What Are the Conditions for Exponential Time-Cubed Echo Decays?

Diffusion of precessing spins through a constant field gradient is well-known to produce two distinctive features: an exp(-bt(3)) decay of the echo amplitude in response to two pulses and a much slower decay of the Carr-Purcell echo train. These features will appear whenever the spin frequency is described by a continuous random-walk. The present work shows that this may also occur in the presence of motions with long correlation times tau(c)-continuous Gaussian frequency noise with an exponential autocorrelation has the correct properties over time durations smaller than tau(c). Thus, time-cubed echo decays will occur in situations other than physical diffusion. The decay rate of the Carr-Purcell echo train is shown to vary with the pulse spacing tau whenever the correlation time tau(c) is long; the slower Carr-Purcell decay compared to the two-pulse echo decay is not unique to diffusion. Simulations are presented that display time-cubed decays. The simulations confirm two important criteria: the echo time must be less than tau(c) and the frequency noise must consist of nearly continuous variations, as opposed to step-like changes. These criteria define the range of physical parameters for which time-cubed decays will be observable.     

Incidence of apparent restricted diffusion in three different models of cerebral infarction

High speed magnetic resonance imaging (MRI) and short diffusion times are used to investigate the appearance of restricted diffusion in three different models of cerebral infarction. The models are: the middle cerebral artery occlusion (MCAO) model in the rat, the carotid occlusion model in the gerbil, and the Rose Bengal microvascular occlusion model in the rat. All three were investigated for 16 b-values equally spaced between 10 and 1510 s/mm² using two distinct experiments. In the ct (constant time) experiment, the diffusion time was held constant at 11.7 ms while the b-value was varied with the gradient strength. In the cg (constant gradient) experiment, the gradient strength was held constant and the b-value increased by varying the diffusion time from 4.4 to 11.7 ms. A monoexponential decay of the signal intensity with b-value in the ct experiment accompanied by nonmonoexponential (NME) decay in the cg experiment is indicative of restricted diffusion. As this phenomenon is detectable only at short diffusion times, it cannot be due to restriction by impermeable membranes, and we have thus termed this apparent restriction. For the MCAO model and the carotid occlusion model, apparent restriction was found both inside the infarct territory and in some regions outside it. No definite evidence for restriction was found for the Rose Bengal model, which was, however, only studied from 24 h post-insult.     

2D(13)C-(13)C MAS NMR correlation spectroscopy with mixing by true (1)H spin diffusion reveals long-range intermolecular distance restraints in ultra high magnetic field

An improved 2D (13)C-(13)C CP(3) MAS NMR correlation experiment with mixing by true (1)H spin diffusion is presented. With CP(3), correlations can be detected over a much longer range than with direct (1)H-(13)C or (13)C-(13)C dipolar recoupling. The experiment employs a (1)H spin diffusion mixing period tau(m) sandwiched between two cross-polarization periods. An optimized CP(3) sequence for measuring polarization transfer on a length scale between 0.3 and 1.0 nm using short mixing times of 0.1 ms < tau(m) < 1 ms is presented. For such a short tau(m), cross talk from residual transverse magnetization of the donating nuclear species after a CP can be suppressed by extended phase cycling. The utility of the experiment for genuine structure determination is demonstrated using a self-aggregated Chl a/H(2)O sample. The number of intramolecular cross-peaks increases for longer mixing times and this obscures the intermolecular transfer events. Hence, the experiment will be useful for short mixing times only. For a short tau(m) = 0.1 ms, intermolecular correlations are detected between the ends of phytyl tails and ring carbons of neighboring Chl a molecules in the aggregate. In this way the model for the structure, with stacks of Chl a that are arranged back to back with interdigitating phytyl chains stretched between two bilayers, is validated.     

