Autocorrelation Decay Research Articles

Single Molecule Study of the Lateral Transport of Four Homooligoncleotides at the Interface of Water and Chemically Modifed Silica

The lateral transport of four single-strand homooligonucleotides on a microscopically flat silica surface chemically modified with chlorodimethyloctadecylsilane, in contact with 0.01 M KCl, was investigated using single-molecule spectroscopy. The deoxynucleotides were 20-mers of poly A, poly C, poly T, and poly G, each labeled at the 5‘ end with tetramethylrhodamine. Autocorrelation of the burst data, for each homooligonucleotide, indicates a single diffusing species with no significant difference in the diffusion coefficient among the individual oligonucleotides (D = 3.2 ± 0.3 × 10-6 cm2/s). Examination of burst data for each homooligonucleotide reveals the presence of diffusing molecules occasionally stopping at strong adsorption sites. The frequency of strong adsorption correlates with the number of the amino and amide groups of the base. A histogram of duration times of the strong adsorption events shows that there are two different time scales for strong adsorption events. The autocorrelation decay f...

Single-Molecule Spectroscopy and Fluorescence Correlation Spectroscopy of the Lateral Transport of the T3 Promoter Primer at a Chemical Interface

Fluorescence correlation spectroscopy reveals that an oligonucleotide, the T3 promoter primer, undergoes only lateral diffusion when adsorbed to the interface of water and silica chemically modified with a hydrocarbon. The autocorrelation decay fits well to the model of simple diffusion, reporting a diffusion coefficient of 1.8 × 10−6 cm2/s. Single-molecule resolution of bursts for the T3 promoter primer reveals that rare, strong adsorption punctuates the lateral diffusion. Removal of the strong adsorption events from the data set, followed by autocorrelation, shows the actual diffusion coefficient to be 2.8 × 10−6 cm2/s, which is comparable to other oligonucleotides of the same size at the same interface. The single-molecule measurements show that average duration of strong adsorption is 0.2 s, and the average fraction of strongly adsorbed molecules is 10% of the molecules at the interface. While single-molecule spectroscopy reveals a process not evident in fluorescence correlation spectroscopy, the precision of the parameters describing strong adsorption is limited by the statistics of small numbers. Fluorescence correlation spectroscopy is suited to observing a much larger number of events, which is needed for high precision. The two methods are complementary: single-molecule spectroscopy gives estimates of the chemical parameters needed for design of the fluorescence correlation spectroscopy, achieving precise measurements with an accurate interpretation.

Analytic Solution to the Autocorrelation Function for Lateral Diffusion and Rare Strong Adsorption

An analytic expression is derived to describe the autocorrelation function for fluorophors interacting with heterogeneous chemical interfaces, where both lateral diffusion and reversible strong adsorption occur. The expression is accurate when the rate of strong adsorption is low compared to the rates of both diffusion and desorption, enabling analysis by nonlinear regression. Simulations of single molecules are employed to investigate the applicability of the analytic equation for interpretation of chemical equilibrium and kinetics of single fluorescent molecules undergoing both lateral diffusion and varying amounts of specific adsorption at chemical interfaces. The simulations show that the analytic equation accurately describes the autocorrelation decay, and the equation begins to deviate, as expected, when the adsorption rate becomes large. The results show that a smaller beam size enhances the ability to extract sorption kinetics from the autocorrelation decay, and that a larger beam size enhances the ability to obtain information about the diffusion coefficient with minimal interference from sorption processes. The expression provides a tool for choosing between fluorescence correlation spectroscopy and single-molecule sorting in studies of heterogeneous surfaces.

Sequences with Uniformly Decaying Auto-Correlation Coefficients

In this paper we present discrete-time signals which are readily implementable and have "random like" uniformly decaying auto-correlation property. Signals with special properties are required in a wide variety of applications ranging from spread-spectrum systems and adaptive equalization in communication systems to real-time and offline identification for the purpose of control design. Traditionally, pseudo random sequences have been widely used to simulate "random like" behavior in signals. However, such inputs are periodic and their auto-correlation coefficients do not uniformly decay with length. Consequently, pseudo-random sequences have serious limitations in highly uncertain environments including model estimation in real-time identification for complex systems and estimation of channel properties in communication systems in an uncertain environment. In this paper we presenta new input to overcome these problems. The new input is a higher order chirp and we show that it not only has uniformly decaying auto-correlation property but also that the auto-correlation decay rate is polynomial with length. These properties bear significant resemblance to random i.i.d. inputs in their first and second order properties.

