Length Fluctuations Research Articles

Passive Optical Phase Stabilization on a Ring Fiber Network

Optical frequency transfer provides the means for high-fidelity frequency transfer across thousands of kilometers. A critical step in the further developing optical frequency transfer is its capability to transfer a high spectral purity feature from ultrastable lasers or optical clocks to any remote locations and, at the same time, its adaptability to incorporate the optical frequency transfer technique into any existing communication networks with different topologies. Here we for the first time report a technique that delivers optical-frequency signals to multiple independent remote hubs along a ring optical-fiber network with passive phase stabilization. The technique automatically corrects optical-fiber length fluctuations of arbitrary hubs along the loop by mixing and shifting optical signals. Without the help of an active phase tracker and a compensator, it could significantly mitigate some technical problems such as the limited compensation speed and phase recovery time, the phase jitter contamination caused by the servo bump in conventional phase noise cancellation. Moreover, by transmitting optical signals along both directions using the same optical source, it can improve the signal-to-noise ratio at each hub. This technique maintains the same delay-limited phase noise correction capability as in conventional techniques and, furthermore, improves the phase jitter by a factor of 3, opening a way to a broad distribution of an ultrastable frequency reference with high spectral purity and enabling a wide range of applications beyond metrology over a ring fiber network with the naturally impressive reliability and scalability.

Molecular Simulation of Tracer Diffusion and Self-Diffusion in Entangled Polymers

The dependence of tracer diffusivity ($D_\infty \sim N^{-x_\infty}$), where probe chains move in an environment of infinitely long matrix chains, and self-diffusion coefficient ($D_s \sim N^{-x_s}$), where probe and matrix chains are identical, on the molecular weight of the probe chain $N$ are investigated using three different molecular simulation methods, viz. molecular dynamics, the bond-fluctuation model (BFM) and the slip-spring (SS) model. Experiments indicate $x_s \approx 2.4 \pm 0.2$ over a wide intermediate molecular weight range, and $x_{\infty} \approx 2.0 \pm 0.1$, although the lower molecular weight limit for observing pure reptation in short probes is unclear. These results are partly inconsistent with some tube theories, and older, somewhat underpowered, molecular simulations. Estimating $x_{\infty}$ using brute-force BFM simulations is difficult because it involves large simulation boxes and long trajectories. To overcome this obstacle, an efficient method to estimate $D_\infty$ in which ends of matrix chains are immobilized, is presented and validated. BFM simulations carried out on systems with different probe and matrix chain lengths reveal that $x_s = 2.43 \pm 0.07$, and $x_\infty = 2.24 \pm 0.03$. Over a wider range of molecular weights, probe diffusivities obtained from the more coarse-grained SS model, calibrated with bead-spring molecular dynamics, reveal $x_s > x_\infty$, and $x_\infty > 2$ for weakly and intermediately entangled chains. Tracer diffusivities obtained by artificially switching off constraint release in the SS simulations essentially overlap with probe diffusivities, strongly suggesting that constraint release is primarily responsible for the difference between $x_s$ and $x_\infty$. Nevertheless, both BFM and SS simulations indicate that below a certain chain length threshold, contributions of contour length fluctuations to $D_s$ and $D_\infty$ are important, and result in deviations from pure reptation scaling.

Quantum corrections to finite radius holography and holographic entanglement entropy

We calculate quantum corrections to holographic entanglement entropy in the proposed duality between Toverline{T} -deformed holographic 2D CFTs and gravity in AdS3 with a finite cutoff. We first establish the dictionary between the two theories by mapping the flow equation of the deformed CFT to the bulk Wheeler-DeWitt equation. The latter reduces to an ordinary differential equation for the sphere partition function, which we solve to find the entanglement entropy for an entangling surface consisting of two antipodal points on a sphere. The entanglement entropy in the inverse central charge expansion yields the expectation value of the bulk length operator plus the entropy of length fluctuations, in accordance with the Ryu-Takayanagi formula and its generalization due to Faulkner, Lewkowycz, and Maldacena. Special attention is paid to the conformal mode problem and its resolution by a choice of contour for the gravitational path integral.