Time course of adaptation and recovery from adaptation in the cat auditory-nerve neurophonic

The auditory-nerve neurophonic (ANN) reflects the ensemble response of phase-locked firing in single auditory-nerve fibers to sustained signals. Consequently, neural response properties such as adaptation and recovery from adaptation can be observed. In this study, ANN responses to 800-Hz, 100-ms tones presented at 10-30-dB SL were recorded using bipolar platinum-iridium electrodes placed on the auditory nerve of the cat. The cat ANN adaptation properties were determined and fit to the equation: A(tp) = Yre(-tp/tau Ar) + Yse(-tp/tau As) + Ass. The rapid time constant of adaptation (tau Ar) was invariant across stimulus level, with a mean value of 4.8 (+/- 2.1) ms. The short-term time constant (tau As) decreased approximately 21 ms for each 10-dB increase in probe amplitude. The mean tau As was 116 ms at 10 dB SL, 83.2 ms at 20 dB SL, and 73.5 ms at 30 dB SL. The ANN recovery from adaptation data was analyzed and fit to the equation: A(delta t) = Amax - Yre(-delta t/tau Rr) - Yse(-delta t/tau Rs). Here, tau Rr, the rapid time constant of recovery, and tau Rs, the short-term time constant, were independent of masker intensity in the studied range, with values of 16.2(+/- 9.8) and 125(+/- 50.1) ms, respectively. The results of this study indicate that ANN time constants are comparable to those measured for single units and that the adaptation behavior of phase-locked and nonphase-locked activity appears to be similar.     

Internal magnetic gradient fields in glass bead packs from numerical simulations and constant time diffusion spin echo measurements

Internal magnetic field gradients in water saturated glass bead packs were studied by numerical simulations and a constant time spin echo (CTSE) experiment. The CTSE is comprised of two spin echo refocusing periods where each of the two evolution periods, tau1 and tau2, is varied so that the total evolution, 2(tau1 + tau2), is held constant. The experiment is similar to that introduced by Norwood and Quilter and allows the effects of dephasing due to diffusion in a magnetic field gradient to be separated from other relaxation mechanisms. In our experiments, the magnetic susceptibility difference between the pore fluid and glass beads creates the internal field gradient. CTSE measurements were performed at 7 T (300 MHz 1H) for water saturated in 50 microm diameter glass bead pack. We find that the internal gradients in the center of the pore bodies, where free diffusion applies, is in the range of 10 to 100 G/cm. This fluid volume accounts for < or =10% of the total pore volume. From direct numerical simulations of the internal magnetic field based on a first principles calculation, we find that the major fraction, >90%, of the pore volume has internal gradients of order 500 to 5,000 G/cm. Signals from water in these large gradients is not observed in our CTSE measurements.     

Correlation time and diffusion coefficient imaging: application to a granular flow system

A parametric method for spatially resolved measurements for velocity autocorrelation functions, R(u)(tau) = , expressed as a sum of exponentials, is presented. The method is applied to a granular flow system of 2-mm oil-filled spheres rotated in a half-filled horizontal cylinder, which is an Ornstein-Uhlenbeck process with velocity autocorrelation function R(u)(tau) = e(- ||tau ||/tau(c)), where tau(c) is the correlation time and D = tau(c) is the diffusion coefficient. The pulsed-field-gradient NMR method consists of applying three different gradient pulse sequences of varying motion sensitivity to distinguish the range of correlation times present for particle motion. Time-dependent apparent diffusion coefficients are measured for these three sequences and tau(c) and D are then calculated from the apparent diffusion coefficient images. For the cylinder rotation rate of 2.3 rad/s, the axial diffusion coefficient at the top center of the free surface was 5.5 x 10(-6) m(2)/s, the correlation time was 3 ms, and the velocity fluctuation or granular temperature was 1.8 x 10(-3) m(2)/s(2). This method is also applicable to study transport in systems involving turbulence and porous media flows.     

