89 research outputs found
Degenerate Mobilities in Phase Field Models are Insufficient to Capture Surface Diffusion
Phase field models frequently provide insight to phase transitions, and are
robust numerical tools to solve free boundary problems corresponding to the
motion of interfaces. A body of prior literature suggests that interface motion
via surface diffusion is the long-time, sharp interface limit of microscopic
phase field models such as the Cahn-Hilliard equation with a degenerate
mobility function. Contrary to this conventional wisdom, we show that the
long-time behaviour of degenerate Cahn-Hilliard equation with a polynomial free
energy undergoes coarsening, reflecting the presence of bulk diffusion, rather
than pure surface diffusion. This reveals an important limitation of phase
field models that are frequently used to model surface diffusion
Existence and equilibration of global weak solutions to finitely extensible nonlinear bead-spring chain models for dilute polymers
We show the existence of global-in-time weak solutions to a general class of
coupled FENE-type bead-spring chain models that arise from the kinetic theory
of dilute solutions of polymeric liquids with noninteracting polymer chains.
The class of models involves the unsteady incompressible Navier-Stokes
equations in a bounded domain in two or three space dimensions for the velocity
and the pressure of the fluid, with an elastic extra-stress tensor appearing on
the right-hand side in the momentum equation. The extra-stress tensor stems
from the random movement of the polymer chains and is defined by the Kramers
expression through the associated probability density function that satisfies a
Fokker-Planck-type parabolic equation, a crucial feature of which is the
presence of a center-of-mass diffusion term. We require no structural
assumptions on the drag term in the Fokker-Planck equation; in particular, the
drag term need not be corotational. With a square-integrable and
divergence-free initial velocity datum for the Navier-Stokes equation and a
nonnegative initial probability density function for the Fokker-Planck
equation, which has finite relative entropy with respect to the Maxwellian of
the model, we prove the existence of a global-in-time weak solution to the
coupled Navier-Stokes-Fokker-Planck system. It is also shown that in the
absence of a body force, the weak solution decays exponentially in time to the
equilibrium solution, at a rate that is independent of the choice of the
initial datum and of the centre-of-mass diffusion coefficient.Comment: 75 page
Numerical analysis of a topology optimization problem for Stokes flow
T. Borrvall and J. Petersson [Topology optimization of fluids in Stokes flow,
International Journal for Numerical Methods in Fluids 41 (1) (2003) 77--107]
developed the first model for topology optimization of fluids in Stokes flow.
They proved the existence of minimizers in the infinite-dimensional setting and
showed that a suitably chosen finite element method will converge in a weak(-*)
sense to an unspecified solution. In this work, we prove novel regularity
results and extend their numerical analysis. In particular, given an isolated
local minimizer to the analytical problem, we show that there exists a sequence
of finite element solutions, satisfying necessary first-order optimality
conditions, that strongly converges to it. We also provide the first numerical
investigation into convergence rates
Existence and equilibration of global weak solutions to Hookean-type bead-spring chain models for dilute polymers
We show the existence of global-in-time weak solutions to a general class of
coupled Hookean-type bead-spring chain models that arise from the kinetic
theory of dilute solutions of polymeric liquids with noninteracting polymer
chains. The class of models involves the unsteady incompressible Navier-Stokes
equations in a bounded domain in two or three space dimensions for the velocity
and the pressure of the fluid, with an elastic extra-stress tensor appearing on
the right-hand side in the momentum equation. The extra-stress tensor stems
from the random movement of the polymer chains and is defined by the Kramers
expression through the associated probability density function that satisfies a
Fokker-Planck-type parabolic equation, a crucial feature of which is the
presence of a center-of-mass diffusion term. We require no structural
assumptions on the drag term in the Fokker-Planck equation; in particular, the
drag term need not be corotational. With a square-integrable and
divergence-free initial velocity datum for the Navier-Stokes equation and a
nonnegative initial probability density function for the Fokker-Planck
equation, which has finite relative entropy with respect to the Maxwellian of
the model, we prove the existence of a global-in-time weak solution to the
coupled Navier-Stokes-Fokker-Planck system. It is also shown that in the
absence of a body force, the weak solution decays exponentially in time to the
equilibrium solution, at a rate that is independent of the choice of the
initial datum and of the centre-of-mass diffusion coefficient.Comment: 86 page
Biological preservative in whole crop wheat ensilage