Suppression of vertical diffusion in strongly stratified turbulence

A spectral approximation for diffusion of passive scalar in stably and strongly stratified turbulence is presented. The approximation is based on a linearized approximation for the Eulerian two-time correlation and Corrsin's conjecture for the Lagrangian two-time correlation. For strongly stratified turbulence, the vertical component of the turbulent velocity field is well approximated by a collection of Fourier modes (waves) each of which oscillates with a frequency depending on the direction of the wavevector. The proposed approximation suggests that the phase mixing among the Fourier modes having different frequencies causes the decay of the Lagrangian two-time vertical velocity autocorrelation, and the highly oscillatory nature of these modes results in the suppression of single-particle dispersion in the vertical direction. The approximation is free from any ad hoc adjusting parameter and shows that the suppression depends on the spectra of the velocity and fluctuating density fields. It is in good agreement with direct numerical simulations for strongly stratified turbulence.

Griffiths-McCoy singularities in the random transverse-field Ising spin chain

We consider the paramagnetic phase of the random transverse-field Ising spin chain and study the dynamical properties by numerical methods and scaling considerations. We extend our previous work [Phys. Rev. B 57, 11404 (1998)] to new quantities, such as the non-linear susceptibility, higher excitations and the energy-density autocorrelation function. We show that in the Griffiths phase all the above quantities exhibit power-law singularities and the corresponding critical exponents, which vary with the distance from the critical point, can be related to the dynamical exponent z, the latter being the positive root of [(J/h)^{1/z}]_av=1. Particularly, whereas the average spin autocorrelation function in imaginary time decays as [G]_av(t)~t^{-1/z}, the average energy-density autocorrelations decay with another exponent as [G^e]_av(t)~t^{-2-1/z}.

Ultrafast phase dynamics of coherent carriers in GaAs

Ultrafast phase dynamics of free-induction decay for carriers in bulk GaAs is studied with differential-phase spectroscopy. The instantaneous phase shifts of the free-induction decay with respect to the excitation pulses are extracted from simultaneously recorded laser pulse autocorrelation and free-induction decay in GaAs. Ultrafast phase dynamics during and immediately after the femtosecond pulse excitation are numerically evaluated with optical Bloch equations using pump pulse and semiconductor exciton parameters as input. Good agreement of the theory with experiment is obtained.

Chaotic balanced state in a model of cortical circuits.

The nature and origin of the temporal irregularity in the electrical activity of cortical neurons in vivo are not well understood. We consider the hypothesis that this irregularity is due to a balance of excitatory and inhibitory currents into the cortical cells. We study a network model with excitatory and inhibitory populations of simple binary units. The internal feedback is mediated by relatively large synaptic strengths, so that the magnitude of the total excitatory and inhibitory feedback is much larger than the neuronal threshold. The connectivity is random and sparse. The mean number of connections per unit is large, though small compared to the total number of cells in the network. The network also receives a large, temporally regular input from external sources. We present an analytical solution of the mean-field theory of this model, which is exact in the limit of large network size. This theory reveals a new cooperative stationary state of large networks, which we term a balanced state. In this state, a balance between the excitatory and inhibitory inputs emerges dynamically for a wide range of parameters, resulting in a net input whose temporal fluctuations are of the same order as its mean. The internal synaptic inputs act as a strong negative feedback, which linearizes the population responses to the external drive despite the strong nonlinearity of the individual cells. This feedback also greatly stabilizes the system's state and enables it to track a time-dependent input on time scales much shorter than the time constant of a single cell. The spatiotemporal statistics of the balanced state are calculated. It is shown that the autocorrelations decay on a short time scale, yielding an approximate Poissonian temporal statistics. The activity levels of single cells are broadly distributed, and their distribution exhibits a skewed shape with a long power-law tail. The chaotic nature of the balanced state is revealed by showing that the evolution of the microscopic state of the network is extremely sensitive to small deviations in its initial conditions. The balanced state generated by the sparse, strong connections is an asynchronous chaotic state. It is accompanied by weak spatial cross-correlations, the strength of which vanishes in the limit of large network size. This is in contrast to the synchronized chaotic states exhibited by more conventional network models with high connectivity of weak synapses.

