits in our understanding of the molecular basis of functional divergence within the kinesin superfamily, we studied kinesin-5s, which are essential mitotic motors whose inhibition blocks cell division. Using cryo-electron microscopy and determination of structure at subnanometer resolution, we have visualized conformations of microtubule-bound human kinesin-5 motor domain at successive steps in its ATPase cycle. After ATP hydrolysis, nucleotide-dependent conformational changes in the active site are allosterically propagated into rotations of the motor domain and uncurling of the drug-binding loop L5. In addition, the mechanical neck-linker element that is crucial for motor stepping undergoes discrete, ordered displacements. We also observed large reorientations of the motor N terminus that indicate its importance for kinesin-5 function through control of neck-linker conformation. A kinesin-5 mutant lacking this N terminus is enzymatically active, and ATP-dependent neck-linker movement and motility are defective, although not ablated. All these aspects of kinesin-5 mechanochemistry are distinct from kinesin-1. Our findings directly demonstrate the regulatory role of the kinesin-5 N terminus in collaboration with the motor's structured neck-linker and highlight the multiple adaptations within kinesin motor domains that tune their mechanochemistries according to distinct functional requirements