303 research outputs found
On a nonlinear partial differential algebraic system arising in technical textile industry: Analysis and numerics
In this paper we explore a numerical scheme for a nonlinear fourth order
system of partial differential algebraic equations that describes the dynamics
of slender inextensible elastica as they arise in the technical textile
industry. Applying a semi-discretization in time, the resulting sequence of
nonlinear elliptic systems with the algebraic constraint for the local length
preservation is reformulated as constrained optimization problems in a Hilbert
space setting that admit a solution at each time level. Stability and
convergence of the scheme are proved. The numerical realization is based on a
finite element discretization in space. The simulation results confirm the
analytically predicted properties of the scheme.Comment: Abstract and introduction are partially rewritten. The numerical
study in Section 4 is completely rewritte
Stochastic fiber dynamics in a spatially semi-discrete setting
We investigate a spatially discrete surrogate model for the dynamics of a
slender, elastic, inextensible fiber in turbulent flows. Deduced from a
continuous space-time beam model for which no solution theory is available, it
consists of a high-dimensional second order stochastic differential equation in
time with a nonlinear algebraic constraint and an associated Lagrange
multiplier term. We establish a suitable framework for the rigorous formulation
and analysis of the semi-discrete model and prove existence and uniqueness of a
global strong solution. The proof is based on an explicit representation of the
Lagrange multiplier and on the observation that the obtained explicit drift
term in the equation satisfies a one-sided linear growth condition on the
constraint manifold. The theoretical analysis is complemented by numerical
studies concerning the time discretization of our model. The performance of
implicit Euler-type methods can be improved when using the explicit
representation of the Lagrange multiplier to compute refined initial estimates
for the Newton method applied in each time step.Comment: 20 pages; typos removed, references adde
Finite volume approach for the instationary Cosserat rod model describing the spinning of viscous jets
The spinning of slender viscous jets can be described asymptotically by
one-dimensional models that consist of systems of partial and ordinary
differential equations. Whereas the well-established string models possess only
solutions for certain choices of parameters and set-ups, the more sophisticated
rod model that can be considered as -regularized string is generally
applicable. But containing the slenderness ratio explicitely in the
equations complicates the numerical treatment. In this paper we present the
first instationary simulations of a rod in a rotational spinning process for
arbitrary parameter ranges with free and fixed jet end, for which the hitherto
investigations longed. So we close an existing gap in literature. The numerics
is based on a finite volume approach with mixed central, up- and down-winded
differences, the time integration is performed by stiff accurate Radau methods
Visualization of bidirectional initiation of chromosomal DNA replication in a human cell free system
Initiation of DNA replication is tightly controlled during the cell cycle to maintain genome integrity. In order to directly study this control we have previously established a cell-free system from human cells that initiates semi-conservative DNA replication. Template nuclei are isolated from cells synchronized in late G(1) phase by mimosine. We have now used DNA combing to investigate initiation and further progression of DNA replication forks in this human in vitro system at single molecule level. We obtained direct evidence for bidirectional initiation of divergently moving replication forks in vitro. We assessed quantitatively replication fork initiation patterns, fork movement rates and overall fork density. Individual replication forks progress at highly heterogeneous rates (304 ± 162 bp/min) and the two forks emanating from a single origin progress independently from each other. Fork progression rates also change at the single fork level, suggesting that replication fork stalling occurs. DNA combing provides a powerful approach to analyse dynamics of human DNA replication in vitro
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