Macroscopic Time Research Articles

Blood Products, Crystalloids, and Rapid Infusion: An Experimental Study With Magnesium

Calcium and magnesium are concentration-dependent pro- and anticoagulant cofactors, and magnesium behaves similarly to calcium in the presence of citrate. The authors hypothesized that magnesium can cause clot formation (primary objective) when mixed with coagulation factor-containing blood products diluted with different crystalloids in a rapid- infuser reservoir. A secondary objective was the observation of any infuser alarms and stops in the event of clotting. An experimental in vitro study with blood products, crystalloids, magnesium, and calcium in a rapid infuser with a reservoir using a closed-loop system. Anesthesia research laboratory at an urban academic tertiary medical center PARTICIPANTS: Not applicable. Exposure of fresh frozen plasma (FFP) and packed red blood cells alone (control) or in combination with either normal saline (NS), lactated Ringer's solution (LR), or Plasma-Lyte A (PL) to increasing concentrations of magnesium sulphate (MgSO4) up to 1 g. After each incremental MgSO4 change, the authors applied a specific pump-flow sequence in a closed-loop system with a rapid-infuser reservoir, and if no clot was observed, the authors incrementally added calcium chloride (CaCl2) up to 1 g. Observation of macroscopic clot and time to event, as well as occurrence and type of any pump alarms or stops. LR experiments resulted in clot observation in the reservoir by a dedicated observer after MgSO4 275 ± 206 mg (95% confidence interval [CI], 9-541). Adding MgSO4 1 g in the NS, PL, or the control experiments did not result in clot observation. Only when CaCl2 166.7 ± 51.64 mg (95% CI, 112.0-22.01) was added to the combination of blood products alone or mixed with NS and PL, clotting occurred. The mean FFP volume was 281 ± 48.6 mL (range, 204-340 mL) and was not different between groups (p=0.44). Pump alarms and stops were inconsistent. The addition of magnesium to a combination of LR with coagulation factor- containing blood products consistently resulted in a visible blood clot in the rapid-infuser reservoir in the authors' experimental setup. In addition to MgSO4 1 g in the control, NS, and PL experiments, CaCl2 is needed before a clot can be observed.

Intrinsic relaxation in a supercooled ZrTiNiCuBe glass forming liquid

We studied structural relaxation in the bulk metallic glass forming alloy ${\mathrm{Zr}}_{46.8}{\mathrm{Ti}}_{8.2}{\mathrm{Cu}}_{7.5}{\mathrm{Ni}}_{10}{\mathrm{Be}}_{27.5}$ on different timescales and length scales, with emphasis on the supercooled liquid state. Using x-ray photon correlation spectroscopy, we determined the microscopic structural relaxation time covering timescales of more than two decades in the supercooled liquid region, down to the subsecond regime. Upon heating across the glass transition, the intermediate scattering function changes from a compressed to a stretched decay, with a smooth transition in the stretching exponent and characteristic relaxation time. In the supercooled liquid state, the macroscopic and microscopic relaxation time and the melt viscosity all exhibit the same temperature dependence. This points to a relaxation mechanism via intrinsic structural relaxation of the majority component Zr, with its microscopic timescale controlling both the stress relaxation and viscous flow of the melt.

The Joy of Markov Models—Channel Gating and Transport Cycling Made Easy

ABSTRACT The behavior of ion channels and transporters is often modeled using discrete state continuous-time Markov models. Such models are helpful for the interpretation of experimental data and can guide the design of experiments by testing specific predictions. Here, we describe a computational tool that allows us to create Markov models of chosen complexity and to calculate the predictions on a macroscopic scale, as well on a single-molecule scale. The program calculates steady-state properties (current, state probabilities, and cycle frequencies), deterministic macroscopic and stochastic time courses, gating currents, dwell-time histograms, and power spectra of channels and transporters. In addition, a visual simulation mode allows us to follow the time-dependent stochastic behavior of a single channel or transporter. After a basic introduction into the concept of Markov models, real-life examples are discussed, including a model of a simple K+ channel, a voltage-gated sodium channel, a 3-state ligand-gated channel, and an electrogenic uniporter. In this manner, the article has a modular architecture, progressing from basic to more advanced topics. This illustrates how the MarkovEditor program can serve students to explore Markov models at a basic level but is also suited for research scientists to test and develop models on the mechanisms of protein function.

