Time Tau Research Articles

Spatial pH Jump Measures Chemical Kinetics in a Steady-State System

We measure chemical kinetics in a steady-state solution where we create a microscopic open region with conditions different from the bulk. Individual reactant molecules spontaneously diffuse through this "reaction volume". We measure the changes which take place within their short residence time in the volume. The advantage of this approach is that the time resolution is limited only by the residence time tau(D) of the molecules in the reaction volume (which can easily be <50 mus), while the time taken to average the data can be arbitrarily long. In addition, if the chemical changes are reversible, the system is always in a steady state, and no replenishment of the reactants is necessary. Also, the total specimen volume required can be very small (<20 muL). We demonstrate the scheme by measuring the protonation induced changes of the fluorescence properties of fluorescein. We first show that a pH jump of >1 unit can be achieved by multiphoton excitation of ortho-nitro benzaldehyde (o-NBA). We then perform fluorescence correlation spectroscopy (FCS) to show that the residence time tau(D) of fluorescein in this low-pH region is approximately 30 mus. Subsequently, we use time correlated single photon counting (a widely used probing technique with an inherently long averaging time), and show that the data can be averaged for an arbitrarily long time, yet it captures the fluorescence lifetime of the low-pH species which exists only for the short time tau(D). Finally, we show that the time resolution can be tuned by over 3 orders of magnitude, by changing the focal volume and by changing the viscosity of the solution. The latter experiment also shows that small chemically induced changes in the fluorescence lifetime can be resolved by our technique.

Structure, Dynamic Properties, and Phase Transitions of Tethered Membranes

A coarse-grained model of a self-avoiding tethered membrane with hexagonal coordination, embedded in three-dimensional space, is studied by means of extensive Monte Carlo computer simulations. The simulations are performed at various temperatures for membranes with linear size 5 < or =L< or = 30. We find that the membrane undergoes several folding transitions from a high-temperature flat phase to multiple-folded structure as the temperature is steadily decreased. Using a suitable order parameter and finite size scaling analysis, these phase transitions are shown to be of first order. The equilibrium shape of the membranes is analyzed by calculating the eigenvalues lambda(2) (max)> or =lambda(2) (med)> or =lambda(2) (min) of the inertia tensor. We present a systematic finite size scaling analysis of the radius of gyration and the eigenvalues of the inertia tensor at different phases of the observed folding transitions. In the high temperature flat phase, the radius of gyration R(g) grows with the linear size of the membrane L as R(g) proportional, variant L(nu), where the exponent nu approximately 1.0. The eigenvalues of the inertia tensor scale as lambda(max) proportional, variant lambda(med) proportional, variant L(nu) and lambda(min) proportional variant L(nu min) whereby the roughness exponent nu(min) approximately 0.7. We also find that the Rouse relaxation time tau(R) of a self-avoiding membrane scales as tau(R) proportional, variant L(2nu+2), in good agreement with the theoretical predictions.

Polymer Translocation through a Nanopore: A Showcase of Anomalous Diffusion

We investigate the translocation dynamics of a polymer chain threaded through a membrane nanopore by a chemical potential gradient that acts on the chain segments inside the pore. By means of diverse methods (scaling theory, fractional calculus, and Monte Carlo and molecular dynamics simulations), we demonstrate that the relevant dynamic variable, the transported number of polymer segments, s(t), displays an anomalous diffusive behavior, both with and without an external driving force being present. We show that in the absence of drag force the time tau, needed for a macromolecule of length N to thread from the cis into the trans side of a cell membrane, scales as tauN(2/alpha) with the chain length. The anomalous dynamics of the translocation process is governed by a universal exponent alpha= 2/(2nu + 2 - gamma(1)), which contains the basic universal exponents of polymer physics, nu (the Flory exponent) and gamma(1) (the surface entropic exponent). A closed analytic expression for the probability to find s translocated segments at time t in terms of chain length N and applied drag force f is derived from the fractional Fokker-Planck equation, and shown to provide analytic results for the time variation of the statistical moments <s(t)> and <s(2) (t)>. It turns out that the average translocation time scales as tau proportional, f(-1)N(2/alpha-1). These results are tested and found to be in perfect agreement with extensive Monte Carlo and molecular dynamics computer simulations.

