14,322 research outputs found
Fibrational induction rules for initial algebras
This paper provides an induction rule that can be used to prove properties of data structures whose types are inductive, i.e., are carriers of initial algebras of functors. Our results are semantic in nature and are inspired by Hermida and Jacobs’ elegant algebraic formulation of induction for polynomial data types. Our contribution is to derive, under slightly different assumptions, an induction rule that is generic over all inductive types, polynomial or not. Our induction rule is generic over the kinds of properties to be proved as well: like Hermida and Jacobs, we work in a general fibrational setting and so can accommodate very general notions of properties on inductive types rather than just those of particular syntactic forms. We establish the correctness of our generic induction rule by reducing induction to iteration. We show how our rule can be instantiated to give induction rules for the data types of rose trees, finite hereditary sets, and hyperfunctions. The former lies outside the scope of Hermida and Jacobs’ work because it is not polynomial; as far as we are aware, no induction rules have been known to exist for the latter two in a general fibrational framework. Our instantiation for hyperfunctions underscores the value of working in the general fibrational setting since this data type cannot be interpreted as a set
Shell Model of Two-dimensional Turbulence in Polymer Solutions
We address the effect of polymer additives on two dimensional turbulence, an
issue that was studied recently in experiments and direct numerical
simulations. We show that the same simple shell model that reproduced drag
reduction in three-dimensional turbulence reproduces all the reported effects
in the two-dimensional case. The simplicity of the model offers a
straightforward understanding of the all the major effects under consideration
Fluid Elasticity Can Enable Propulsion at Low Reynolds Number
Conventionally, a microscopic particle that performs a reciprocal stroke
cannot move through its environment. This is because at small scales, the
response of simple Newtonian fluids is purely viscous and flows are
time-reversible. We show that by contrast, fluid elasticity enables propulsion
by reciprocal forcing that is otherwise impossible. We present experiments on
rigid objects actuated reciprocally in viscous fluids, demonstrating for the
first time a purely elastic propulsion set by the object's shape and boundary
conditions. We describe two different artificial "swimmers" that experimentally
realize this principle.Comment: 5 pages, 4 figure
Thermodiffusion in model nanofluids by molecular dynamics simulations
In this work, a new algorithm is proposed to compute single particle
(infinite dilution) thermodiffusion using Non-Equilibrium Molecular Dynamics
simulations through the estimation of the thermophoretic force that applies on
a solute particle. This scheme is shown to provide consistent results for
simple Lennard-Jones fluids and for model nanofluids (spherical non-metallic
nanoparticles + Lennard-Jones fluid) where it appears that thermodiffusion
amplitude, as well as thermal conductivity, decrease with nanoparticles
concentration. Then, in nanofluids in the liquid state, by changing the nature
of the nanoparticle (size, mass and internal stiffness) and of the solvent
(quality and viscosity) various trends are exhibited. In all cases the single
particle thermodiffusion is positive, i.e. the nanoparticle tends to migrate
toward the cold area. The single particle thermal diffusion 2 coefficient is
shown to be independent of the size of the nanoparticle (diameter of 0.8 to 4
nm), whereas it increases with the quality of the solvent and is inversely
proportional to the viscosity of the fluid. In addition, this coefficient is
shown to be independent of the mass of the nanoparticle and to increase with
the stiffness of the nanoparticle internal bonds. Besides, for these
configurations, the mass diffusion coefficient behavior appears to be
consistent with a Stokes-Einstein like law
Polymeric filament thinning and breakup in microchannels
The effects of elasticity on filament thinning and breakup are investigated
in microchannel cross flow. When a viscous solution is stretched by an external
immiscible fluid, a low 100 ppm polymer concentration strongly affects the
breakup process, compared to the Newtonian case. Qualitatively, polymeric
filaments show much slower evolution, and their morphology features multiple
connected drops. Measurements of filament thickness show two main temporal
