Random field sampling for a simplified model of melt-blowing considering turbulent velocity fluctuations

In melt-blowing very thin liquid fiber jets are spun due to high-velocity air streams. In literature there is a clear, unsolved discrepancy between the measured and computed jet attenuation. In this paper we will verify numerically that the turbulent velocity fluctuations causing a random aerodynamic drag on the fiber jets -- that has been neglected so far -- are the crucial effect to close this gap. For this purpose, we model the velocity fluctuations as vector Gaussian random fields on top of a k-epsilon turbulence description and develop an efficient sampling procedure. Taking advantage of the special covariance structure the effort of the sampling is linear in the discretization and makes the realization possible

A Dynamic Stochastic Model for DNA Replication Initiation in Early Embryos

Background: Eukaryotic cells seem unable to monitor replication completion during normal S phase, yet must ensure a reliable replication completion time. This is an acute problem in early Xenopus embryos since DNA replication origins are located and activated stochastically, leading to the random completion problem. DNA combing, kinetic modelling and other studies using Xenopus egg extracts have suggested that potential origins are much more abundant than actual initiation events and that the time-dependent rate of initiation, I(t), markedly increases through S phase to ensure the rapid completion of unreplicated gaps and a narrow distribution of completion times. However, the molecular mechanism that underlies this increase has remained obscure.Methodology/Principal Findings: Using both previous and novel DNA combing data we have confirmed that I(t) increases through S phase but have also established that it progressively decreases before the end of S phase. To explore plausible biochemical scenarios that might explain these features, we have performed comparisons between numerical simulations and DNA combing data. Several simple models were tested: i) recycling of a limiting replication fork component from completed replicons; ii) time-dependent increase in origin efficiency; iii) time-dependent increase in availability of an initially limiting factor, e. g. by nuclear import. None of these potential mechanisms could on its own account for the data. We propose a model that combines time-dependent changes in availability of a replication factor and a fork-density dependent affinity of this factor for potential origins. This novel model quantitatively and robustly accounted for the observed changes in initiation rate and fork density.Conclusions/Significance: This work provides a refined temporal profile of replication initiation rates and a robust, dynamic model that quantitatively explains replication origin usage during early embryonic S phase. These results have significant implications for the organisation of replication origins in higher eukaryotes

A discrete geometric approach for simulating the dynamics of thin viscous threads

We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the kinematical constraints linking the centerline's tangent to the orientation of the material frame is used to eliminate two out of three degrees of freedom associated with rotations. Based on a description of twist inspired from discrete differential geometry and from variational principles, we build a full-fledged discrete viscous thread model, which includes in particular a discrete representation of the internal viscous stress. Consistency of the discrete model with the classical, smooth equations is established formally in the limit of a vanishing discretization length. The discrete models lends itself naturally to numerical implementation. Our numerical method is validated against reference solutions for steady coiling. The method makes it possible to simulate the unsteady behavior of thin viscous jets in a robust and efficient way, including the combined effects of inertia, stretching, bending, twisting, large rotations and surface tension

Evidence for Sequential and Increasing Activation of Replication Origins along Replication Timing Gradients in the Human Genome

Genome-wide replication timing studies have suggested that mammalian chromosomes consist of megabase-scale domains of coordinated origin firing separated by large originless transition regions. Here, we report a quantitative genome-wide analysis of DNA replication kinetics in several human cell types that contradicts this view. DNA combing in HeLa cells sorted into four temporal compartments of S phase shows that replication origins are spaced at 40 kb intervals and fire as small clusters whose synchrony increases during S phase and that replication fork velocity (mean 0.7 kb/min, maximum 2.0 kb/min) remains constant and narrowly distributed through S phase. However, multi-scale analysis of a genome-wide replication timing profile shows a broad distribution of replication timing gradients with practically no regions larger than 100 kb replicating at less than 2 kb/min. Therefore, HeLa cells lack large regions of unidirectional fork progression. Temporal transition regions are replicated by sequential activation of origins at a rate that increases during S phase and replication timing gradients are set by the delay and the spacing between successive origin firings rather than by the velocity of single forks. Activation of internal origins in a specific temporal transition region is directly demonstrated by DNA combing of the IGH locus in HeLa cells. Analysis of published origin maps in HeLa cells and published replication timing and DNA combing data in several other cell types corroborate these findings, with the interesting exception of embryonic stem cells where regions of unidirectional fork progression seem more abundant. These results can be explained if origins fire independently of each other but under the control of long-range chromatin structure, or if replication forks progressing from early origins stimulate initiation in nearby unreplicated DNA. These findings shed a new light on the replication timing program of mammalian genomes and provide a general model for their replication kinetics

