Spatial survival probability for one-dimensional fluctuating interfaces in the steady state

We report numerical and analytic results for the spatial survival probability for fluctuating one-dimensional interfaces with Edwards-Wilkinson or Kardar-Parisi-Zhang dynamics in the steady state. Our numerical results are obtained from analysis of steady-state profiles generated by integrating a spatially discretized form of the Edwards-Wilkinson equation to long times. We show that the survival probability exhibits scaling behavior in its dependence on the system size and the "sampling interval" used in the measurement for both "steady-state" and "finite" initial conditions. Analytic results for the scaling functions are obtained from a path-integral treatment of a formulation of the problem in terms of one-dimensional Brownian motion. A "deterministic approximation" is used to obtain closed-form expressions for survival probabilities from the formally exact analytic treatment. The resulting approximate analytic results provide a fairly good description of the numerical data.

The 2D Coulomb gas on a 1D lattice

The statistical mechanics of a two-dimensional Coulomb gas confined to one dimension is studied, wherein hard core particles move on a ring. Exact self-duality is shown for a version of the sine-Gordon model arising in this context, thereby locating the transition temperature exactly. We present asymptotically exact results for the correlations in the model and characterize the low- and high-temperature phases. Numerical simulations provide support to these renormalization group calculations. Connections with other interesting problems, such as the quantum Brownian motion of a panicle in a periodic potential and impurity problems, are pointed out.

An instantaneous control model for flow control in an ATM network

This paper is concerned with the optimal flow control of an ATM switching element in a broadband-integrated services digital network. We model the switching element as a stochastic fluid flow system with a finite buffer, a constant output rate server, and a Gaussian process to characterize the input, which is a heterogeneous set of traffic sources. The fluid level should be maintained between two levels namely b1 and b2 with b1Brownian motion analysis and derive the limiting distribution for the queue length touching the critical levels. Also the application of instantaneous control on the ATM network is considered

Diffusing-wave spectroscopy in an inhomogeneous object: Local viscoelastic spectra from ultrasound-assisted measurement of correlation decay arising from the ultrasound focal volume

We demonstrate diffusing-wave spectroscopy (DWS) in a localized region of a viscoelastically inhomogeneous object by measurement of the intensity autocorrelation g(2)(tau)] that captures only the decay introduced by the temperature-induced Brownian motion in the region. The region is roughly specified by the focal volume of an ultrasound transducer which introduces region specific mechanical vibration owing to insonification. Essential characteristics of the localized non-Markovian dynamics are contained in the decay of the modulation depth M(tau)], introduced by the ultrasound forcing in the focal volume selected, on g(2)(tau). The modulation depth M(tau(i)) at any delay time tau(i) can be measured by short-time Fourier transform of g(2)(tau) and measurement of the magnitude of the spectrum at the ultrasound drive frequency. By following the established theoretical framework of DWS, we are able to connect the decay in M(tau) to the mean-squared displacement (MSD) of scattering centers and the MSD to G*(omega), the complex viscoelastic spectrum. A two-region composite polyvinyl alcohol phantom with different viscoelastic properties is selected for demonstrating local DWS-based recovery of G*(omega) corresponding to these regions from the measured region specific M(tau(i))vs tau(i). The ultrasound-assisted measurement of MSD is verified by simulating, using a generalized Langevin equation (GLE), the dynamics of the particles in the region selected as well as by the usual DWS experiment without the ultrasound. It is shown that whereas the MSD obtained by solving the GLE without the ultrasound forcing agreed with its experimental counterpart covering small and large values of tau, the match was good only in the initial transients in regard to experimental measurements with ultrasound.