A User-Friendly Computational Tool for Markov Modelling Channel Gating and Transport Cycling

The behavior of ion channels and transporters is often modelled using discrete-state continuous-time Markov models. Such models are helpful for the interpretation of experimental data and can guide the design of experiments by testing specific predictions. Here, we present a computational tool that allows to create Markov models of chosen complexity, and to calculate their predictions on a macroscopic as well on a single-molecule scale. The program (https://github.com/mikpusch/MarkovEditor) calculates steady-state properties (current, state-probabilities, cycle frequencies), deterministic macroscopic and stochastic time courses, gating currents, dwell time histograms, and power spectra of channels and transporters. In addition, a visual simulation mode allows to follow the time-dependent stochastic behavior of a single channel or transporter. After a basic introduction into the concept of Markov models, real-life examples are discussed, including a model of a simple K+ channel, a voltage-gated sodium channel, a three-state ligand-gated channel, and an electrogenic uniporter. The MarkovEditor program can serve students to explore Markov models at a basic level, but is also suited for research scientists to test and develop models on the mechanisms of protein function.

Enhancement of the dielectric properties of low density polyethylene grad (LA071) via γ irradiation

In this work, we have investigated the dielectric properties of low density polyethylene (LDPE) grad (LA071) samples exposed to different γ irradiation doses ranging from 0 to 50 Gy. The distribution of the relaxation is demonstrated by Cole–Cole plots, depending on γ irradiation dose. Some parameters like optical dielectric constant, oscillating strength of the dipoles, macroscopic relaxation time and molecular relaxation time of LDPE samples have been estimated from Cole–Cole plots at room temperature. The γ irradiation enhances energy storage and energy loss of LDPE samples. It is concluded that γ irradiation can be considered as an alternative tool to improve the dielectric properties of polymer.

Anisotropy-driven reversal of magnetisation in Blume–Capel ferromagnet: a Monte Carlo study

The two dimensional Spin-1 Blume-Capel ferromagnet is studied by Monte Carlo simulation with Metropolis algorithm. Starting from initial ordered spin configuration the reversal of magnetisation is investigated in presence of a magnetic field ($h$) applied in the opposite direction. The variations of the reversal time with the strength of single site anisotropy are investigated in details. The exponential dependence was observed. The systematic variations of the mean reversal time with positive and negative anisotropy was found. The mean macroscopic reversal time was observed to be linearly dependent on a suitably defined microscopic reversal time. The saturated magnetisation $M_f$ after the reversal was noticed to be dependent of the strength of anisotropy $D$. An interesting scaling relation was obtained, $|M_f| \sim |h|^{\beta}f(D|h|^{-\alpha})$ with the scaling function of the form $f(x)= \frac{1}{1+e^{(x-a)/b}}$. The temporal evolution of density of $S_i^z=0$ (surrounded by all $S_i^z=+1$) is observed to be exponentially decaying. The growth of mean density of $S_i^z=-1$ has been fitted in a function $\rho_{-1}(t) \sim \frac{1}{a+e^{(t_c-t)/c}}$. The characteristic time shows $t_c \sim e^{-rD}$ and a crossover in the rate of exponential falling is observed at $D=1.5$. The metastable volume fraction has been found to obey the Avrami's law.

Nanosecond protein dynamics in a red/green cyanobacteriochrome revealed by transient IR spectroscopy.

Over the last decades, photoreceptive proteins were extensively studied with biophysical methods to gain a fundamental understanding of their working mechanisms and further guide the development of optogenetic tools. Time-resolved infrared (IR) spectroscopy is one of the key methods to access their functional non-equilibrium processes with high temporal resolution but has the major drawback that experimental data are usually highly complex. Linking the spectral response to specific molecular events is a major obstacle. Here, we investigate a cyanobacteriochrome photoreceptor with a combined approach of transient absorption spectroscopy in the visible and IR spectral regions. We obtain kinetic information in both spectral regions by analysis with two different fitting methods: global multiexponential fitting and lifetime analysis. We investigate the ground state dynamics that follow photoexcitation in both directions of the bi-stable photocycle (Pr* and Pg*) in the nanosecond and microsecond time regimes. We find two ground state intermediates associated with the decay of Pr* and four with Pg* and report the macroscopic time constants of their interconversions. One of these processes is assigned to a structural change in the protein backbone.

A Step-by-Step Process-Induced Unidirectional Oriented Water Wire in the Nanotube.