Microstructural characterization of a star-linear polymer blend under shear flow by using rheo-SANS

We present an investigation into the dynamic relaxation mechanisms of a polybutadiene blend composed of a four-arm star (10 wt. %) and a linear polymer matrix in the presence of an applied shear flow. Our focus was the response of the star polymer, which cannot be unambiguously assessed via linear viscoelastic measurements since the signature of the star polymer can barely be detected due to the dominant contribution of the linear matrix. By utilizing small-angle neutron scattering (SANS) coupled with a Couette shear device and a deuterated matrix polymer, we investigated the dynamics of the minority star component of the blend. Our results confirm that the stars deform anisotropically with increasing shear rate. We have compared the SANS data with predictions from the well-established scattering adaptation of the state-of-the-art tube model for entangled linear polymer melts undergoing shear, i.e., Graham, Likhtman, Milner, and McLeish (GLaMM) approach, appropriately modified following earlier studies in order to apply to the star. This modified model, GLaMM-R, includes the physics necessary to understand stress relaxation in both the linear and nonlinear flow regimes, i.e., contour length fluctuations, constraint release, convective constraint release, and chain retraction. The full scattering signal is due to the minority star component and, although the contribution of the linear chains is hidden from the neutron scattering, they still influence the star polymer molecular dynamics, with the applied shear rate ranging from approximately 8 to 24 s−1, below the inverse relaxation time of the linear component. This study provides another confirmation that the combination of rheology and neutron scattering is an indispensable tool for investigating the nonlinear dynamics of complex polymeric systems.

Manufacturing Tolerance Analysis of Deep-Ridged 90° Hybrid Based on InP 4 × 4 MMI

An optical 90° hybrid based on an InGaAsP/InP deep-ridged 4 × 4 multimode interference (MMI) coupler is proposed and fabricated. Manufacturing tolerances on structural parameters of the 90° hybrid including multimode waveguide width and length, waveguide core thickness, and refractive index are analyzed over the whole C-band using a three-dimensional beam propagation method (3D BPM). The simulation results show that the 90° hybrid is insensitive to the interference length with a deviation of 10 μm. However, the width fluctuations produce far stronger performance variations than length fluctuations. The common-mode rejection ratios (CMRRs) are always above 40 dB, and the phase error (PE) is always below 2.5° with the fluctuations of the refractive index by 0.01 and the thickness by 0.1 μm of the core layer. The fabricated device exhibited a quadrature phase response with a high common-mode rejection ratio of more than 25 dB and a small phase error of less than 5° from 1545 nm to 1560 nm.

Effects of Day Length and Air Temperature Fluctuation on the Occurrence of Leaf Browning in Sesame Seedlings Cultured in a Plant Factory under Artificial Light

Effects of Day Length and Air Temperature Fluctuation on the Occurrence of Leaf Browning in Sesame Seedlings Cultured in a Plant Factory under Artificial Light

Slip-spring simulations of different constraint release environments for linear polymer chains.

The constraint release (CR) mechanism has important effects on polymer relaxation and the chains will show different relaxation behaviour in conditions of monodisperse, bidisperse and other topological environments. By comparing relaxation data of linear polyisoprene (PI) chains dissolved in very long matrix and monodisperse melts, Matsumiya et al. showed that CR mechanism accelerates both dielectric and viscoelastic relaxation (Matsumiya et al. 2013 Macromolecules 46, 6067. (doi:10.1021/ma400606n)). In this work, the experimental data reported by Matsumiya et al. are reproduced using the single slip-spring (SSp) model and the CR accelerating effects on both dielectric and viscoelastic relaxation are validated by simulations. This effect on viscoelastic relaxation is more pronounced. The coincidence for end-to-end relaxation and the viscoelastic relaxation has also been checked using probe version SSp model. A variant of SSp with each entanglement assigning a characteristic lifetime is also proposed to simulate various CR environment flexibly. Using this lifetime version SSp model, the correct relaxation function can be obtained with equal numbers of entanglement destructions by CR and reptation/contour length fluctuation (CLF) for monodisperse melts. Good agreement with published experiment data is also obtained for bidisperse melts, which validates the ability to correctly describe the CR environment of the lifetime version model.

Mechanisms of chromosome biorientation and bipolar spindle assembly analyzed by computational modeling.

The essential functions required for mitotic spindle assembly and chromosome biorientation and segregation are not fully understood, despite extensive study. To illuminate the combinations of ingredients most important to align and segregate chromosomes and simultaneously assemble a bipolar spindle, we developed a computational model of fission-yeast mitosis. Robust chromosome biorientation requires progressive restriction of attachment geometry, destabilization of misaligned attachments, and attachment force dependence. Large spindle length fluctuations can occur when the kinetochore-microtubule attachment lifetime is long. The primary spindle force generators are kinesin-5 motors and crosslinkers in early mitosis, while interkinetochore stretch becomes important after biorientation. The same mechanisms that contribute to persistent biorientation lead to segregation of chromosomes to the poles after anaphase onset. This model therefore provides a framework to interrogate key requirements for robust chromosome biorientation, spindle length regulation, and force generation in the spindle.