Steric interactions in cellular structures formed in a water/oil/surfactant/cosurfactant mixture

Dynamics of dense microemulsion droplets forming ordered cellular phases as temperature increases are investigated by neutron spin echo spectroscopy (NSE). The shape fluctuations of droplets are shown using a specific contrast. Their relaxation time tau(f) is obtained by analysis of the NSE curves, which also reveals the short-range Brownian motion (diffusion constant D0) of the "caged" droplets. The thermal dependence of D0 and tau(f) supports the notion of entropically driven interdroplet steric repulsion stabilizing the cellular phases.     

Two-dimensional 109Ag NMR and random-walk simulation studies of silver dynamics in glassy silver ion conductors

By applying one- and two-dimensional 109Ag NMR, we demonstrate that silver diffusion in silver iodide/silver phosphate glasses is governed by a very broad, continuous distribution of correlation times G(lg tau). As a consequence, over a wide temperature range, the 109Ag NMR spectra can be described by a weighted superposition of a Gaussian and a Lorentzian where these line-shape components result from the slow and the fast silver ions in G(lg tau), respectively. For the 109Ag NMR two-time correlation functions F2(t), measured as a stimulated echo, a very stretched decay to F2SS(t(m)) = 0 is observed. When fitting to a Kohlrausch function, exp[-(t/tau)beta], a stretching parameter beta approximately = 0.2 is found. The temperature dependence of the mean correlation time of silver dynamics is described by an Arrhenius law where the activation energy is consistent with the one reported for the dc conductivity sigma(dc). In addition, it is shown that the effect of complex dynamical processes on NMR multi-time correlation functions can easily be calculated when performing random-walk simulations for schematic models such as the random-barrier model and the random-energy model. Based on these models it is possible to simulate various NMR observables and the mean square displacement, thus revealing the information content of multi-dimensional NMR experiments on solid ion conductors.     

Search for the Decay B+-->K+ tau-/+ mu+/-

We present a search for the lepton flavor violating decay B+-->K+ tau-/+ mu+/- using 383 x 10;{6} BB[over ] events collected by the BABAR experiment. The branching fraction for this decay can be substantially enhanced in new physics models. The kinematics of the tau from the signal B decay are inferred from the K+, mu, and other B in the event, which is fully reconstructed in one of a variety of hadronic decay modes, allowing the signal B candidate to be fully reconstructed. We observe no excess of events over the expected background and set a limit of B(B+-->K+ tau mu)<7.7 x 10(-5) at 90% confidence level, where the branching fraction is for the sum of the K+ tau- mu+ and K+ tau+mu- final states. We use this result to improve a model-independent bound on the energy scale of flavor-changing new physics.     

Quantum chaos of atoms in a resonant cavity

A system of atoms interacting with a radiation field in a resonant cavity is studied under conditions when the dynamics in the classical limit is stochastic. This situation is called quantum chaos. Equations of motion are obtained for the quantum-mechanical expectation values which take into account the quantum correlation functions. It is shown that in a situation corresponding to quantum chaos, the quantum corrections grow exponentially, making the evolution of the system essentially quantal after a certain time tau( variant Planck's over 2pi ) has elapsed. Analytical and numerical analysis show that in this regime the time tau( variant Planck's over 2pi ) obeys the logarithmic law tau( variant Planck's over 2pi ) approximately ln N (N is the number of atoms), and not the law tau( variant Planck's over 2pi ) approximately N(alpha) (alpha is a certain constant of order unity), as would be the case in the absence of chaos.     