The orientation of water molecules is a key requirement for the fast transport of water in nanotubes. It has been accepted that the flip of the water chain follows a concerted mechanism, which has led to the view that bidirectional water flux in nanotubes can be transformed into unidirectional transport when the orientation of water molecules is maintained in long nanotubes under the external field. In this Letter, on the basis of molecular dynamics simulations and first-principles calculations, we confirmed that the flip of the water chain is a step-by-step process, which is different from the perceived concerted mechanism. Further analysis indicated that without an external field, it needed more than 20 water molecules to maintain the unidirectional single-file water flow in a carbon nanotube at a duration time of seconds. Considering that the thickness of the cell membrane (normally 5-10 nm) is larger than the length threshold of the unidirectional water wire, this study suggested that it may not require the external field to maintain the unidirectional flow in the water channel at the macroscopic time scale.

Prediction of Kinetically Stable Nanotheranostic Superstructures: Integral of First-Passage Times from Constrained Simulations.

The kinetics of forming multifunctional nanostructures, such as nanotheranostic superstructures, is often highly protracted, involving macroscopic time scales and resulting in nanostructures that correspond to kinetically stable states rather than thermodynamic equilibrium. Predicting such kinetically stable nanostructures becomes a great challenge due to the widely different, relevant time scales that are implicated in the formation kinetics of nano-objects. We develop a methodology, integral of first-passage times from constrained simulations (IFS), to predict kinetically stable, planet-satellite nanotheranostic superstructures. The simulation results are consistent with our experimental observations. The developed methodology enables the exploration of time scales from molecular vibrations of 10-3 ns toward macroscopic scales, 1010 ns, which permits the rational design and prediction of kinetically stable nanotheranostic superstructures for applications in nanomedicine.

Kinetic limit for a chain of harmonic oscillators with a point Langevin thermostat

We consider an infinite chain of coupled harmonic oscillators whose Hamiltonian dynamics is perturbed by a random exchange of momentum between particles such that total energy and momentum are conserved, modeling collision between atoms. This random exchange is rarefied in the limit, that corresponds to the hypothesis that in the macroscopic unit time only a finite number of collisions takes place (the Boltzmann-Grad limit). Furthermore, the system is in contact with a Langevin thermostat at temperature T through a single particle. We prove that, after the hyperbolic space-time rescaling, the Wigner distribution, describing the energy density of phonons in space-frequency domain, converges to a positive energy density function W(t,y,k) that evolves according to a linear kinetic equation, with the interface condition at y=0 that corresponds to reflection, transmission and absorption of phonons caused by the presence of the thermostat. The paper extends the results of [15], where a harmonic chain (with no inter-particle scattering) in contact with a Langevin thermostat has been considered.

The Obstruction Effect of Ni Layer on the Interdiffusion of Cu Substrate and Sn Solder: A Theoretical Investigation

The protective effect of a Ni layer on Cu-Sn solder joints was investigated from the perspective of interface diffusion. The results indicate that temperature is the primary external factor affecting interfacial diffusion, and the effect of external load also has an influence. Atom diffusion is promoted by the increasing temperature and applied compressive load perpendicular to the interface. In contrast, the tensile load perpendicular to the interface inhibited the diffusion behavior. Ni atoms at both the Ni/Cu and Ni/Sn interfaces act as the main diffusion factor and play a vital role in the growth and evolution of the diffusion layer. Because of the high stability of the Ni lattice and the large radii of Cu and Sn atoms, it is difficult for Cu and Sn atoms to migrate to the Ni atoms, which effectively delays the contact and reaction between Cu and Sn. To reveal the micro-mechanism of the diffusion, the diffusion coefficient and activation energy were studied. Ni atoms need more energy than Cu and Sn atoms to drive the diffusion, which delays the consumption of Ni and helps to maintain the Ni layer. The single vacancy formation energy of the Ni lattice is the largest, which means that it is difficult for Cu and Sn atoms to migrate into the lattice. By comparing the atomic diffusion rate, the final formation of Cu-Sn intermetallic compounds in the Ni layer on the side of tin-based solder was predicted at a macroscopic time scale. Using density functional calculation, the slight lattice distortion of the interfaces was measured. The analysis of charge transfer and electronic properties show that a strong electron transfer and energy level overlap occurs between the Ni and Cu atoms, implying that the Ni/Cu interface has a more considerable electronic thermal conductivity and should be more sensitive to the increasing temperature.