Polymer translocation in a double-force arrangement

Using Langevin dynamics simulations, we investigate the translocation dynamics of an externally driven polymer chain through a nanopore, where a pulling force F is exerted on the first monomer whilst there is an opposing force F(E) < F within the pore. Such a double-force arrangement has been proposed recently to allow better dynamical control of the translocation process in order to sequence biopolymers. We find that in the double-force arrangement translocation becomes slower as compared to the case under a single monomer pulling force of magnitude F-F(E), but scaling of the translocation time as a function of the chain length tau approximately N2 does not change. The waiting time tau(m) for monomer m to exit the pore is found to be a monotonically increasing function of the bead number almost until m approximately N , which indicates relatively well-defined slowing down and control of the chain velocity during translocation. We also study the waiting time distributions for the beads in the chain, and characterize in detail fluctuations in the bead positions and their transverse position coordinates during translocation. These data should be useful in estimating position-dependent sequencing errors in double-force experiments.

Statistical Mechanics and Dynamics of a Three-Dimensional Glass-Forming System

In the context of a classical example of glass formation in three dimensions, we exemplify how to construct a statistical-mechanical theory of the glass transition. At the heart of the approach is a simple criterion for verifying a proper choice of upscaled quasispecies that allow the construction of a theory with a finite number of "states." Once constructed, the theory identifies a typical scale xi that increases rapidly with lowering the temperature and which determines the alpha-relaxation time tau(alpha) as tau(alpha) approximately exp(muxi/T), with mu a typical chemical potential. The theory can predict relaxation times at temperatures that are inaccessible to numerical simulations.

Linear stochastic system with delay: Energy balance and entropy production

We study the energy balance in a linear stochastic dynamics with delay under the impact of an external periodic force. The linearity of the model, in combination with a response function method, enables us to perform detailed analytic calculations of each term in the energy balance equation. From this, we discuss thermodynamics and entropy production rate sigma . With use of the delay time tau and strength of the external force A0 , sigma is simply expressed as sigma=sigma_{D,1}(tau)+A_{0};{2}eta(tau) , with both sigma_{D,1}(tau) and eta(tau) positive definite. We thus conclude that even when there is no external force (A_{0}=0) , the entropy production rate sigma=sigma_{D,1}(tau) is positive, meaning that the delay force produces work, which is dissipated into a reservoir. Numerical experiments are performed to confirm theoretical results.

Phosphatidylcholine “Wobble” in Vesicles Assessed by High-Resolution 13C Field Cycling NMR Spectroscopy

High resolution (13)C NMR field cycling (covering 11.7 down to 0.002 T) relaxation studies of the sn-2 carbonyl of phosphatidylcholines in vesicles provide a detailed look at the dynamics of this position of the phospholipid in vesicles. The spin-lattice relaxation rate, R(1), observed down to 0.05 T is the result of dipolar and CSA relaxation components characterized by a single correlation time tau(c), with a small contribution from a faster motion contributing to CSA relaxation. At lower fields, R(1) increases further with a correlation time consistent with vesicle tumbling. The tau(c) is particularly interesting since it is 2-3 times slower than what is observed for (31)P of the same phospholipid. However, cholesterol increases the tau(c) for both (31)P and (13)C sites to the same value, approximately 25 ns. These observations suggest faster local motion dominates the dipolar relaxation of the (31)P, while a slower rotation or wobble dominates the relaxation of the carbonyl carbon by the alpha-CH(2) group. The faster motion must be damped with the sterol present. As a general methodology, high resolution (13)C field cycling may be useful for quantifying dynamics in other complex systems as long as a (13)C label (without attached protons) can be introduced.

