Search results for "Critical value"
showing 7 items of 57 documents
Surface sulci in squeezed soft solids
2013
The squeezing of soft solids, the constrained growth of biological tissues, and the swelling of soft elastic solids such as gels can generate large compressive stresses at their surfaces. This causes the otherwise smooth surface of such a solid to become unstable when its stress exceeds a critical value. Previous analyses of the surface instability have assumed two-dimensional plane-strain conditions, but in experiments isotropic stresses often lead to complex three-dimensional sulcification patterns. Here we show how such diverse morphologies arise by numerically modeling the lateral compression of a rigidly clamped elastic layer. For incompressible solids, close to the instability thresho…
Convective Roll Instabilities of Vertical Throughflow with Viscous Dissipation in a Horizontal Porous Layer
2009
Published version of an article from the journal: Transport in Porous Media. The original publication is available at Spingerlink. http://dx.doi.org/10.1007/s11242-009-9417-y The vertical throughflow with viscous dissipation in a horizontal porous layer is studied. The horizontal plane boundaries are assumed to be isothermal with unequal temperatures and bottom heating. A basic stationary solution of the governing equations with a uniform vertical velocity field (throughflow) is determined. The temperature field in the basic solution depends only on the vertical coordinate. Departures from the linear heat conduction profile are displayed by the temperature distribution due to the forced con…
Stability of Flow with Viscous Dissipation in a Horizontal Porous Layer with an Open Boundary Having a Prescribed Temperature Gradient
2010
Published version of an article in the journal: Transport in Porous Media. The original publication is available at www.springerlink.com, http://dx.doi.org/10.1007/s11242-010-9588-6 A buoyancy-induced stationary flow with viscous dissipation in a horizontal porous layer is investigated. The lower boundary surface is impermeable and subject to a uniform heat flux. The upper open boundary has a prescribed, linearly varying, temperature distribution. The buoyancy-induced basic velocity profile is parallel and non-uniform. The linear stability of this basic solution is analysed numerically by solving the disturbance equations for oblique rolls arbitrarily oriented with respect to the basic velo…
Slow Crystallization Kinetics of Poly(vinyl alcohol) in Confined Environment during Cryotropic Gelation of Aqueous Solutions
2006
The gelation kinetics of aqueous solutions of poly(vinyl alcohol) (PVA) during freezing at −13 °C has been investigated with time-resolved small angle neutron scattering. Crystallization of PVA takes place inside an unfrozen liquid microphase that forms in the matrix of ice crystals and follows a first-order kinetics during the early stages and becomes very slow in the later stages with an apparent Avrami exponent lower than 1. Crystallization of PVA at low temperatures is responsible of formation of strong physical gels upon defrosting, provided that the concentration of PVA is higher than a critical value.
Zero-range model of traffic flow.
2005
A multi--cluster model of traffic flow is studied, in which the motion of cars is described by a stochastic master equation. Assuming that the escape rate from a cluster depends only on the cluster size, the dynamics of the model is directly mapped to the mathematically well-studied zero-range process. Knowledge of the asymptotic behaviour of the transition rates for large clusters allows us to apply an established criterion for phase separation in one-dimensional driven systems. The distribution over cluster sizes in our zero-range model is given by a one--step master equation in one dimension. It provides an approximate mean--field dynamics, which, however, leads to the exact stationary s…
Die Bestimmung der Molekulargewichtsverteilung von nichtkristallisierenden Polymeren mit dem Elektronenmikroskop, 6. Fehlerkorrektur der experimentel…
1977
A mathematical treatment is described, by means of which the effect of the measuring errors on the number molecular weight distribution of polymers, as obtained with an electron microscope (EM), can be eliminated. It is shown, that the difference in the nonuniformities of the measured and the corrected distribution would be negligible only in the case of samples with high average degrees of polymerization and sufficiently broad distributions. Otherwise differences of 10% or more can be found, depending on the size of the actual measuring error. This is shown by means of four practical examples. For a practical application the measuring error may not exceed some critical value, which, though…
Unexpectedly normal phase behavior of single homopolymer chains
2006
Employing Monte Carlo simulations, we show that the topology of the phase diagram of a single flexible homopolymer chain changes in dependence on the range of an attractive square well interaction between the monomers. For a range of attraction larger than a critical value, the equilibrium phase diagram of the single polymer chain and the corresponding polymer solution phase diagram exhibit vapor (swollen coil, dilute solution), liquid (collapsed globule, dense solution), and solid phases. Otherwise, the liquid-vapor transition vanishes from the equilibrium phase diagram for both the single chain and the polymer solution. This change in topology of the phase diagram resembles the behavior k…