全光纤速度干涉仪设计及应用

针对冲击波物理与爆轰物理等研究领域中对高速运动物体进行连续速度测量的需求,设计了一种全光纤速度干涉仪.该干涉仪采用单模光纤作为光传输和延迟元件,对t和t-τ两个时刻由于速度变化而引起的多普勒差拍信号进行检测.由于两个时刻的两束光信号对应的待测物体速度变化不大,因而两者几乎有相等的频移量,从而大大降低了差拍信号频率.并且,通过光纤长度的改变,灵活调节条纹常量（τ值）,使差拍信号频率不超过记录系统的带宽,从原理上解决记录系统响应带宽受限问题,拓展测速的上限.单模光纤的采用,对漫反射光起到了较好的选模作用,使干涉仪实现了对漫反射靶的测量.实验设计了1.5 m·s-1和150 m·s-1两种条纹常量,对低速过程的霍普金森杆实验和高速过程的激光驱动实验分别进行了测试,取得较好结果,证明了该干涉测试技术的有效性.     

Dynamics of phason fluctuations in the i-AlPdMn quasicrystal

We report on the study of the dynamics of long wavelength phason fluctuations in the i-AlPdMn icosahedral phase using coherent x-ray scattering. When measured with a coherent x-ray beam, the diffuse intensity due to phasons presents strong fluctuations or speckles pattern. From room temperature to 500 degrees C the speckle pattern is time independent. At 650 degrees C the time correlation of the speckle pattern exhibits an exponential time decay, from which a characteristic time tau is extracted. We find that tau is proportional to the square of the phason wavelength, which demonstrates that phasons are collective diffusive modes in quasicrystals, in agreement with theoretical predictions.     

Multi-gradient pulse investigations of fluid transport in porous media.

NMR pulsed field gradient (PFG) experiments employing the application of n gradient pulses k(1) ellipsis k(n) are discussed in a general way as an n-fold encoding of position at successive times. The experiments are then represented by a sampling of n-dimensional k-space, K(n). Various parameters of motion can be derived from the evolution of correlations within the n-dimensional position (r-)space, R(n), which is the Fourier conjugate space to K(n). A wide class of NMR experiments may be described by this formalism, where the dimension of the experiment is often reduced by imposing conditions to the free variables. This is demonstrated for the case of displacement measurements where the condition summation operatork(i) = 0 is met. The two simplest pulse sequences which allow one to correlate displacements at two different times with each other are presented. While the three-pulse version of SERPENT encodes displacements in two interleaved time intervals Delta(1) and Delta(2), the four-pulse VEXSY experiment includes a mixing time tau(m) in between both encoding intervals Delta. The behaviour of fluid transport subject to external pressure through a model porous system is demonstrated by means of numerical simulations of SERPENT and VEXSY experiments for water flowing through a packed bed of monosized spherical particles. Displacements parallel (Z) and perpendicular (X) to the main flow direction are determined and the 2-D joint probability densities and the conditional probabilities are discussed along with the correlation coefficients related to the displacements at different encoding times. It is shown that all possible correlations between Z and X(2) in VEXSY decay with time constants comparable to the average time needed for a fluid molecule to cover one bead diameter, while a negative correlation is observed between transverse (X) displacements which is explained by molecules flowing along streamlines which follow the circumference of the spherical particles. Correlations for displacements during the different times in SERPENT generally decay much slower and provide complementary information about the evolution of displacements with time.     

Dynamics of paramagnetic agents by off-resonance rotating frame technique

Off-resonance rotating frame technique offers a novel tool to explore the dynamics of paramagnetic agents at high magnetic fields (B0 > 3T). Based on the effect of paramagnetic relaxation enhancement in the off-resonance rotating frame, a new method is described here for determining the dynamics of paramagnetic ion chelates from the residual z-magnetizations of water protons. In this method, the dynamics of the chelates are identified by the difference magnetization profiles, which are the subtraction of the residual z-magnetization as a function of frequency offset obtained at two sets of RF amplitude omega(1) and pulse duration tau. The choices of omega(1) and tau are guided by a 2-D magnetization map that is created numerically by plotting the residual z-magnetization as a function of effective field angle theta and off-resonance pulse duration tau. From the region of magnetization map that is the most sensitive to the alteration of the paramagnetic relaxation enhancement efficiency R(1rho)/R1, the ratio of the off-resonance rotating frame relaxation rate constant R(1rho) verse the laboratory frame relaxation rate constant R(1), three types of difference magnetization profiles can be generated. The magnetization map and the difference magnetization profiles are correlated with the rotational correlation time tauR of Gd-DTPA through numerical simulations, and further validated by the experimental data for a series of macromolecule conjugated Gd-DTPA in aqueous solutions. Effects of hydration water number q, diffusion coefficient D, magnetic field strength B0 and multiple rotational correlation times are explored with the simulations of the magnetization map. This method not only provides a simple and reliable approach to determine the dynamics of paramagnetic labeling of molecular/cellular events at high magnetic fields, but also a new strategy for spectral editing in NMR/MRI based on the dynamics of paramagnetic labeling in vivo.     