Phase ordering of the O(2) model in the post-Gaussian approximation

The Gaussian closure approximation previously used to study the growth kinetics of the non-conserved O(n) model is shown to be the zeroth-order approximation in a well-defined sequence of approximations composing a more elaborate theory. This paper studies the effects of including the next nontrivial correction in this sequence for the case n=2. The scaling forms for the order-parameter and order-parameter squared correlation functions are determined for the physically interesting cases of the O(2) model in two and three spatial dimensions. The post-Gaussian versions of these quantities show improved agreement with simulations. Post-Gaussian formulas for the defect density and the defect-defect correlation function g-tilde(x) are derived. As in the previous Gaussian theory, the addition of fluctuations allows one to eliminate the unphysical divergence in g-tilde(x) at short scaled distances. The nontrivial exponent \ensuremath{\lambda}, governing the decay of order-parameter autocorrelations, is computed in this approximation both with and without fluctuations.

Bounds on the decay of the autocorrelation in phase ordering dynamics.

We investigate the decay of temporal correlations in phase ordering dynamics by obtaining bounds on the decay exponent \ensuremath{\lambda} of the autocorrelation function [defined by ${\mathrm{lim}}_{{\mathit{t}}_{2}\mathrm{\ensuremath{\gg}}{\mathit{t}}_{1}}$〈\ensuremath{\varphi}(r,${\mathit{t}}_{1}$)\ensuremath{\varphi}(r,${\mathit{t}}_{2}$)〉\ensuremath{\sim}L (${\mathit{t}}_{2}$${)}^{\mathrm{\ensuremath{-}}\ensuremath{\lambda}}$]. For a nonconserved order parameter, we recover the Fisher and Huse inequality, \ensuremath{\lambda}\ensuremath{\ge}d/2. For a conserved order parameter, we find \ensuremath{\lambda}\ensuremath{\ge}d/2 only if ${\mathit{t}}_{1}$ = 0. If ${\mathit{t}}_{1}$ is in the scaling regime, then \ensuremath{\lambda}\ensuremath{\ge}d/2+2 for d\ensuremath{\ge}2 and \ensuremath{\lambda}\ensuremath{\ge}3/2 for d=1. For the one-dimensional scalar case, this, in conjunction with previous results, implies that the value of \ensuremath{\lambda} depends on whether ${\mathit{t}}_{1}$=0 or ${\mathit{t}}_{1}$\ensuremath{\gg}1. Our numerical simulations for the two-dimensional, conserved scalar order parameter show that \ensuremath{\lambda}\ensuremath{\approxeq}4 for ${\mathit{t}}_{1}$ in the scaling regime, consistent with our bound. The asymptotic decay when ${\mathit{t}}_{1}$=0, while exhibiting an unexpected sensitivity to the amplitude of the initial correlations, is slower than when ${\mathit{t}}_{1}$\ensuremath{\gg}1 and obeys the bound \ensuremath{\lambda}\ensuremath{\ge}d/2. \textcopyright{} 1996 The American Physical Society.

Aggregate Structure, Gelling, and Coacervation within the L1 Phase of the Quasi-ternary System Alkyltrimethylammonium Bromide-Sodium Desoxycholate-Water