Demonstration of a length control system for ALPS II with a high finesse 9.2 m cavity

Light-shining-through-a-wall experiments represent a new experimental approach in the search for undiscovered elementary particles not accessible with accelerator based experiments. The next generation of these experiments, such as ALPS II, require high finesse, long baseline optical cavities with fast length control. In this paper we report on a length stabilization control loop used to keep a 9.2 m cavity resonant. The finesse of this cavity was measured to be 101,300 ±500 for 1064 nm light. Fluctuations in the differential cavity length as seen with 1064 nm and 532 nm light were measured. Such fluctuations are of high relevance, since 532 nm light will be used to sense the length of the ALPS II regeneration cavity. Limiting noise sources and different control strategies are discussed, in order to fulfill the length stability requirements for ALPS II.

Spectral Analysis of a Fast Biomolecular Transition in Magnetic Tweezers Measurements

Dynamic structural changes in biomolecules such as proteins and DNA are crucial for their correct function. These processes often involve transient intermediate states that occur on the (sub-)millisecond timescale. The investigation of such fast dynamics is experimentally challenging in particular in single molecule measurements. Here we investigate the limited branch migration of a Holliday junction within the torsionally constraint DNA of a magnetic tweezers setup. We gain access to the force-dependent stepping dynamics of the junction in the xx µs to x ms range using power spectral density analysis of the DNA length fluctuations. We expect that this technique can be extended to other biological systems where the individual structural transitions are too short and fast to be resolved in real-time. In our experiments the DNA length is obtained from the position of an attached magnetic particle. Our spectral analysis also reveals the rotational fluctuations of the magnetic particle due to an imperfect pinning in the magnetic field and its influence on the spatiotemporal resolution of magnetic tweezers.

Variation of Energy Transfer Rates across Protein-Water Contacts with Equilibrium Structural Fluctuations of a Homodimeric Hemoglobin.

Molecular dynamics simulations of the homodimeric hemoglobin from Scapharca inaequivalvis (HbI) have been carried out to examine relations between rates of vibrational energy transfer across nonbonded contacts and equilibrium structural fluctuations, with emphasis on protein-water contacts. The scaling of rates of energy transfer with equilibrium fluctuations of the contact length is found to hold up well for contacts between residues and hemes at the interface and the cluster of 17 interface water molecules in the unliganded state of HbI, as well as for the liganded state, for which the cluster contains on average 11 water molecules. In both states, the rate of energy transfer is also found to satisfy a diffusion relation. Within each globule, the scaling for polar contacts is similar to that found in an earlier analysis of myoglobin. Entropy associated with dynamics of polar contacts within each globule and with contacts between the hemes and water cluster is found to increase upon ligation. Energy exchange networks (EENs) for liganded and unliganded states obtained from the simulations are also presented and discussed. Energy transport networks through which nonbonded contacts transport energy in HbI, referred to as nonbonded networks (NBNs), are determined from the EENs and compared for the two states.

GIGANTEA Shapes the Photoperiodic Rhythms of Thermomorphogenic Growth in Arabidopsis

Plants maintain their internal temperature under environments with fluctuating temperatures by adjusting their morphology and architecture, an adaptive process termed thermomorphogenesis. Notably, the rhythmic patterns of plant thermomorphogenesis are governed by day-length information. However, it remains elusive how thermomorphogenic rhythms are regulated by photoperiod. Here, we show that warm temperatures enhance the accumulation of the chaperone GIGANTEA (GI), which thermostabilizes the DELLA protein, REPRESSOR OF ga1-3 (RGA), under long days, thereby attenuating PHYTOCHROME INTERACTING FACTOR 4 (PIF4)-mediated thermomorphogenesis. In contrast, under short days, when GI accumulation is reduced, RGA is readily degraded through the gibberellic acid-mediated ubiquitination-proteasome pathway, promoting thermomorphogenic growth. These data indicate that the GI–RGA–PIF4 signaling module enables plant thermomorphogenic responses to occur in a day-length-dependent manner. We propose that the GI-mediated integration of photoperiodic and temperature information shapes thermomorphogenic rhythms, which enable plants to adapt to diel fluctuations in day length and temperature during seasonal transitions.