How to Avoid Absolute Determinismin Two Boundary Quantum Dynamics

Arguments for a two boundary theory are briefly outlined. Plausible concepts of how in such a theory an approximate causal macroscopic theory can emerge are presented. A problem with simple implementations of the two boundary theory is that effective or real willful decisions can not be added as there is no consecutive macroscopic time ordering. In this letter, we present a somewhat drastic but beautiful way to avoid it.

Asymptotic analysis for a homogeneous bubbling regime Vlasov–Fokker–Planck/Navier–Stokes system

The evolution of a cloud of particles in a compressible fluid can be modeled with a Vlasov–Fokker–Planck equation for the distribution function of the particles coupled with Navier–Stokes or Euler equations for the density and velocity of the fluid. Formal calculations have established the convergence of solution to the mesoscopic model to solutions to the macroscopic Navier–Stokes or Euler model coupled with a Smoluchowski equation as the ratio of the settling time for the microscopic velocity fluctuation of the particles to the characteristic macroscopic time scale goes to zero. This paper provides a rigorous asymptotic analysis for a homogeneous mesoscopic fluid–particle interaction model for particles dispersed in a compressible fluid is provided for the bubbling regime. A relative entropy inequality for a mixed hyperbolic/parabolic system of equations is employed.

Influence of Network Topology on the Viscoelastic Properties of Dynamically Crosslinked Hydrogels.

Biological materials combine stress relaxation and self-healing with non-linear stress-strain responses. These characteristic features are a direct result of hierarchical self-assembly, which often results in fiber-like architectures. Even though structural knowledge is rapidly increasing, it has remained a challenge to establish relationships between microscopic and macroscopic structure and function. Here, we focus on understanding how network topology determines the viscoelastic properties, i.e., stress relaxation, of biomimetic hydrogels. We have dynamically crosslinked two different synthetic polymers with one and the same crosslink. The first polymer, a polyisocyanopeptide (PIC), self-assembles into semi-flexible, fiber-like bundles, and thus displays stress-stiffening, similar to many biopolymer networks. The second polymer, 4-arm poly(ethylene glycol) (starPEG), serves as a reference network with well-characterized structural and viscoelastic properties. Using one and the same coiled coil crosslink allows us to decouple the effects of crosslink kinetics and network topology on the stress relaxation behavior of the resulting hydrogel networks. We show that the fiber-containing PIC network displays a relaxation time approximately two orders of magnitude slower than the starPEG network. This reveals that crosslink kinetics is not the only determinant for stress relaxation. Instead, we propose that the different network topologies determine the ability of elastically active network chains to relax stress. In the starPEG network, each elastically active chain contains exactly one crosslink. In the absence of entanglements, crosslink dissociation thus relaxes the entire chain. In contrast, each polymer is crosslinked to the fiber bundle in multiple positions in the PIC hydrogel. The dissociation of a single crosslink is thus not sufficient for chain relaxation. This suggests that tuning the number of crosslinks per elastically active chain in combination with crosslink kinetics is a powerful design principle for tuning stress relaxation in polymeric materials. The presence of a higher number of crosslinks per elastically active chain thus yields materials with a slow macroscopic relaxation time but fast dynamics at the microscopic level. Using this principle for the design of synthetic cell culture matrices will yield materials with excellent long-term stability combined with the ability to locally reorganize, thus facilitating cell motility, spreading, and growth.

Microscopic model for switching kinetics in organic ferroelectrics following the Merz law

From an application perspective, one of the most important parameters of a ferroelectric is its switching time, and understanding its limiting factors is key to improve device performance. While there is a variety of competing models for switching kinetics in realistic (disordered) ferroelectrics, they are often merely descriptive and provide little insight into the underlying microscopic mechanisms. This holds in particular for the classical Merz law, which describes the commonly observed exponential field dependence of the switching time. Here, we investigate the switching kinetics in the archetypical molecular ferroelectric trialkylbenzene-1,3,5- tricarboxamide using an electrostatic kinetic Monte Carlo model. The simulated field dependence follows the Merz law, which shows that a simple system of interacting dipoles is sufficient to obtain this behavior, even without explicitly considering domain walls or defects that are commonly thought to be involved in the emergence of the Merz law. Through a detailed analysis of the nucleation process, we can relate the macroscopic switching time to the microscopic nucleation energy barrier, which in turn is related to a field-dependent nucleus size. Finally, we use the acquired insight into the nucleation process to derive the Merz law from the theory of thermally activated nucleation-limited switching. This analytical model provides a physically transparent description of the switching kinetics in both experiments and simulations.