Phase space path integral approach to harmonic oscillator with a time-dependent force constant

The quantum statistical mechanical propagator for a harmonic oscillator with a time-dependent force constant, m omega(2)(t), has been investigated in the past and was found to have only a formal solution in terms of the solutions of certain ordinary differential equations. Such path integrals are frequently encountered in semiclassical path integral evaluations and having exact analytical expressions for such path integrals is of great interest. In a previous work, we had obtained the exact propagator for motion in an arbitrary time-dependent harmonic potential in the overdamped limit of friction using phase space path integrals in the context of Levy flights - a result that can be easily extended to Brownian motion. In this paper, we make a connection between the overdamped Brownian motion and the imaginary time propagator of quantum mechanics and thereby get yet another way to evaluate the latter exactly. We find that explicit analytic solution for the quantum statistical mechanical propagator can be written when the time-dependent force constant has the form omega(2)(t) = lambda(2)(t) - d lambda(t)/dt where lambda(t) is any arbitrary function of t and use it to evaluate path integrals which have not been evaluated previously. We also employ this method to arrive at a formal solution of the propagator for both Levy flights and Brownian subjected to a time-dependent harmonic potential in the underdamped limit of friction. (C) 2015 Elsevier B.V. All rights reserved.

Detection and estimation of liquid flow through a pipe in a tissue-like object with ultrasound-assisted diffuse correlation spectroscopy

Using coherent light interrogating a turbid object perturbed by a focused ultrasound (US) beam, we demonstrate localized measurement of dynamics in the focal region, termed the region-of-interest (ROI), from the decay of the modulation in intensity autocorrelation of light. When the ROI contains a pipe flow, the decay is shown to be sensitive to the average flow velocity from which the mean-squared displacement (MSD) of the scattering centers in the flow can be estimated. While the MSD estimated is seen to be an order of magnitude higher than that obtainable through the usual diffusing wave spectroscopy (DWS) without the US, it is seen to be more accurate as verified by the volume flow estimated from it. It is further observed that, whereas the MSD from the localized measurement grows with time as tau(alpha) with alpha approximate to 1.65, without using the US, a is seen to be much less. Moreover, with the local measurement, this super-diffusive nature of the pipe flow is seen to persist longer, i.e., over a wider range of initial tau, than with the unassisted DWS. The reason for the super-diffusivity of flow, i.e., alpha < 2, in the ROI is the presence of a fluctuating (thermodynamically nonequilibrium) component in the dynamics induced by the US forcing. Beyond this initial range, both methods measure MSDs that rise linearly with time, indicating that ballistic and near-ballistic photons hardly capture anything beyond the background Brownian motion. (C) 2015 Optical Society of America

Towards an Understanding of the Influence of Sedimentation on Colloidal Aggregation by Peclet Number

The Peclet number is a useful index to estimate the importance of sedimentation as compared to the Brownian motion. However, how to choose the characteristic length scale for the Peclet number evaluation is rather critical because the diffusion length increases as the square root of the time whereas the drifting length is linearly related to time. Our Brownian dynamics simulation shows that the degree of sedimentation influence on the coagulation decreases when the dispersion volume fraction increases. Therefore using a fixed length, such as the diameter of particle, as the characteristic length scale for Peclet number evaluation is not a good choice when dealing with the influence of sedimentation on coagulation. The simulations demonstrated that environmental factors in the coagulation process, such as dispersion volume fraction and size distribution, should be taken into account for more reasonable evaluation of the sedimentation influence.

Computer simulation on the collision-sticking dynamics of two colloidal particles in an optical trap

Collisions of a particle pair induced by optical tweezers have been employed to study colloidal stability. In order to deepen insights regarding the collision-sticking dynamics of a particle pair in the optical trap that were observed in experimental approaches at the particle level, the authors carry out a Brownian dynamics simulation. In the simulation, various contributing factors, including the Derjaguin-Landau-Verwey-Overbeek interaction of particles, hydrodynamic interactions, optical trapping forces on the two particles, and the Brownian motion, were all taken into account. The simulation reproduces the tendencies of the accumulated sticking probability during the trapping duration for the trapped particle pair described in our previous study and provides an explanation for why the two entangled particles in the trap experience two different statuses. (c) 2007 American Institute of Physics.

