Compressible flows at small Reynolds numbers

The problem of the slow viscous flow of a gas past a sphere is considered. The fluid cannot be treated incompressible in the limit when the Reynolds number Re, and the Mach number M, tend to zero in such a way that Re ~ o(M^2 ). In this case, the lowest order approximation to the steady Navier-Stokes equations of motion leads to a paradox discovered by Lagerstrom and Chester. This paradox is resolved within the framework of continuum mechanics using the classical slip condition and an iteration scheme that takes into account certain terms in the full Navier-Stokes equations that drop out in the approximation used by the above authors. It is found however that the drag predicted by the theory does not agree with R. A. Millikan's classic experiments on sphere drag.

The whole question of the applicability of the Navier-Stokes theory when the Knudsen number M/Re is not small is examined. A new slip condition is proposed. The idea that the Navier-Stokes equations coupled with this condition may adequately describe small Reynolds number flows when the Knudsen number is not too large is looked at in some detail. First, a general discussion of asymptotic solutions of the equations for all such flows is given. The theory is then applied to several concrete problems of fluid motion. The deductions from this theory appear to interpret and summarize the results of Millikan over a much wider range of Knudsen numbers (almost up to the free molecular or kinetic limit) than hitherto Believed possible by a purely continuum theory. Further experimental tests are suggested and certain interesting applications to the theory of dilute suspensions in gases are noted. Some of the questions raised in the main body of the work are explored further in the appendices.

Nearly free molecular heat transfer from a sphere

Consider a sphere immersed in a rarefied monatomic gas with zero mean flow. The distribution function of the molecules at infinity is chosen to be a Maxwellian. The boundary condition at the body is diffuse reflection with perfect accommodation to the surface temperature. The microscopic flow of particles about the sphere is modeled kinetically by the Boltzmann equation with the Krook collision term. Appropriate normalizations in the near and far fields lead to a perturbation solution of the problem, expanded in terms of the ratio of body diameter to mean free path (inverse Knudsen number). The distribution function is found directly in each region, and intermediate matching is demonstrated. The heat transfer from the sphere is then calculated as an integral over this distribution function in the inner region. Final results indicate that the heat transfer may at first increase over its free flow value before falling to the continuum level.

Response of multiple simultaneously recorded macaque area LIP neurons in a memory saccade task

Cells in the lateral intraparietal cortex (LIP) of rhesus macaques respond vigorously and in spatially-tuned fashion to briefly memorized visual stimuli. Responses to stimulus presentation, memory maintenance, and task completion are seen, in varying combination from neuron to neuron. To help elucidate this functional segmentation a new system for simultaneous recording from multiple neighboring neurons was developed. The two parts of this dissertation discuss the technical achievements and scientific discoveries, respectively.

Technology. Simultanous recordings from multiple neighboring neurons were made with four-wire bundle electrodes, or tetrodes, which were adapted to the awake behaving primate preparation. Signals from these electrodes were partitionable into a background process with a 1/f-like spectrum and foreground spiking activity spanning 300-6000 Hz. Continuous voltage recordings were sorted into spike trains using a state-of-the-art clustering algorithm, producing a mean of 3 cells per site. The algorithm classified 96% of spikes correctly when tetrode recordings were confirmed with simultaneous intracellular signals. Recording locations were verified with a new technique that creates electrolytic lesions visible in magnetic resonance imaging, eliminating the need for histological processing. In anticipation of future multi-tetrode work, the chronic chamber microdrive, a device for long-term tetrode delivery, was developed.