Modulating the Stiffness of the Myosin VI Single α-Helical Domain

Highly charged, single α-helical (SAH) domains contain a high percentage of Arg, Lys, and Glu residues. Their dynamic salt bridge pairing creates the exceptional stiffness of these helical rods, with a persistence length of more than 200 Å for the myosin VI SAH domain. With the aim of modulating the stiffness of the helical structure, we investigated the effect, using NMR spectroscopy, of substituting key charged Arg, Lys, Glu, and Asp residues by Gly or His. Results indicate that such mutations result in the transient breaking of the helix at the site of mutation but with noticeable impact on amide hydrogen exchange rates extending as far as ±2 helical turns, pointing to a substantial degree of cooperativity in SAH stability. Whereas a single Gly substitution caused transient breaks ∼20% of the time, two consecutive Gly substitutions break the helix ∼65% of the time. NMR relaxation measurements indicate that the exchange rate between an intact and a broken helix is fast (>300,000 s−1) and that for the wild-type sequence, the finite persistence length is dominated by thermal fluctuations of backbone torsion angles and H-bond lengths, not by transient helix breaking. The double mutation D27H/E28H causes a pH-dependent fraction of helix disruption, in which the helix breakage increases from 26% at pH 7.5 to 53% at pH 5.5. The ability to modulate helical integrity by pH may enable incorporation of externally tunable dynamic components in the design of molecular machines.

An Adaptive Active Queue Management Based on Model Predictive Control

In recent years, active queue management (AQM) has gained more and more attention as an important part of network congestion control. Although there are many AQM algorithms, these algorithms show weaknesses to detect and control congestion due to the complexity and dynamics of the networks. Hence, this paper proposes a new AQM algorithm based on model predictive control (MPC) theory which has been widely applied in nonlinear and time-delay systems. In order to adjust the parameters of the MPC-based AQM algorithm adaptively according to network scenario variations, the adaptive mechanism is introduced into the new algorithm, named PHAQM, by using the Hebb learning rules from the neural network control theory. The simulation results show that the algorithm is effective in avoiding network congestion. Compared to the traditional AQM schemes, such as PI, REM, and GPC algorithm, the PHAQM has a faster convergence rate and smaller queue length fluctuations and outperforms especially under dynamically changing network situations.

Simulation of the dynamics of the Hansbreen tidal glacier (Svalbard) based on the stochastic model

The dynamics of the Hansbreen tidal glacier (Svalbard) is manifested at different time scales. In addition to the long-term trend, there are noticeable inter-annual fluctuations. And the last ones are precisely the subject of this work. Based on general conclusions of the theory of temporal dynamics of the massive inertial objects, the observed inter-annual changes in the length of the glacier can be explained as a result of the accumulation of anomalies of the heat fluxes and water flows. In spite the fact that the initial model of glacier dynamics is deterministically based on the physical law of conservation of ice mass (the so-called the «minimal model» was used), the model of length change is interpreted as stochastic. From this standpoint, it is the Langevin equation, which includes the effect of random temperature anomalies that can be interpreted as a white noise. From a mathematical point of view, this process is analogous to Brownian motion, i.e. the length of the Hansbreen glacier randomly fluctuates in the vicinity of its stable equilibrium position. Based on the Langevin equation, we passed to the Fokker–Planck equation, the solution of which allowed us to obtain the distribution function of the probabilities of interannual fluctuations of glacier length, which is close to the normal law. It was shown that the possible range of the variability covers the observed interval of the length fluctuations. The pdf is close to normal distribution.

Quantitative investigation on morphology and intracellular transport dynamics of migrating cells.

In this paper, we present a phase correlation imaging technique employing quantitative phase microscopy to study the migration properties of living cells. The phase correlation map relies on time-lapse quantitative phase stacks, which are achieved by single-shot quantitative phase imaging based on the transport of intensity equation. The phase correlation imaging maps can reveal tiny fluctuations in cellular optical path length and dynamic subdomains in living cells. We find that the morphology dynamics and intracellular mass transport rates are significantly different as cells exhibit different levels of migratory capabilities.

Bubbling/slugging flow behavior in a cylindrical fluidized bed: ECT measurements and two-fluid simulations

While the Eulerian two-fluid models (TFM) are now reasonably well established to predict the “time-averaged” flow behavior of gas–solid flow in fluidized beds, quantitative predictions of inherently unsteady local solid-phase distribution and bubbling/slugging behavior using the TFM continues to be a challenge. In the present work, we have investigated time-evolution of solid volume fraction (αs) distribution and bubbling/slugging behavior in a laboratory-scale fluidized bed using the Electrical Capacitance Tomography (ECT) measurements and TFM simulations. The ECT was used to measure temporally- and spatially-resolved local αs distribution and these measurements were used further to characterize the bubble chord length fluctuations, bubbling frequency and bubble size distributions. The effects of different models used to calculate gas-solid momentum exchange on fluidization behavior were investigated. The results showed that the predicted time-averaged αs distribution differed marginally and were in a satisfactory agreement with the corresponding measurements. However, the predicted bubbling frequency and bubble size distribution, in particular, the formation of large bubbles/slugs predicted using different drag models were considerably different and were not even in a qualitative agreement with the measurements. The modification proposed to the drag model in the present work led to an improvement in the predicted bubbling behavior and showed a qualitative agreement with the measurements. Further, simulations performed to investigate the effect of solid-phase frictional viscosity (μs,fr) showed that an increase in the solid-phase frictional pressure leads to an increase in μs,fr. Such an increase in μs,fr leads to compaction of the solid phase and to the formation of large bubbles/slugs, in line with what is observed experimentally. The predicted bubbling frequency and bubble size distribution were in a quantitative agreement with those measured using the ECT for different gas velocities.