SPT方法在纳米粒子布朗运动观测中的应用

纳米粒子布朗运动特性对Micro-/Nano-PIV的使用和与粒子相关的物理现象的研究有重要意义.观测了200nm荧光粒子的布朗运动,利用单粒子追踪(SPT)算法和自编程序处理图像,获得粒子的均方位移,计算了实验扩散系数D_(exp)为2.09×10~(-12) m~2/s.与Stokes-Einstein公式估计的理论扩散系数D_(th)相比,二者量阶一致,但实验扩散系数的数值偏小约5%.对相关的实验误差进行了分析.

Risk-sensitive optimal feedback control accounts for sensorimotor behavior under uncertainty.

Many aspects of human motor behavior can be understood using optimality principles such as optimal feedback control. However, these proposed optimal control models are risk-neutral; that is, they are indifferent to the variability of the movement cost. Here, we propose the use of a risk-sensitive optimal controller that incorporates movement cost variance either as an added cost (risk-averse controller) or as an added value (risk-seeking controller) to model human motor behavior in the face of uncertainty. We use a sensorimotor task to test the hypothesis that subjects are risk-sensitive. Subjects controlled a virtual ball undergoing Brownian motion towards a target. Subjects were required to minimize an explicit cost, in points, that was a combination of the final positional error of the ball and the integrated control cost. By testing subjects on different levels of Brownian motion noise and relative weighting of the position and control cost, we could distinguish between risk-sensitive and risk-neutral control. We show that subjects change their movement strategy pessimistically in the face of increased uncertainty in accord with the predictions of a risk-averse optimal controller. Our results suggest that risk-sensitivity is a fundamental attribute that needs to be incorporated into optimal feedback control models.

Electroosmotic flow analysis of a branched U-turn nanofluidic device.

In this paper, we present the analysis of electroosmotic flow in a branched -turn nanofluidic device, which we developed for detection and sorting of single molecules. The device, where the channel depth is only 150 nm, is designed to optically detect fluorescence from a volume as small as 270 attolitres (al) with a common wide-field fluorescent setup. We use distilled water as the liquid, in which we dilute 110 nm fluorescent beads employed as tracer-particles. Quantitative imaging is used to characterize the pathlines and velocity distribution of the electroosmotic flow in the device. Due to the device's complex geometry, the electroosmotic flow cannot be solved analytically. Therefore we use numerical flow simulation to model our device. Our results show that the deviation between measured and simulated data can be explained by the measured Brownian motion of the tracer-particles, which was not incorporated in the simulation.

Risk-sensitive optimal feedback control accounts for sensorimotor behavior under uncertainty

Many aspects of human motor behavior can be understood using optimality principles such as optimal feedback control. However, these proposed optimal control models are risk-neutral; that is, they are indifferent to the variability of the movement cost. Here, we propose the use of a risk-sensitive optimal controller that incorporates movement cost variance either as an added cost (risk-averse controller) or as an added value (risk-seeking controller) to model human motor behavior in the face of uncertainty. We use a sensorimotor task to test the hypothesis that subjects are risk-sensitive. Subjects controlled a virtual ball undergoing Brownian motion towards a target. Subjects were required to minimize an explicit cost, in points, that was a combination of the final positional error of the ball and the integrated control cost. By testing subjects on different levels of Brownian motion noise and relative weighting of the position and control cost, we could distinguish between risk-sensitive and risk-neutral control. We show that subjects change their movement strategy pessimistically in the face of increased uncertainty in accord with the predictions of a risk-averse optimal controller. Our results suggest that risk-sensitivity is a fundamental attribute that needs to be incorporated into optimal feedback control models. © 2010 Nagengast et al.