Plx1 is required for chromosomal DNA replication under stressful conditions

Polo-like kinase (Plk)1 is required for mitosis progression. However, although Plk1 is expressed throughout the cell cycle, its function during S-phase is unknown. Using Xenopus laevis egg extracts, we demonstrate that Plx1, the Xenopus orthologue of Plk1, is required for DNA replication in the presence of stalled replication forks induced by aphidicolin, etoposide or reduced levels of DNA-bound Mcm complexes. Plx1 binds to chromatin and suppresses the ATM/ATR-dependent intra-S-phase checkpoint that inhibits origin firing. This allows Cdc45 loading and derepression of DNA replication initiation. Checkpoint activation increases Plx1 binding to the Mcm complex through its Polo box domain. Plx1 recruitment to chromatin is independent of checkpoint mediators Tipin and Claspin. Instead, ATR-dependent phosphorylation of serine 92 of Mcm2 is required for the recruitment of Plx1 to chromatin and for the recovery of DNA replication under stress. Depletion of Plx1 leads to accumulation of chromosomal breakage that is prevented by the addition of recombinant Plx1. These data suggest that Plx1 promotes genome stability by regulating DNA replication under stressful conditions

Modeling and validation of a stochastic drag for fibers in turbulent flows

The understanding of the motion of long slender elastic fibers in turbulent flows is of great interest to research, development and production in technical textiles manufacturing. The fiber dynamics depend on the drag forces that are imposed on the fiber by the fluid. Their computation requires in principle a coupling of fiber and flow with no-slip interface conditions. However, theneeded high resolution and adaptive grid refinement make the direct numerical simulation of the three-dimensional fluid-solid-problem for slender fibers and turbulent flows not only extremely costly and complex, but also still impossible for practically relevant applications. Embedded in a slender body theory, an aerodynamic force concept for a general drag model was therefore derived on basis of a stochastic k-o; description for a turbulent flow field in [23]. The turbulence effects on the fiber dynamics were modeled by a correlated random Gaussian force and its asymptotic limit on a macroscopic fiber scale by Gaussian white noise with flow-dependent amplitude. The concept was numerically studied under the conditions of a melt-spinning process for nonwoven materials in [24] – for the specific choice of a non-linear Taylor drag model. Taylor [35] suggested the heuristic model for high Reynolds number flows, Re in [20, 3 · 105], around inclined slender objects under an angle of attack of alpha in (pi/36, pi/2] between flow and object tangent. Since the Reynolds number is considered with respect to the relative velocity between flow and fiber, the numerical results lackaccuracy evidently for small Re that occur in cases of flexible light fibers moving occasionally with the flow velocity. In such a regime (Re << 1), linear Stokes drag forces were successfully applied for the prediction of small particles immersed in turbulent flows, see e.g. [25, 26, 32, 39], a modifiedStokes force taking also into account the particle oscillations was presented in [14]. The linear drag relation was also conferred to longer filaments by imposing free-draining assumptions [29, 8]. Apart from this, the Taylor drag suffers from its non-applicability to tangential incident flow situations (alpha = 0) that often occur in fiber and nonwoven production processes

Dynamics of curved viscous fibers with surface tension

In this paper we extend the slender body theory for the dynamics of a curved inertial viscous Newtonian fiber [23] by the inclusion of surface tension in the systematic asymptotic framework and the deduction of boundary conditions for the free fiber end, as it occurs in rotational spinning processes of glass fibers. The fiber ow is described by a three-dimensional free boundary value problem in terms of instationary incompressible Navier-Stokes equations under the neglect of temperature dependence. From standard regular expansion techniques in powers of the slenderness parameter we derive asymptotically leading-order balance laws for mass and momentum combining the inner viscous transport with unrestricted motion and shape of the fiber center-line which becomes important in the practical application. For the numerical investigation of the effects due to surface tension, viscosity, gravity and rotation on the fiber behavior we apply a fnite volume method with implicit flux discretization

On adjoint-based optimization of a free surface Stokes flow

This work deals with the optimal control of a free surface Stokes flow which responds to an applied outer pressure. Typical applications are fiber spinning or thin film manufacturing. We present and discuss two adjoint-based optimization approaches that differ in the treatment of the free boundary as either state or control variable. In both cases the free boundary is modeled as the graph of a function. The PDE-constrained optimization problems are numerically solved by the BFGS method, where the gradient of the reduced cost function is expressed in terms of adjoint variables. Numerical results for both strategies are finally compared with respect to accuracy and efficiency

Asymptotic transition from Cosserat rod to string models for curved viscous inertial jets

This work deals with the modeling and simulation of slender viscous jets exposed to gravity and rotation, as they occur in rotational spinning processes. In terms of slender-body theory we show the asymptotic reduction of a viscous Cosserat rod to a string system for vanishing slenderness parameter. We propose two string models, i.e. inertial and viscous-inertial string models, that differ in the closure conditions and hence yield a boundary value problem and an interface problem, respectively. We investigate the existence regimes of the string models in the four-parametric space of Froude, Rossby, Reynolds numbers and jet length. The convergence regimes where the respective string solution is the asymptotic limit to the rod turn out to be disjoint and to cover nearly the whole parameter space. We explore the transition hyperplane and derive analytically low and high Reynolds number limits. Numerical studies of the stationary jet behavior for different parameter ranges complete the work