Supramolecular Mimic for Bottlebrush Polymers in Bulk.

A series of poly(tetrahydrofuran)s with molecular weights above entanglement molecular weight Me were synthesized, and one of their end-groups was functionalized with a supramolecular entity so that the corresponding polymers form a brushlike structure suitable for comparison with conventional irreversible bottlebrush polymers. To compare their relaxation mechanisms, linear rheology was employed and showed that a hierarchical relaxation, which is usually observed in bottlebrush polymers, occurs in these materials, too. The polymer chain segments close to the supramolecular backbone are highly immobilized due to strong association in the center of polymer brush and cannot relax via reptation mechanism, which is mainly responsible for linear entangled polymer relaxations. Therefore, disentanglement can take much longer through contour length fluctuations and arm retraction processes similar to covalent bottlebrush polymers and combs. The relaxed ends of polymers then act as solvent to let the remaining segments of the polymeric brush undergo Rouse-like motions (constraint release Rouse). At longer times, additional plateau appears, which can be attributed to the relaxation of the entire supramolecular bottlebrush polymer via hopping or reptative motions. With an increase of temperature, viscoelastic solid behavior turns into viscoelastic liquid due to reversible depolymerization of the supramolecular backbone of the bottlebrush polymer. The elastic modulus (G′ in the order of kPa) was much less than the values found for the entanglement plateau modulus of linear poly(tetrahydrofuran) (in order of MPa). This low modulus value, which exists up to very low frequencies (high temperatures), makes them a good candidate for supersoft elastomers.

Dynamics of Water Molecules and Ions in Concentrated Lithium Chloride Solutions Probed with Ultrafast 2D IR Spectroscopy.

Water and ion dynamics in concentrated LiCl solutions were studied using ultrafast 2D IR spectroscopy with the methyl thiocyanate (MeSCN) CN stretch as the vibrational probe. The IR absorption spectrum of MeSCN has two peaks, one peak for water associated with the nitrogen lone pair of MeSCN (W) and the other peak corresponding to Li+ associated with the lone pair (L). To extract the spectral diffusion (structural dynamics) of W and L species, we developed a method that isolates the peak of interest by subtracting the 2D Gaussian proxies of multiple interfering peaks. Center line slope data (normalized frequency-frequency correlation function) for 2D bands from the W and L are fit with triexponential functions. The fastest component (1.1-1.6 ps) is assigned to local hydrogen bond length fluctuations. The intermediate timescale (∼4.0 ps) corresponds to the hydrogen bond network rearrangement. The slowest component decays in ∼40 ps and corresponds to ion pair and ion cluster dynamics. The very similar W and L spectral diffusion indicates that the motions of the water and ions are strongly coupled. Orientational relaxations of the W and L species were extracted using a new method to eliminate the effects of overlapping peaks. The results show that MeSCN bound to water undergoes orientational relaxation significantly faster than MeSCN bound to Li+. The orientational and spectral diffusion results are compared. A Stark coupling model is used to extract the root mean square average electric field caused by the ion clouds along the CN moiety as a function of concentration.

Evaluation of Fiber Noise Induced in Ultrastable Environments

Phase noise induced by environmental disturbance was greatly reduced when the optical fiber was installed in an ultrastable environment. In this paper, the optical fiber length was 10 m, and the reduction in the phase noise power spectral density was approximately 70 and 30 dB at Fourier frequencies of 10 mHz and 10 Hz, respectively. To evaluate faint fiber noise, we developed a modified Mach–Zehnder heterodyne interferometer with reduced optical path length fluctuation. The Allan deviation calculated from the phase noise was $7 \times 10^{-20}$ at a 1-s averaging time and reached $2 \times 10^{-21}$ at a 10 000-s averaging time (measurement bandwidth: 500 Hz). In addition, we revealed the frequency bands in which fiber noise is reduced by selectively removing the environmental stabilization measures of evacuation, vibration isolation, acoustic shielding, and temperature stabilization from an ultrastable environment.