13,388 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
Magnetorotational-type instability in Couette-Taylor flow of a viscoelastic polymer liquid
We describe an instability of viscoelastic Couette-Taylor flow that is
directly analogous to the magnetorotational instability (MRI) in astrophysical
magnetohydrodynamics, with polymer molecules playing the role of magnetic field
lines. By determining the conditions required for the onset of instability and
the properties of the preferred modes, we distinguish it from the centrifugal
and elastic instabilities studied previously. Experimental demonstration and
investigation should be much easier for the viscoelastic instability than for
the MRI in a liquid metal. The analogy holds with the case of a predominantly
toroidal magnetic field such as is expected in an accretion disk and it may be
possible to access a turbulent regime in which many modes are unstable.Comment: 4 pages, 4 figures, to be published in Physical Review Letter
Reactive self-heating model of aluminum spherical nanoparticles
Aluminum-oxygen reaction is important in many highly energetic, high pressure
generating systems. Recent experiments with nanostructured thermites suggest
that oxidation of aluminum nanoparticles occurs in a few microseconds. Such
rapid reaction cannot be explained by a conventional diffusion-based mechanism.
We present a rapid oxidation model of a spherical aluminum nanoparticle, using
Cabrera-Mott moving boundary mechanism, and taking self-heating into account.
In our model, electric potential solves the nonlinear Poisson equation. In
contrast with the Coulomb potential, a "double-layer" type solution for the
potential and self-heating leads to enhanced oxidation rates. At maximal
reaction temperature of 2000 C, our model predicts overall oxidation time scale
in microseconds range, in agreement with experimental evidence.Comment: submitte
Single polymer dynamics: coil-stretch transition in a random flow
By quantitative studies of statistics of polymer stretching in a random flow
and of a flow field we demonstrate that the stretching of polymer molecules in
a 3D random flow occurs rather sharply via the coil-stretch transition at the
value of the criterion close to theoretically predicted.Comment: 4 pages, 5 figure
A principled approach to programming with nested types in Haskell
Initial algebra semantics is one of the cornerstones of the theory of modern functional programming languages. For each inductive data type, it provides a Church encoding for that type, a build combinator which constructs data of that type, a fold combinator which encapsulates structured recursion over data of that type, and a fold/build rule which optimises modular programs by eliminating from them data constructed using the buildcombinator, and immediately consumed using the foldcombinator, for that type. It has long been thought that initial algebra semantics is not expressive enough to provide a similar foundation for programming with nested types in Haskell. Specifically, the standard folds derived from initial algebra semantics have been considered too weak to capture commonly occurring patterns of recursion over data of nested types in Haskell, and no build combinators or fold/build rules have until now been defined for nested types. This paper shows that standard folds are, in fact, sufficiently expressive for programming with nested types in Haskell. It also defines buildcombinators and fold/build fusion rules for nested types. It thus shows how initial algebra semantics provides a principled, expressive, and elegant foundation for programming with nested types in Haskell
Stress Tensors of Multiparticle Collision Dynamics Fluids
Stress tensors are derived for the multiparticle collision dynamics
algorithm, a particle-based mesoscale simulation method for fluctuating fluids,
resembling those of atomistic or molecular systems. Systems with periodic
boundary conditions as well as fluids confined in a slit are considered. For
every case, two equivalent expressions for the tensor are provided, the
internal stress tensor, which involves all degrees of freedom of a system, and
the external stress, which only includes the interactions with the confining
surfaces. In addition, stress tensors for a system with embedded particles are
determined. Based on the derived stress tensors, analytical expressions are
calculated for the shear viscosity. Simulations illustrate the difference in
fluctuations between the various derived expressions and yield very good
agreement between the numerical results and the analytically derived expression
for the viscosity
Velocity Slip and Temperature Jump in Hypersonic Aerothermodynamics
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76543/1/AIAA-2007-208-226.pd
Microcanonical entropy inflection points: Key to systematic understanding of transitions in finite systems
We introduce a systematic classification method for the analogs of phase
transitions in finite systems. This completely general analysis, which is
applicable to any physical system and extends towards the thermodynamic limit,
is based on the microcanonical entropy and its energetic derivative, the
inverse caloric temperature. Inflection points of this quantity signal
cooperative activity and thus serve as distinct indicators of transitions. We
demonstrate the power of this method through application to the long-standing
problem of liquid-solid transitions in elastic, flexible homopolymers.Comment: 4 pages, 3 figure
Mixing by polymers: experimental test of decay regime of mixing
By using high molecular weight fluorescent passive tracers with different
diffusion coefficients and by changing the fluid velocity we study dependence
of a characteristic mixing length on the Peclet number, , which controls
the mixing efficiency. The mixing length is found to be related to by a
power law, , and increases faster than
expected for an unbounded chaotic flow. Role of the boundaries in the mixing
length abnormal growth is clarified. The experimental findings are in a good
quantitative agreement with the recent theoretical predictions.Comment: 4 pages,5 figures. accepted for publication in PR
Functional connectivity varies across scales in a fragmented landscape
Species of different sizes interact with the landscape differently because ecological structure varies with scale, as do species movement capabilities and habitat requirements. As such, landscape connectivity is dependent upon the scale at which an animal interacts with its environment. Analyses of landscape connectivity must incorporate ecologically relevant scales to address scale-specific differences. Many evaluations of landscape connectivity utilize incrementally increasing buffer distances or other arbitrary spatial delineations as scales of analysis. Instead, we used a mammalian body mass discontinuity analysis to objectively identify scales in the Central Platte River Valley (CPRV) of Nebraska, U.S.A. We implemented a graph-theoretic network analysis to evaluate the connectivity of two wetland land cover types in the CPRV, wet meadow and emergent marsh, at multiple scales represented by groupings of species with similar body mass. Body mass is allometric with multiple traits of species, including dispersal distances. The landscape was highly connected at larger scales but relatively unconnected at smaller scales. We identified a threshold at which the landscape becomes highly connected between 500 m and 6,500 m dispersal distances. The presence of a connectivity threshold suggests that species with dispersal distances close to the threshold may be most vulnerable to habitat loss or reconfiguration and management should account for the connectivity threshold. Furthermore, we propose that a multiscale approach to management will be necessary to ensure landscape connectivity for diverse species
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