High Frequency Limit for a Chain of Harmonic Oscillators with a Point Langevin Thermostat

We consider an infinite chain of coupled harmonic oscillators with a Langevin thermostat attached at the origin and energy, momentum and volume conserving noise that models the collisions between atoms. The noise is rarefied in the limit, {that corresponds to the hypothesis} that in the macroscopic unit time only a finite number of collisions takes place (Boltzmann-Grad limit). We prove that, after the hyperbolic space-time rescaling, the Wigner distribution, describing the energy density of phonons in space-frequency domain, converges to a positive energy density function $W(t, y, k)$ that evolves according to a linear kinetic equation, with the interface condition at $y=0$ that corresponds to reflection, transmission and absorption of phonons. The paper extends the results of [3], where a thermostatted harmonic chain (with no inter-particle scattering) has been considered.

Thickness-dependent electron momentum relaxation times in iron films

Terahertz time-domain conductivity measurements in 2–100 nm thick iron films resolve the femtosecond time delay between the applied electric fields and the resulting currents. This current response time decreases from 29 fs for the thickest films to 7 fs for the thinnest films. The macroscopic response time is not strictly proportional to the conductivity. This excludes the existence of a single relaxation time universal for all conduction electrons. We must assume a distribution of microscopic momentum relaxation times. The macroscopic response time depends on the average and variation of this distribution; the observed deviation between the response time and conductivity scaling corresponds to the scaling of the variation. The variation of microscopic relaxation times depends on the film thickness because electrons with different relaxation times are affected differently by the confinement since they have different mean free paths.

Effect of microscopic pausing time distributions on the dynamical limit shapes for random Young diagrams

The irreducible decomposition of successive restriction and induction of irreducible representations of a symmetric group gives rise to a Markov chain on Young diagrams keeping the Plancherel measure invariant. Starting from this Res-Ind chain, we introduce a not necessarily Markovian continuous time random walk on Young diagrams by considering a general pausing time distribution between jumps according to the transition probability of the Res-Ind chain. We show that, under appropriate assumptions for the pausing time distribution, a diffusive scaling limit brings us concentration at a certain limit shape depending on macroscopic time which leads to a similar consequence to the exponentially distributed case studied in our earlier work. The time evolution of the limit shape is well described by using free probability theory. On the other hand, we illustrate an anomalous phenomenon observed with a pausing time obeying a one-sided stable distribution, heavy-tailed without the mean, in which a nontrivial behavior appears under a non-diffusive regime of the scaling limit.

Area Occupancy-Based Adaptive Density Estimation for Mixed Road Traffic

Managing congestion in mixed traffic conditions, characterized by heterogeneous and lane-less traffic, is a challenging task. Traditionally density, defined as the number of vehicles in a road stretch, is used to quantify congestion. However, direct measurement of density is difficult and hence is usually estimated from other variables. In this paper, a relationship is derived between traffic density and area occupancy, a variable that can incorporate heterogeneity and lane-less movement. Using the derived density-area occupancy relation, a non-continuum macroscopic single state linear time varying model was developed. Estimation of density was done by using the Kalman filtering technique and corroborated with simulated density. The need for dynamic estimation is motivated by evaluating the performance of two static estimation schemes in the presence of uncertainties. Performance was tested for different traffic scenarios such as congestion and non-recurrent traffic incidents. Further, to improve the estimation accuracy in scenarios involving transitions in traffic conditions, an adaptive estimator was developed. It was found that the adaptive estimator provided the best estimation accuracy.

Aging of living polymer networks: a model with patchy particles.

Microrheology experiments show that viscoelastic media composed by wormlike micellar networks display complex relaxations lasting seconds even at the scale of micrometers. By mapping a model of patchy colloids with suitable mesoscopic elementary motifs to a system of worm-like micelles, we are able to simulate its relaxation dynamics, upon a thermal quench, spanning many decades, from microseconds up to tens of seconds. After mapping the model to real units and to experimental scission energies, we show that the relaxation process develops through a sequence of non-local and energetically challenging arrangements. These adjustments remove undesired structures formed as a temporary energetic solution for stabilizing the thermodynamically unstable free caps of the network. We claim that the observed scale-free nature of this stagnant process may complicate the correct quantification of experimentally relevant time scales as the Weissenberg number.