regimes: flow- and capillary-driven. At early times both polymeric and
Newtonian fluids are flow-driven, and filament thinning is exponential. At
later times, Newtonian filament thinning crosses over to a capillary-driven
regime, in which the decay is algebraic. By contrast, the polymeric fluid first
crosses over to a second type of flow-driven behavior, in which viscoelastic
stresses inside the filament become important and the decay is again
exponential. Finally, the polymeric filament becomes capillary-driven at late
times with algebraic decay. We show that the exponential flow thinning behavior
allows a novel measurement of the extensional viscosities of both Newtonian and
polymeric fluids.Comment: 7 pages, 7 figure
Mechanical properties of coated titanium Beta-21S after exposure to air at 700 and 800 C
Mechanical properties of Beta-21S (Ti-15Mo-3Al-2.7Nb-0.2Si, wt percent) with glass, aluminide, and glass-on-aluminide coatings less than 3-micron thick were studied. Coatings were deposited by sol-gel processing or electron-beam evaporation onto 4.5-mil (113-micron) thick Beta-21S sheet from which, after oxidizing in air at 700 or 800 C, tensile test specimens were machined. Plastic elongation was the most severely degraded of the tensile properties; the glass-on-aluminide coatings were the most effective in preventing degradation. It was found that oxygen trapping by forming oxides in the coating, and reactions between the coatings and the Beta-21S alloy played significant roles
Elastic waves and transition to elastic turbulence in a two-dimensional viscoelastic Kolmogorov flow
We investigate the dynamics of the two-dimensional periodic Kolmogorov flow
of a viscoelastic fluid, described by the Oldroyd-B model, by means of direct
numerical simulations. Above a critical Weissenberg number the flow displays a
transition from stationary to randomly fluctuating states, via periodic ones.
The increasing complexity of the flow in both time and space at progressively
higher values of elasticity accompanies the establishment of mixing features.
The peculiar dynamical behavior observed in the simulations is found to be
related to the appearance of filamental propagating patterns, which develop
even in the limit of very small inertial non-linearities, thanks to the
feedback of elastic forces on the flow.Comment: 10 pages, 14 figure
Photomechanical Investigation of Structural Behavior of Gyroscope Components. Task IV - Analysis of Initial Redesign of AB5-K8 GYROSCOPE
Photomechanics of structure and materials in redesigned AB5-K8 gyroscope component
Rouse Chains with Excluded Volume Interactions: Linear Viscoelasticity
Linear viscoelastic properties for a dilute polymer solution are predicted by
modeling the solution as a suspension of non-interacting bead-spring chains.
The present model, unlike the Rouse model, can describe the solution's
rheological behavior even when the solvent quality is good, since excluded
volume effects are explicitly taken into account through a narrow Gaussian
repulsive potential between pairs of beads in a bead-spring chain. The use of
the narrow Gaussian potential, which tends to the more commonly used
delta-function repulsive potential in the limit of a width parameter "d" going
to zero, enables the performance of Brownian dynamics simulations. The
simulations results, which describe the exact behavior of the model, indicate
that for chains of arbitrary but finite length, a delta-function potential
leads to equilibrium and zero shear rate properties which are identical to the
predictions of the Rouse model. On the other hand, a non-zero value of "d"
gives rise to a prediction of swelling at equilibrium, and an increase in zero
shear rate properties relative to their Rouse model values. The use of a
delta-function potential appears to be justified in the limit of infinite chain
length. The exact simulation results are compared with those obtained with an
approximate solution which is based on the assumption that the non-equilibrium
configurational distribution function is Gaussian. The Gaussian approximation
is shown to be exact to first order in the strength of excluded volume
interaction, and is found to be accurate above a threshold value of "d", for
given values of chain length and strength of excluded volume interaction.Comment: Revised version. Long chain limit analysis has been deleted. An
improved and corrected examination of the long chain limit will appear as a
separate posting. 32 pages, 9 postscript figures, LaTe
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