The phase behavior of mixtures of a cationic surfactant, cetyltrimethylammonium bromide (CTAB), with a bile salt, sodium desoxycholate (NaDOC), in water has been studied at 25°C. Mixing of the two surfactants at equimolar composition gave an associative type of phase separation similar to that observed in mixed polyelectrolyte surfactant systems. A partial ternary phase diagram was obtained in the water-rich corner and the limits of the two-phase (2L1) region were determined. The structural properties of the mixed bile salt-CTAB aggregates and their connection with phase separation were investigated by the application of dynamic light scattering (DLS) complemented with cryo-transmission electron microscopy (TEM) studies in the L1 phase surrounding the two-phase island and the gel region. In dilute concentrations both DLS and cryo-TEM techniques provide evidence for the presence of flexible cylindrical micelles at above mole fraction of NaDOC of 0.2. A progressive change in the appearance of the mixed micelles is directly visualized from cryo-TEM studies. At a mole fraction of 0.2 and below, small globular micelles exist; above mole fraction 0.3, flexible cylindrical thread-like micelles are found. A further increase in NaDOC gives structures with decreased extension and increased contortions, in many cases branching with Y-junctions. DLS autocorrelation decay curves have been analyzed using the REPES program which makes a smoothed inverse La-place transformation of the autocorrelation function. The hydrodynamic screening length evaluated using the Stokes-Einstein equation shows in a highly sensitive way the approach to the two-phase region. Critical dynamics behavior, i.e., an approach to a q3 -dependence of the average relaxation rate, is observed in the crossover region close to the coacervation boundary. DLS and rheology measurements were performed at higher concentrations, both in a region with gel-like composition and at several bile salt-CTAB mole fractions. The DLS and rheological properties observed are interpreted using concepts analogous to a solution of entangled polymers. The study was extended to include the influence of varied alkyl chain length and similar trends in aggregation and phase separation were observed when CTAB was replaced by other alkyltrimethylammonium bromides (C18TAB, C14TAB, and C12TAB).

NMR signal loss from turbulence: Models of time dependence compared with data.

This paper reviews theoretical models of nuclear magnetic resonance signal loss due to turbulence in the presence of a magnetic gradient and presents measurements of signal loss from pipe flow as a function of echo time. The models all treat homogeneous turbulence as a random velocity superimposed on a steady velocity. Theoretical signal losses were calculated using previous hot wire anemometry data from dynamically similar air flow. Theoretical pipe cross sections were partitioned into nine concentric homogeneous regions with distinct turbulent diffusivities and intensities. Experimental pipes were 0.95 and 5.0 cm diameter with average water velocities of 1 m ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ providing Reynolds numbers of 12 000 and 55 000. Magnetic gradient strengths ranged from 0.01 to 0.04 G ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$; echo times ranged from 24 to 120 ms. The models that include the decay of the velocity autocorrelation with time (i.e., consider that turbulence appears more diffusive as the observation time increases) fit the data better than those that do not.

Phase ordering of two-dimensionalXYsystems below the Kosterlitz-Thouless transition temperature

We consider quenches in non-conserved two-dimensional XY systems between any two temperatures below the Kosterlitz-Thouless transition. The evolving systems are defect free at coarse-grained scales, and can be exactly treated. Correlations scale with a characteristic length $L(t) \propto t^{1/2}$ at late times. The autocorrelation decay exponent, $\bar{\lambda} = (\eta_i+\eta_f)/2$, depends on both the initial and the final state of the quench through the respective decay exponents of equilibrium correlations, $C_{EQ}(r) \sim r^{-\eta}$. We also discuss time-dependent quenches.

Growth of long-range correlations after a quench in conserved-order-parameter systems.

We develop a general Langevin formalism for the dynamics after a quench to a critical point or an ordered phase, and use this to study a few specific cases. We present a general argument that for $d$ spatial dimensions and conserved order parameter, the local autocorrelations decay as $〈\ensuremath{\varphi}(\mathbf{r},0)\ensuremath{\varphi}(\mathbf{r},t)〉\ensuremath{\sim}{L}^{\ensuremath{-}d}(t)$, where $L(t)$ is the correlation length at time $t$, and $\ensuremath{\varphi}$ is the order parameter. We also present new analytical and numerical results for the coarsening process after a quench to zero temperature in the ferromagnetic Ising chain with conserved magnetization.

Effects of flipping rules in cluster algorithms

Studying rules for flipping cluster spins, one with the fastest decay of autocorrelations is found. It turns out that connectivity of clusters is an additional crucial parameter. Another result is that there are only a few eigenvalues of the transition matrix which play a role. One eigenvalue dominates if the flipped cluster distribution is extended. The lattice size dependence of the weights of the eigenvalues is observed for the first time.

Phase ordering dynamics of a vector order parameter

Mazenko's theory of phase ordering dynamics is generalized to an n-component nonconserved vector order parameter. The scaling functions for the equal-time and two-time correlation functions are calculated, as well as the exponent characterizing the decay of autocorrelations. The equal-time correlation function is numerically quite close to that recently calculated by Bray and Puri (1991), and by Toyoki (1991), and exhibits the same power-law tail in its Fourier transform, the time-dependent structure factor.