Ensilage of whole crop wheat is popular in Europe and America for feeding of ruminant animals, but it is quite rare in Hungary. It can be introduced for replacement of shortage of silomaize silages in drought season. The quality of wheat silage could improve by biological inoculants. Silage additives are expected to ensure a more efficient fermentation phase as well as reduce the risk of aerobic deterioration when silages are exposed to air. Many additives have been developed to improve the ensiling process and nutritive value of silage. Nowadays the 3rd generation biological inoculants –containing lactic acid bacteria and enzymes – are used in order to coordinate the fermentation in such a way that they increase lactic acid production at the beginning of the fermentation and improve the quality and stability of silage during the fermentation and feeding. The quality of raw material (maturity of plant, chop length, spreading of inoculant uniformly) and the proper filling, compacting, covering and wrapping have a great influence on the effectiveness of the inoculant. The mycotoxin content of malfermented silages is an undesirable risk factor. The objective of our research was to determine the effect of two silage inoculant strains Lactobacillus buchneri and Pediococcus acidilactici mixture combined with amilase-, glucanase-, xylanase and galactomannase enzymes on whole crop wheat silage fermentation characteristics, nutritive value and aerobic stability compare to untreated control. Experimental ensilage procedure started with the basic whole crop raw material originated from waxen ripeness of wheat (hard cheddar stage of maturity of seeds) at the time of harvesting. The DM content of chopped raw material was 44%. The LAB inoculants were applied to raw material at 2.5x105 CFU/g fresh material (FM). Because of quite good quality of untreated silages also, the priority of LAB treatment could not proven in the aerobic stability test. The biological preservative (LAB+enzymes) promoted better fermentation and forced back the undesirable butyric acid production in the silages
Which are Better Conditioned Meshes Adaptive, Uniform, Locally Refined or Localised
Adaptive, locally refined and locally adjusted meshes are preferred over
uniform meshes for capturing singular or localised solutions. Roughly speaking,
for a given degree of freedom a solution associated with adaptive, locally
refined and locally adjusted meshes is more accurate than the solution given by
uniform meshes. In this work, we answer the question which meshes are better
conditioned. We found, for approximately same degree of freedom (same size of
matrix), it is easier to solve a system of equations associated with an
adaptive mesh.Comment: 4 Page
Heisenberg-limited metrology with a squeezed vacuum state, three-mode mixing, and information recycling
We have previously shown that quantum-enhanced atom interferometry can be achieved by mapping the quantum state of squeezed optical vacuum to one of the atomic inputs via a beamsplitter-like process [Phys. Rev. A 90, 063630 (2014)]. Here we ask the question: is a better phase sensitivity possible if the quantum state transfer (QST) is described by a three-mode-mixing model, rather than a beamsplitter? The answer is yes, but only if the portion of the optical state not transferred to the atoms is incorporated via information recycling. Surprisingly, our scheme gives a better sensitivity for lower QST efficiencies and with a sufficiently large degree of squeezing can attain near-Heisenberg-limited sensitivities for arbitrarily small QST efficiencies. Furthermore, we use the quantum Fisher information to demonstrate the near optimality of our scheme
Existence of global weak solutions to dumbbell models for dilute polymers with microscopic cut-off
Accepted versio
On the influence of the Kozai mechanism in habitable zones of extrasolar planetary systems
Aims. We investigate the long-term evolution of inclined test particles representing a small Earth-like body with negligible gravitational effects (hereafter called massless test-planets) in the restricted three-body problem, and consisting of a star, a gas giant, and a massless test-planet. The test-planet is initially on a circular orbit and moves around the star at distances closer than the gas giant. The aim is to show the influences of the eccentricity and the mass of the gas giant on the dynamics, for various inclinations of the test-planet, and to investigate in more detail the Kozai mechanism in the elliptic problem.
Methods. We performed a parametric study, integrating the orbital evolution of test particles whose initial conditions were distributed on the semi-major axis – inclination plane. The gas giant’s initial eccentricity was varied. For the calculations, we used the Lie integration method and in some cases the Bulirsch-Stoer algorithm. To analyze the results, the maximum eccentricity and the Lyapunov characteristic indicator were used. All integrations were performed for 105 periods of the gas giant.
Results. Our calculations show that inclined massless test-planets can be in stable configurations with gas giants on either circular or elliptic orbits. The higher the eccentricity of the gas giant, the smaller the possible range in semi-major axis for the test-planet. For gas giants on circular orbits, our results illustrate the well-known results associated with the Kozai mechanism, which do not allow stable orbits above a critical inclination of approximately 40°. For gas giants on eccentric orbits, the dynamics is quite similar, and the massless companion exhibits limited variations in eccentricity. In addition, we identify a region around 35° consisting of long-time stable, low eccentric orbits. We show that these results are also valid for Earth-mass companions, therefore they can be applied to extrasolar systems: for instance, the extrasolar planetary system HD 154345 can possess a 35° degree inclined, nearly circular, Earth-mass companion in the habitable zone
Experimental Inactivated Concentrated Adjuvant Rabies Vaccine. Evaluation of its Efficacy in Cattle
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