Science. Simultaneously recorded neighboring LIP neurons were found to have similar preferred targets in the memory saccade paradigm, but dissimilar peristimulus time histograms, PSTH). A majority of neighboring cell pairs had a difference in preferred directions of under 45° while the trial time of maximal response showed a broader distribution, suggesting homogeneity of tuning with het erogeneity of function. A continuum of response characteristics was present, rather than a set of specific response types; however, a mapping experiment suggests this may be because a given cell's PSTH changes shape as well as amplitude through the response field. Spike train autocovariance was tuned over target and changed through trial epoch, suggesting different mechanisms during memory versus background periods. Mean frequency-domain spike-to-spike coherence was concentrated below 50 Hz with a significant maximum of 0.08; mean time-domain coherence had a narrow peak in the range ±10 ms with a significant maximum of 0.03. Time-domain coherence was found to be untuned for short lags (10 ms), but significantly tuned at larger lags (50 ms).

7 fs超快强激光驱动Ar原子产生支持单个阿秒脉冲的高次谐波连续谱

采用脉冲宽度为7 fs，脉冲能量为0．4mJ的超快强激光脉冲与气体盒子中Ar原子作用获得了高次谐波截止区连续谱，并发现当驱动激光稳定在不同的载波包络相位时，高次谐波的谱结构、谱调制深度和连续谱的带宽都有很大区别。在某些载波包络相位时获得了平滑的连续谱，调制深度小于17％，连续带宽达10eV，从而支持时域上获得变换极限500as的单个阿秒脉冲。

Enhancing Kerr nonlinearity in an asymmetric double quantum well via Fano interference

We investigate the enhancement of Kerr nonlinearity in an asymmetric GaAs double quantum well via Fano interference, which is caused by tunneling from the excited subband to the continuum. In our structure, owing to Fano interference, the Kerr nonlinearity can be enhanced by appropriately choosing the values of the detunings and the intensity of the pump field, while cancel the linear and nonlinear absorptions.

Space-frequency coupling, conical waves, and small-scale filamentation in water

Numerical simulations of fs laser propagation in water have been made to explain the small-scale filaments in water we have observed by a nonlinear fluorescence technique. Some analytical descriptions combined with numerical simulations show that a space-frequency coupling mainly from the interplay among self-phase modulation, dispersion and phase mismatching will reshape the laser beam into a conical wave which plays a major role of energy redistribution and can prevent laser beam from self-guiding over a long distance. An effective group velocity dispersion is introduced to explain the pulse broadening and compression in the filamentation. (c) 2005 American Institute of Physics.

Few-cycle spatiotemporal soliton wave excited by filamentation of a femtosecond laser pulse in materials with anomalous dispersion

The nonlinear dynamics of 1.6-mu m fs laser pulses propagating in fused silica is investigated by employing a full-order dispersion model. Different from the x-wave generation in normally dispersive media, a few-cycle spatiotemporally compressed soliton wave is generated with the contrary contributions of anomalous group velocity dispersion (GVD) and self-phase-modulation. However, at the tailing edge of the pulse forms a shock wave which generates separate and strong supercontinuum peaked at 670 nm. It is also the origin of conical emission formed both in time and frequency domain with the contribution of normal GVD at visible light.

Nonlinear propagation of fs laser pulses in liquids and evolution of supercontinuum generation

Nonlinear propagation of fs laser pulses in liquids and the dynamic processes of filamentation such as self-focusing, intensity clamping, and evolution of white light production have been analyzed by using one- and two-photon fluorescence. The energy losses of laser pulses caused by multiphoton absorption and conical emission have been measured respectively by z-scan technique. Numerical simulations of fs laser propagation in water have been made to explain the evolution of white light production as well as the small-scale filaments in liquids we have observed by a nonlinear fluorescence technique. (c) 2005 Optical Society of America.

Physical investigations of small particles : (I) aerosol particle charging and flux enhancement and (II) whispering gallery mode sensing

Part I

Particles are a key feature of planetary atmospheres. On Earth they represent the greatest source of uncertainty in the global energy budget. This uncertainty can be addressed by making more measurement, by improving the theoretical analysis of measurements, and by better modeling basic particle nucleation and initial particle growth within an atmosphere. This work will focus on the latter two methods of improvement.