Cluster mechanisms, autocorrelation functions, and related markov spectra for ising systems in 2, 3, and 4 dimensions

Various prescriptions for selecting the clusters to be flipped have been studied and a new one with the fastest decay of autocorrelations has been found. From the analysis of the data of several observables detailed information about the modes which occur in each of four algorithms has been obtained.

Polyelectrolyte properties of proteoglycan monomers

Light scattering measurements were made on proteoglycan monomers (PGM) over a wide range of ionic strengths Cs, and proteoglycan concentrations [PG]. At low Cs there were clear peaks in the angular scattering intensity curve I(q), which moved towards higher scattering wave numbers q, as [PG]1/3. This differs from the square root dependence of scattering peaks found by neutron scattering from more concentrated polyelectrolyte solutions. The peaks remained roughly fixed as Cs increased, but diminished in height, and superposed I(q) curves yielded a sort of isosbestic point. Under certain assumptions the static structure factor S(q) could be extracted from the measured I(q), and was found to retain a peak. A simple hypothesis concerning coexisting disordered and liquidlike correlated states is presented, which qualitatively accounts for the most salient features of the peaks. There was evidence of a double component scattering autocorrelation decay at low Cs, which, when resolved into two apparent diffusion coefficients, gave the appearance of simultaneous ‘‘ordinary’’ and ‘‘extraordinary’’ phases. The extraordinary phase was ‘‘removable,’’ however, by filtering. At higher Cs the proteoglycans appear to behave as random nonfree draining polyelectrolyte coils, with a near constant ratio of 0.67 between hydrodynamic radius and radius of gyration. The apparent persistence length varied as roughly the −0.50 power of ionic strength, similar to various linear synthetic and biological polyelectrolytes. Electrostatic excluded volume theory accounted well for the dependence of A2 on Cs.

Dynamics of droplets in random Ising magnetic systems.

We calculate the spin autocorrelation functions in random Ising magnets, within the framework of a Fokker-Planck model for the evolution of the droplet size. This model, which is equivalent to a diffusion process in a one-dimensional disordered medium, is treated by means of an effective-medium-type theory. Our analysis predicts a power-law decay for the autocorrelations in random-bond ferromagnets, of the form ${\mathit{t}}^{\mathrm{\ensuremath{-}}\mathit{Y}}$, where the nonuniversal exponent Y depends on both the temperature and the properties of the random-bond distribution. For weakly frustrated random-bond systems, with a finite fraction of antiferromagnetic defect bonds, the variation of Y with the parameters of the system exhibits a nonanalytic behavior at a freezing-type transition. We argue, however, that there are no corresponding nonanalyticities in the thermodynamic properties of the system. Spin autocorrelations in Ising spin glasses are also considered, by means of the effective-medium theory and the zero-temperature scaling hypothesis of Bray and Moore, Huse, and Fisher, and McMillan for the droplet energies. Our results are in agreement with the form of decay of autocorrelations proposed by Huse and Fisher.

A stochastic model for the large scale dynamics of some fluctuating interfaces

The Kuramoto-Sivashinsky-Tsuzuki equation and a similar model describing irregularly modulated interfaces are investigated in a very large length regime. This corresponds to a permanent chaotic state with a large number of nonlinear degrees of freedom. The dynamics of the small wavenumber modes is analyzed. A simulation of the equation allows to show that these very slow modes obey an effective stochastic partial differential equation, i.e. a Burgers equation with a rapidly fluctuating forcing term. This deterministic forcing “noise” is computed numeracally. A surprisingly robust property of this noise is that its autocorrelations decay rapidly in time for all parameter values and wavenumber. A consequence of the existence of such an effective equation is that the correlations of the slow modes should scale as if they obeyed a Burgers equation with a stochastic forcing. For this latter equation predictions made using the dynamic renormalisation group and direct simulations exist. These predictions are compared to the data obtained for the spontaneously fluctuating equations. The method employed in this paper to demonstrate that the slow modes obey an effective stochastic equation is of some generality and can be applied to other chaotic partial differential equations.