Quasielastic neutron scattering investigation of motion of water molecules in n-propyl alcohol-water mixture

The dynamics of water molecules in the n-propyl alcohol-water mixtures is investigated by using quasielastic neutron scattering measurements. The dynamic structure factor S(Q,E) obtained from incoherent scattering of hydrogen atoms of water is fitted with jump diffusion and relaxing cage models. The diffusion constant obtained from the relaxing cage model, which gives better fitting with S(Q,E), shows better agreement to the experimental value than that of jump diffusion model. The dependence of translational relaxation time tau(T)(Q) and stretched exponent beta(T)(Q) on the fraction of hydrophobic hydrating water molecules in the solution is discussed.

Nondriven polymer translocation through a nanopore: Computational evidence that the escape and relaxation processes are coupled

Most of the theoretical models describing the translocation of a polymer chain through a nanopore use the hypothesis that the polymer is always relaxed during the complete process. In other words, models generally assume that the characteristic relaxation time of the chain is small enough compared to the translocation time that nonequilibrium molecular conformations can be ignored. In this paper, we use molecular dynamics simulations to directly test this hypothesis by looking at the escape time of unbiased polymer chains starting with different initial conditions. We find that the translocation process is not quite in equilibrium for the systems studied, even though the translocation time tau is about 10 times larger than the relaxation time tau{r}. Our most striking result is the observation that the last half of the chain escapes in less than approximately 12% of the total escape time, which implies that there is a large acceleration of the chain at the end of its escape from the channel.

Routes to chaos and multiple time scale dynamics in broadband bandpass nonlinear delay electro-optic oscillators

The response of a nonlinear optical oscillator subject to a delayed broadband bandpass filtering feedback is studied experimentally, numerically, and analytically. The oscillator loop is characterized by a high cutoff frequency with a response time tau approximately 10 ps and by a low cutoff frequency with a response time theta approximately 1 micros. Moreover, the optoelectronic feedback also consists of a significant delay tauD of the order of 100 ns. Depending on two key physical parameters, the loop gain beta and the nonlinearity operating point Phi, a large variety of multiple time scale regimes are reported, including slow or fast periodic oscillations with different waveforms, regular or chaotic breathers, slow time envelope dynamics, complex and irregular self-pulsing, and fully developed chaos. Many of these regimes are exhibiting new features that are absent in the classical first-order scalar nonlinear delay differential equations (DDEs), which differ in the modeling by the low cutoff only. Nearly all kinds of solutions are recovered numerically by a new class of integro-DDE (iDDE) that take into account both the high and low cutoff frequencies of the feedback loop. For moderate feedback gain, asymptotic solutions are determined analytically by taking advantage of the relative values of the time constants tau, theta, and tauD. We confirm the experimental observation of two distinct routes to oscillatory instabilities depending on the value of Phi. One route is reminiscent of the square wave oscillations of the classical first-order DDE, but the other route is quite different and allows richer wave forms. For higher feedback gain, these two distinct regimes merge leading to complex nonperiodic regimes that still need to be explored analytically and numerically. Finally, we investigate the theoretical limits of our iDDE model by experimentally exploring phenomena at extreme physical parameter setting, namely, high-frequency locking at strong feedback gain or pulse packages for very large delays. The large variety of oscillatory regimes of our broadband bandpass delay electro-optic oscillator is attractive for applications requiring rich optical pulse sources with different frequencies and/or wave forms (chaos-based communications, random number generation, chaos computing, and generation of stable multiple GHz frequency oscillations).