Uncertainty in measurements is largely due to particle charging. Accurate descriptions of particle charging are challenging because one deals with particles in a gas as opposed to a vacuum, so different length scales come into play. Previous studies have considered the effects of transition between the continuum and kinetic regime and the effects of two and three body interactions within the kinetic regime. These studies, however, use questionable assumptions about the charging process which resulted in skewed observations, and bias in the proposed dynamics of aerosol particles. These assumptions affect both the ions and particles in the system. Ions are assumed to be point monopoles that have a single characteristic speed rather than follow a distribution. Particles are assumed to be perfect conductors that have up to five elementary charges on them. The effects of three body interaction, ion-molecule-particle, are also overestimated. By revising this theory so that the basic physical attributes of both ions and particles and their interactions are better represented, we are able to make more accurate predictions of particle charging in both the kinetic and continuum regimes.

The same revised theory that was used above to model ion charging can also be applied to the flux of neutral vapor phase molecules to a particle or initial cluster. Using these results we can model the vapor flux to a neutral or charged particle due to diffusion and electromagnetic interactions. In many classical theories currently applied to these models, the finite size of the molecule and the electromagnetic interaction between the molecule and particle, especially for the neutral particle case, are completely ignored, or, as is often the case for a permanent dipole vapor species, strongly underestimated. Comparing our model to these classical models we determine an “enhancement factor” to characterize how important the addition of these physical parameters and processes is to the understanding of particle nucleation and growth.

Part II

Whispering gallery mode (WGM) optical biosensors are capable of extraordinarily sensitive specific and non-specific detection of species suspended in a gas or fluid. Recent experimental results suggest that these devices may attain single-molecule sensitivity to protein solutions in the form of stepwise shifts in their resonance wavelength, \lambda_{R}, but present sensor models predict much smaller steps than were reported. This study examines the physical interaction between a WGM sensor and a molecule adsorbed to its surface, exploring assumptions made in previous efforts to model WGM sensor behavior, and describing computational schemes that model the experiments for which single protein sensitivity was reported. The resulting model is used to simulate sensor performance, within constraints imposed by the limited material property data. On this basis, we conclude that nonlinear optical effects would be needed to attain the reported sensitivity, and that, in the experiments for which extreme sensitivity was reported, a bound protein experiences optical energy fluxes too high for such effects to be ignored.

Nonlinear copropagation of two optical pulses of different frequencies in photonic crystal fibers

A theoretical investigation of the nonlinear copropagation of two optical pulses of different frequencies in a photonic crystal fiber is presented. Different phenomena are observed depending on whether the wavelength of the signal pulse is located in the normal or the anomalous dispersion region. In particular, it is found that the phenomenon of pulse trapping occurs when the signal wavelength is located in the normal dispersion region while the pump wavelength is located in the anomalous dispersion region. The signal pulse suffers cross-phase modulation by the Raman shifted soliton pulse and it is trapped and copropagates with the Raman soliton pulse along the fiber. As the input peak power of the pump pulse is increased, the red-shift of the Raman soliton is considerably enhanced with the simultaneous further blue-shift of the trapped pulse to satisfy the condition of group velocity matching.

Grain growth in protoplanetary disks

The majority of young, low-mass stars are surrounded by optically thick accretion disks. These circumstellar disks provide large reservoirs of gas and dust that will eventually be transformed into planetary systems. Theory and observations suggest that the earliest stage toward planet formation in a protoplanetary disk is the growth of particles, from sub-micron-sized grains to centimeter- sized pebbles. Theory indicates that small interstellar grains are well coupled into the gas and are incorporated to the disk during the proto-stellar collapse. These dust particles settle toward the disk mid-plane and simultaneously grow through collisional coagulation in a very short timescale. Observationally, grain growth can be inferred by measuring the spectral energy distribution at long wavelengths, which traces the continuum dust emission spectrum and hence the dust opacity. Several observational studies have indicated that the dust component in protoplanetary disks has evolved as compared to interstellar medium dust particles, suggesting at least 4 orders of magnitude in particle- size growth. However, the limited angular resolution and poor sensitivity of previous observations has not allowed for further exploration of this astrophysical process.