P-Ga(1-x)InxAsyP1-y/InP材料的扩散长度测量

用激光扫描和电荧光衰减法测定了液相外延片p-Ga1-xInxAsyP1-y/InP(x=0.74,y=0.61)的少子扩散长度Im,并对这二种测试结果进行了比较,结果符合得很好。从这二种独立的实验结果获得表面复合速率S。S为6-7×104cm/s,扩散长度Lm为1.6～2.2μm。此外对p-Gε1-xInxAsyP1.y与InP衬底间的少数载流子行为进行了讨论。     

Various velocity correlations functions in a Lorentz gas - simulation and mode coupling theory

We present computer simulation results for several types of velocity correlation function in the two dimensional, overlapping Lorentz gas. Only the normal velocity autocorrelation function, whose integral gives the diffusion constant, shows obvious anomalous behaviour at the percolation transition. The other functions are fairly well approximated by the Lorentz-Boltzmann equation, even for densities at which the travelling particle is trapped. We do, however, at a sub-percolation density, examine the long time behaviour of the autocorrelation function corresponding to the second rank, irreducible tensor of the velocity, and find an algebraic decay with an exponent of 3.0 ± 0.1, consistent with the theoretically expected value of 3. With these observations in mind we re-examine the mode coupling theory of Götze, Leutheusser and Yip (Phys. Rev. A 23 (1981) 2634,) replacing their one (frequency dependent) relaxation time approximation to a kinetic operator by a two (frequency dependent) relaxation time model. We find that this leads to a significantly better estimate of the diffusions constant at low density. Furthermore the theory correctly predicts no striking anomalous behaviour in the types of velocity correlation function that are unrelated to diffusion as the percolation threshold is crossed.     

Probing Ultrafast Dissociation Dynamics of Chloroiodomethane in the B Band by Time-Resolved Mass Spectrometry

Ultrafast dissociation dynamics of chloroiodomethane(CH_2ICl)in the B band is studied by femtosecond timeresolved time-of-flight(TOF)mass spectrometry.Time-resolved TOF mass signal of parent ion(CH_2ICl~+)and main daughter ion(CH_2 Cl~+)are obtained.The curve for the transient signal of CH_2ICl~+ is simple and can be well fitted by an exponential decay convoluted with a Gaussian function.The decay constant determined to be less than 35 fs reflects the lifetime of the B band.Significant substituent effects on photodissociation dynamics of CH_2ICl compared with CH3I are discussed.The dissociation time from the parent ion CH_2ICl~+ to the daughter ion CH_2 Cl~+ is determined in the experiment.The optimized geometry of the ionic state of CH_2ICl and the ionization energy are calculated for further analysis of the measurements.In addition,compared with the parent ion,a new decay component with time constant of ~596 fs is observed for CH_2 Cl~+,and reasonable mechanisms are proposed for the explanation.     

Low-frequency velocity correlation spectrum of fluid in a porous media by modulated gradient spin echo.