X-ray emission current scaling experiments for compact single-tungsten-wire arrays at80−nanosecondimplosion times

We report the results of a series of current scaling experiments with the Z accelerator for the compact, single, 20-mm diameter, 10-mm long, tungsten-wire arrays employed for the double-ended hohlraum ICF concept [M. E. Cuneo, Plasma Phys. Controlled Fusion 48, R1 (2006)]. We measured the z -pinch peak radiated x-ray power and total radiated x-ray energy as a function of the peak current, at a constant implosion time tau_{imp}=80ns . Previous x-ray emission current scaling for these compact arrays was obtained at tau_{imp}=95ns in the work of Stygar [Phys. Rev. E 69, 046403 (2004)]. In the present study we utilized lighter single-tungsten-wire arrays. For all the measurements, the load hardware dimensions, materials, and array wire number (N=300) were kept constant and were the same as the previous study. We also kept the normalized load current spatial and temporal profiles the same for all experiments reported in this work. Two different currents, 11.2+/-0.2MA and 17.0+/-0.3MA , were driven through the wire arrays. The average peak x-ray power for these compact wire arrays increased by 26%+/-7%to158+/-26TW at 17+/-0.3MA from the 125+/-24TW obtained at a peak current of 18.8+/-0.5MA with tau_{imp}=95ns . The higher peak power of the faster implosions may possibly be attributed to a higher implosion velocity, which in turn improves the implosion stability, and/or to shorter wire ablation times, which may lead to a decrease in trailing mass and trailing current. Our results show that the scaling of the radiated x-ray peak power and total radiated x-ray energy scaling with peak drive current to be closer to quadratic than the results of Stygar We find that the x-ray peak radiated power is P_{r} proportional, variantI;{1.57+/-0.20} and the total x-ray radiated energy E_{r} proportional, variantI;{1.9+/-0.24} . We also find that the current scaling exponent of the power is sensitive to the inclusion of a single data point with a peak power at least 1.9sigma below the average. If we eliminate this particular shot from our analysis (shot 1608), the power and energy scaling becomes closer to quadratic. Namely, we find that the dependence on the peak load current of the peak x-ray radiated power and the total x-ray radiated energy become P_{r} proportional, variantI;{1.71+/-0.10} and E_{r} proportional, variantI;{2.01+/-0.21} , respectively. In this case, the power scaling exponent is different by more than 2sigma from the previously published results of Stygar Larger data sets are likely required to resolve this uncertainty and eliminate the sensitivity to statistical fluctuations in any future studies of this type. Nevertheless, with or without the inclusion of shot 1608, our results with tau_{imp}=80ns fall short of an I2 scaling of the peak x-ray radiated power by at least 2sigma . In either case, the results of our study are consistent with the heuristic wire ablation model proposed by Stygar (P_{r} proportional, variantI;{1.5}) . We also derive an empirical predictive relation that connects the power scaling exponent with certain array parameters.

Octylglucopyranoside and Cyclodextrin in Water. Self-Aggregation and Complex Formation

At 25 degrees C ultrasonic attenuation spectra between 100 kHz and 400 MHz as well as sound velocities and densities of aqueous solutions of the surfactant n-octyl-beta-d-glucopyranoside and of the cage compound alpha-cyclodextrin have been measured. The liquid system reveals a critical association concentration (cac) exceeding the cmc of the surfactant almost by the cyclodextrin concentration and thus indicating a significant formation of cyclodextrin-surfactant inclusion complexes. The ultrasonic spectra display altogether four relaxation regions. The one with largest relaxation time (0.27 mus < or = tau(1) < or = 1.6 mus) exhibits a noticeable amplitude at surfactant concentrations larger than the cac only. It is assigned to the monomer exchange between the micelles and the suspending phase. A term with relaxation time tau(2) (33 ns < or = tau(2) < or = 135 ns) is characteristic for solutions containing both solutes. It is assumed to reflect the inclusion complex formation. Complexes with 1:1, 2:1, and 1:2 stoichiometry appear to exist. The terms at higher frequencies (4.8 ns < or = tau(3) < or = 9.8 ns; 0.8 ns <or = tau(4) < or = 2 ns) are due to fluctuations of the carbohydrate residues around the glucosidic bond angles and to the rotational isomerization of the exocyclic hydroxymethyl groups, respectively.