As part of my thesis, I embarked in an observational program to search for evidence of radial variations in the dust properties across a protoplanetary disk, which may be indicative of grain growth. By making use of high angular resolution observations obtained with CARMA, VLA, and SMA, I searched for radial variations in the dust opacity inside protoplanetary disks. These observations span more than an order of magnitude in wavelength (from sub-millimeter to centimeter wavelengths) and attain spatial resolutions down to 20 AU. I characterized the radial distribution of the circumstellar material and constrained radial variations of the dust opacity spectral index, which may originate from particle growth in these circumstellar disks. Furthermore, I compared these observational constraints with simple physical models of grain evolution that include collisional coagulation, fragmentation, and the interaction of these grains with the gaseous disk (the radial drift problem). For the parameters explored, these observational constraints are in agreement with a population of grains limited in size by radial drift. Finally, I also discuss future endeavors with forthcoming ALMA observations.

Nuclear weak interaction rates during stellar evolution and collapse

Nuclear weak interaction rates, including electron and positron emission rates, and continuum electron and positron capture rates , as well as the associated v and –/v energy loss rates are calculated on a detailed grid of temperature and density for the free nucleons and 226 nuclei with masses between A = 21 and 60. Gamow-Teller and Fermi discrete-state transition matrix element systematics and the Gamow-Teller T^< →/← T^> resonance transitions are discussed in depth and are implemented in the stellar rate calculations. Results of the calculations are presented on an abbreviated grid of temperature and density and comparison is made to terrestrial weak transition rates where possible. Neutron shell blocking of allowed electron capture on heavy nuclei during stellar core collapse is discussed along with several unblocking mechanisms operative at high temperature and density. The results of one-zone collapse calculations are presented which suggest that the effect of neutron shell blocking is to produce a larger core lepton fraction at neutrino trapping which leads to a larger inner-core mass and hence a stronger post-bounce shock.

超短激光脉冲在不同色散参量光子晶体光纤中传输的数值模拟

为了使得数值模拟更为精确, 采用广义非线性薛定谔方程(GNSE)描述超短激光脉冲在光子晶体光纤中的传输演化过程, 并利用二阶分步傅里叶方法通过求解方程, 数值计算了相同脉宽和能量的超短脉冲在不同色散参量的光子晶体光纤中非线性传输和超连续谱的产生。比较了超短脉冲在光纤不同色散区传输时, 高阶色散和非线性效应对超连续谱的产生以及对脉冲波形演化的影响。结果表明, 相对于超短脉冲中心波长位于光子晶体光纤的正常和反常色散区, 可以相应获得短波波段和长波波段的超连续谱输出, 当超短脉冲中心波长位于零色散波长点时, 通

Optimization of multi-cycle two-color laser fields for the generation of an isolated attosecond pulse

The effect of the mixing of pulsed two color fields on the generation of an isolated attosecond pulse has been systematically investigated. One main color is 800 nm and the other color (or secondary color) is varied from 1.2 to 2.4 mu m. This work shows that the continuum length behaves in a similar way to the behavior of the difference in the square of the amplitude of the strongest and next strongest cycle. As the mixing ratio is increased, the optimal wavelength for the extended continuum shifts toward shorter wavelength side. There is a certain mixing ratio of intensities at which the continuum length bifurcates, i.e., the existence of two optimal wavelengths. As the mixing ratio is further increased, each branch bifurcates again into two sub-branches. This 2D map analysis of the mixing ratio and the wavelength of the secondary field easily allows one to select a proper wavelength and the mixing ratio for a given pulse duration of the primary field. The study shows that an isolated sub-100 attosecond pulse can be generated mixing an 11 fs full-width-half-maximum (FWHM), 800 laser pulse with an 1840 nm FWHM pulse. Furthermore the result reveals that a 33 fs FWHM, 800 nm pulse can produce an isolated pulse below 200 as, when properly mixed. (c) 2008 Optical Society of America.