In addition to the fast correlation for local stochastic motion, the molecular velocity correlation function in a fluid enclosed within the pore boundaries features a slow long time-tail decay. Here we present its study by the NMR modulated gradient spin-echo method (MGSE) [1] on a system of water trapped in the space between the closely packed polystyrene beads. With MGSE pulse sequence, a repetitive train of RF pulses with interspersed gradient pulses periodically modulates the spin phase. It gives the spin echo attenuation proportional to a value of the molecular velocity correlation spectrum at the modulation frequency. Covering the frequency range between Hz and MHz, it is a complement to the quasi-elastic neutron scattering, and so a suitable technique for the investigation of low frequency molecular dynamics in fluids. In our experiment, it enables to extract the low frequency correlation spectrum of water molecules confined in porous media. The function exhibits a negative long time-tail characteristic (a low frequency decay of the spectrum), which can be interpreted as a molecular back scattering on boundaries. The results can be well fitted with the spectrum calculated from the solution of the Langevin equation for restricted diffusion (which exhibits an exponential decay) [2] as well as with the spectrum obtained when simulating the hydrodynamics of molecular motion constrained by capillary walls (which gives an algebraic decay) [3]. Despite much work on theories and simulation, which predict slow negative long time tail of molecular velocity correlation dynamics in confined fluids, the obtained velocity correlation spectrum is the first experimental evidence to confirm these effects. The obtained dependence of spin echo attenuation on time, gradient strength and modulation frequency is also the first experimental verification of the recently developed approach to the spin echo in porous media, that uses the spin phase average with the cumulant expansion to get the attenuation as a discord of spin spatial coherence [4].     

Analytical and Numerical Studies of the One-Dimensional Spin Facilitated Kinetic Ising Model

The one-dimensional spin facilitated kinetic Ising model is studied analytically using the master equation and by simulations. The local state of the spins (corresponding to mobile and immobile cells) can change depending on the state of the neighbored spins, which reflects the high cooperativity inherent in glassy materials. The short-time behavior is analyzed using a Fock space representation for the master equation. The hierarchy of evolution equations for the averaged spin state and the time dependence of the spin autocorrelation function are calculated with different methods (mean-field theory, expansion in powers of the time, partial summation) and compared with numerical simulations. The long-time behavior can be obtained by mapping the one-dimensional spin facilitated kinetic Ising model onto a one-dimensional diffusion model containing birth and death processes. The resulting master equation is solved by van Kampen's size expansion, which leads to a Langevin equation with Gaussian noise. The predicted autocorrelation function and the global memory offer in the long-time limit a screened algebraic decay and a stretched exponential decay, respectively, consistent with numerical simulations.     

Observation of restricted diffusion in the presence of a free diffusion compartment: Single- and double-PFG experiments

Theoretical and experimental studies of restricted diffusion have been conducted for decades using single pulsed field gradient (s-PFG) diffusion experiments. In homogenous samples, the diffusion–diffraction phenomenon arising from a single population of diffusing species has been observed experimentally and predicted theoretically. In this study, we introduce a composite bi-compartmental model which superposes restricted diffusion in microcapillaries with free diffusion in an unconfined compartment, leading to fast and slow diffusing components in the NMR signal decay. Although simplified (no exchange), the superposed diffusion modes in this model may exhibit features seen in more complex porous materials and biological tissues. We find that at low q-values the freely diffusing component masks the restricted diffusion component, and that prolongation of the diffusion time shifts the transition from free to restricted profiles to lower q-values. The effect of increasing the volume fraction of freely diffusing water was also studied; we find that the transition in the signal decay from the free mode to the restricted mode occurs at higher q-values when the volume fraction of the freely diffusing water is increased. These findings were then applied to a phantom consisting of crossing fibers, which demonstrated the same qualitative trends in the signal decay. The angular d-PGSE experiment, which has been recently shown to be able to measure small compartmental dimensions even at low q-values, revealed that microscopic anisotropy is lost at low q-values where the fast diffusing component is prominent. Our findings may be of importance in studying realistic systems which exhibit compartmentation.