基于显式分形插值的高保真地震数据重建方法研究

Based on the fractal theories, contractive mapping principles as well as the fixed point theory, by means of affine transform, this dissertation develops a novel Explicit Fractal Interpolation Function（EFIF）which can be used to reconstruct the seismic data with high fidelity and precision. Spatial trace interpolation is one of the important issues in seismic data processing. Under the ideal circumstances, seismic data should be sampled with a uniform spatial coverage. However, practical constraints such as the complex surface conditions indicate that the sampling density may be sparse or for other reasons some traces may be lost. The wide spacing between receivers can result in sparse sampling along traverse lines, thus result in a spatial aliasing of short-wavelength features. Hence, the method of interpolation is of very importance. It not only needs to make the amplitude information obvious but the phase information, especially that of the point that the phase changes acutely. Many people put forward several interpolation methods, yet this dissertation focuses attention on a special class of fractal interpolation function, referred to as explicit fractal interpolation function to improve the accuracy of the interpolation reconstruction and to make the local information obvious. The traditional fractal interpolation method mainly based on the randomly Fractional Brown Motion (FBM) model, furthermore, the vertical scaling factor which plays a critical role in the implementation of fractal interpolation is assigned the same value during the whole interpolating process, so it can not make the local information obvious. In addition, the maximal defect of the traditional fractal interpolation method is that it cannot obtain the function values on each interpolating nodes, thereby it cannot analyze the node error quantitatively and cannot evaluate the feasibility of this method. Detailed discussions about the applications of fractal interpolation in seismology have not been given by the pioneers, let alone the interpolating processing of the single trace seismogram. On the basis of the previous work and fractal theory this dissertation discusses the fractal interpolation thoroughly and the stability of this special kind of interpolating function is discussed, at the same time the explicit presentation of the vertical scaling factor which controls the precision of the interpolation has been proposed. This novel method develops the traditional fractal interpolation method and converts the fractal interpolation with random algorithms into the interpolation with determined algorithms. The data structure of binary tree method has been applied during the process of interpolation, and it avoids the process of iteration that is inevitable in traditional fractal interpolation and improves the computation efficiency. To illustrate the validity of the novel method, this dissertation develops several theoretical models and synthesizes the common shot gathers and seismograms and reconstructs the traces that were erased from the initial section using the explicit fractal interpolation method. In order to compare the differences between the theoretical traces that were erased in the initial section and the resulting traces after reconstruction on waveform and amplitudes quantitatively, each missing traces are reconstructed and the residuals are analyzed. The numerical experiments demonstrate that the novel fractal interpolation method is not only applicable to reconstruct the seismograms with small offset but to the seismograms with large offset. The seismograms reconstructed by explicit fractal interpolation method resemble the original ones well. The waveform of the missing traces could be estimated very well and also the amplitudes of the interpolated traces are a good approximation of the original ones. The high precision and computational efficiency of the explicit fractal interpolation make it a useful tool to reconstruct the seismic data; it can not only make the local information obvious but preserve the overall characteristics of the object investigated. To illustrate the influence of the explicit fractal interpolation method to the accuracy of the imaging of the structure in the earth’s interior, this dissertation applies the method mentioned above to the reverse-time migration. The imaging sections obtained by using the fractal interpolated reflected data resemble the original ones very well. The numerical experiments demonstrate that even with the sparse sampling we can still obtain the high accurate imaging of the earth’s interior’s structure by means of the explicit fractal interpolation method. So we can obtain the imaging results of the earth’s interior with fine quality by using relatively small number of seismic stations. With the fractal interpolation method we will improve the efficiency and the accuracy of the reverse-time migration under economic conditions. To verify the application effect to real data of the method presented in this paper, we tested the method by using the real data provided by the Broadband Seismic Array Laboratory, IGGCAS. The results demonstrate that the accuracy of explicit fractal interpolation is still very high even with the real data with large epicenter and large offset. The amplitudes and the phase of the reconstructed station data resemble the original ones that were erased in the initial section very well. Altogether, the novel fractal interpolation function provides a new and useful tool to reconstruct the seismic data with high precision and efficiency, and presents an alternative to image the deep structure of the earth accurately.