Robust entrainment phenomena of oscillations by delay time in the photosensitive Oregonator model

The influences of delayed feedback on the oscillating behaviors are numerically investigated by using the photosensitive Oregonator model with a Hopf point. We find that the time delay in the robust entrainment phenomena determines the time scale of the system, that is, T_{m}=(tau+delta)N (N=1,2,cdots, three dots, centered) , where T_{m} is the mean period of the oscillation and delta is a small constant compared with the delay time tau . Further, our numerical simulation shows that, when the system has a characteristic period T0 under the feedback with time delay, there exists an asymptotical line delta=delta_{0}T_{0} ( delta_{0} independent of any parameters) in the entrainment region with increasing strength of the feedback control c ; when the system has no characteristic period, the above linear relation is also kept, and delta decreases with increasing c .

Resonant control of stochastic spatiotemporal dynamics in a tunnel diode by multiple time-delayed feedback

We study the control of noise-induced spatiotemporal current density patterns in a semiconductor nanostructure (double-barrier resonant tunneling diode) by multiple time-delayed feedback. We find much more pronounced resonant features of noise-induced oscillations compared to single time feedback, rendering the system more sensitive to variations in the delay time tau . The coherence of noise-induced oscillations measured by the correlation time exhibits sharp resonances as a function of tau , and can be strongly increased by optimal choices of tau . Similarly, the peaks in the power spectral density are sharpened. We provide analytical insight into the control mechanism by relating the correlation times and mean frequencies of noise-induced breathing oscillations to the stability properties of the deterministic stationary current density filaments under the influence of the control loop. Moreover, we demonstrate that the use of multiple time delays enlarges the regime in which the deterministic dynamical properties of the system are not changed by delay-induced bifurcations.

Percolation Model for Slow Dynamics in Glass-Forming Materials

We identify a link between the glass transition and percolation of regions of mobility in configuration space. We find that many hallmarks of glassy dynamics, for example, stretched-exponential response functions and a diverging structural relaxation time, are consequences of the critical properties of mean-field percolation. Specific predictions of the percolation model include the range of possible stretching exponents 1/3< or =beta< or =1 and the functional dependence of the structural relaxation time tau_{alpha} and exponent beta on temperature, density, and wave number.

On rearrangeability of tandem connection of banyan-type networks

A multistage interconnection network (MIN) consisting of 2 times 2 nodes constructs a nonblocking switch if the network is rearrangeable. When a 2n times 2n bit-permuting network is rearrangeable with the minimum depth of 2n-1, the initial (resp. final) n stages of the network form a banyan-type network and hence the network is equivalent to the tandem connection between two banyan-type networks. Let gamma denote the guide permutation of a 2n times 2n banyan-type network and tau the trace permutation of another. These are permutations on numbers from 1 to n. This paper proves that, when the permutation gammatau-1 is the transposition between the number n and some number k < n, the tandem connection between the two networks is rearrangeable. This sufficient condition for rearrangeability covers a wide class of tandem connections. For example, the first network in tandem can be the omega network appended with the banyan exchange of any rank while the second is the reversed omega network.

Thermal stability of interaction between the CO molecules and the Al doped graphene

The thermal stability of interaction between CO molecules and Al doped graphene is studied using ab initio molecular dynamics calculations to reveal the adsorption/desorption behavior of the system. With these results, an adsorption-desorption phase diagram was established with atomic thermodynamics. The temperature (T) dependent desorption time tau(T) was determined with a thermal desorption method. The results show that the optimal desorption temperature is 400 K. The effect of T on atomic structure parameters and electrical properties were analyzed. It shows that the maximum variation of electrical conductivity induced by the adsorption occurs at 400 K, indicating that the best sensing performance of the devices should be at this particular temperature.

Rheological Properties of Wormlike Micellar Solutions Being Available in Wide Temperature Range in Sucrose Palmitate Systems

We investigated the melting point of the hydrated solid and rheological property of wormlike micellar solutions in the water/sucrose monopalmitate (C(16)SE)/tri (oxyethylene) dodecyl ether (C(12)EO(3)) system when a part of C(16)SE was substituted with the surfactants which have lower Krafft point than C(16)SE. The melting point of the hydrated solid of the water/C(16)SE/C(12)EO(3) system is around 34 degrees C. When C(16)SE is substituted with sodium dodecyl sulfate (SDS), the melting point of the hydrated solid decreases below 5 degrees C at alpha (weight fraction of SDS in C(16)SE+SDS mixture) being greater than 0.3 and the zero shear viscosity (eta(0)) increases from the original nonionic system. When C(16)SE is substituted with octa (oxyethylene) dodecyl ether (C(12)EO(8)), the melting point of the hydrated solid decreases down to 24 degrees C and the maximum zero shear viscosity (eta(0)(max)) decreases with the increase in alpha (weight fraction of C(12)EO(8) in C(16)SE+C(12)EO(8) mixture). eta(0)(max) is dramatically increased by the substitution of C(16)SE with SDS. With further increase of alpha, eta(0)(max) decreases gradually. The dynamic rheology data of highly viscous wormlike micellar solutions fit well to the Maxwell's mechanical model of viscoelastic material, indicating the formation of rigid network of entangled wormlike micelles. Shear (plateau) modulus G(0) is almost unchanged, whereas relaxation time tau(R) shows similar behavior to eta(0)(max). Hence, the behavior of eta(0)(max) can be explained from the behavior of tau(R) by considering the equation relating these quantities, eta(0)=G(0)tau(R). Since tau(R) is proportional to the length of wormlike micelles, the behavior of eta(0)(max) can be explained in terms of the change in the length of wormlike micelles caused by the addition of SDS.

Cytochrome c folds through a smooth funnel.

A dominant feature of folding of cytochrome c is the presence of nonnative His-heme kinetic traps, which either pre-exist in the unfolded protein or are formed soon after initiation of folding. The kinetically trapped species can constitute the majority of folding species, and their breakdown limits the rate of folding to the native state. A temperature jump (T-jump) relaxation technique has been used to compare the unfolding/folding kinetics of yeast iso-2 cytochrome c and a genetically engineered double mutant that lacks His-heme kinetic traps, H33N,H39K iso-2. The results show that the thermodynamic properties of the transition states are very similar. A single relaxation time tau(obs) is observed for both proteins by absorbance changes at 287 nm, a measure of solvent exclusion from aromatic residues. At temperatures near Tm, the midpoint of the thermal unfolding transitions, tau(obs) is four to eight times faster for H33N,H39K iso-2 (tau(obs) approximately 4-10 ms) than for iso-2 (tau(obs) approximately 20-30 ms). T-jumps show that there are no kinetically unresolved (tau < 1-3 micros T-jump dead time) "burst" phases for either protein. Using a two-state model, the folding (k(f)) and unfolding (k(u)) rate constants and the thermodynamic activation parameters standard deltaGf, standard deltaGu, standard deltaHf, standard deltaHu, standard deltaSf, standard deltaSu are evaluated by fitting the data to a function describing the temperature dependence of the apparent rate constant k(obs) (= tau(obs)(-1)) = k(f) + k(u). The results show that there is a small activation enthalpy for folding, suggesting that the barrier to folding is largely entropic. In the "new view," a purely entropic kinetic barrier to folding is consistent with a smooth funnel folding landscape.

Critical evaluation of the computational methods used in the forced polymer translocation

In forced polymer translocation, the average translocation time tau scales with respect to pore force f and polymer length N as tau approximately f;{-1}N;{beta} . We demonstrate that an artifact in the Metropolis Monte Carlo method resulting in breakage of the force scaling with large f may be responsible for some of the controversies between different computationally obtained results and also between computational and experimental results. Using Langevin dynamics simulations we show that the scaling exponent beta<or=1+nu is not universal, but depends on f . Moreover, we show that forced translocation can be described by a relatively simple force balance argument and beta to arise solely from the initial polymer configuration.