810 research outputs found
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
Spontaneous Raman scattering for simultaneous measurements of in-cylinder species
A technique for multi-species mole fraction measurement in internal combustion engines is described. The technique is based on the spontaneous Raman scattering. It can simultaneously provide the mole fractions of several species of N-2, O-2, H2O, CO2 and fuel. Using the system, simultaneous measurement of air/fuel ratio and burnt residual gas are carried out during the mixture process in a Controlled Auto Ignition (CAI) combustion engine. The accuracy and consistency of the measured results were confirmed by the measured air fuel ratio using an exhaust gas analyzer and independently calculated mole fraction values. Measurement of species mole fractions during combustion process has also been demonstrated. It shows that the SRS can provide valuable data on this process in a CAI combustion engine
Constructing applicative functors
Applicative functors define an interface to computation that is more general, and correspondingly weaker, than that of monads. First used in parser libraries, they are now seeing a wide range of applications. This paper sets out to explore the space of non-monadic applicative functors useful in programming. We work with a generalization, lax monoidal functors, and consider several methods of constructing useful functors of this type, just as transformers are used to construct computational monads. For example, coends, familiar to functional programmers as existential types, yield a range of useful applicative functors, including left Kan extensions. Other constructions are final fixed points, a limited sum construction, and a generalization of the semi-direct product of monoids. Implementations in Haskell are included where possible
Anisotropic Local Stress and Particle Hopping in a Deeply Supercooled Liquid
The origin of the microscopic motions that lead to stress relaxation in
deeply supercooled liquid remains unclear. We show that in such a liquid the
stress relaxation is locally anisotropic which can serve as the driving force
for the hopping of the system on its free energy surface. However, not all
hopping are equally effective in relaxing the local stress, suggesting that
diffusion can decouple from viscosity even at local level. On the other hand,
orientational relaxation is found to be always coupled to stress relaxation.Comment: 4 pages, 3 figure
Some relations between Lagrangian models and synthetic random velocity fields
We propose an alternative interpretation of Markovian transport models based
on the well-mixedness condition, in terms of the properties of a random
velocity field with second order structure functions scaling linearly in the
space time increments. This interpretation allows direct association of the
drift and noise terms entering the model, with the geometry of the turbulent
fluctuations. In particular, the well known non-uniqueness problem in the
well-mixedness approach is solved in terms of the antisymmetric part of the
velocity correlations; its relation with the presence of non-zero mean helicity
and other geometrical properties of the flow is elucidated. The well-mixedness
condition appears to be a special case of the relation between conditional
velocity increments of the random field and the one-point Eulerian velocity
distribution, allowing generalization of the approach to the transport of
non-tracer quantities. Application to solid particle transport leads to a model
satisfying, in the homogeneous isotropic turbulence case, all the conditions on
the behaviour of the correlation times for the fluid velocity sampled by the
particles. In particular, correlation times in the gravity and in the inertia
dominated case, respectively, longer and shorter than in the passive tracer
case; in the gravity dominated case, correlation times longer for velocity
components along gravity, than for the perpendicular ones. The model produces,
in channel flow geometry, particle deposition rates in agreement with
experiments.Comment: 54 pages, 8 eps figures included; contains additional material on
SO(3) and on turbulent channel flows. Few typos correcte
Inertial range scaling of scalar flux spectra in uniformly sheared turbulence
A model based on two-point closure theory of turbulence is proposed and
applied to study the Reynolds number dependency of the scalar flux spectra in
homogeneous shear flow with a cross-stream uniform scalar gradient. For the
cross-stream scalar flux, in the inertial range the spectral behavior agrees
with classical predictions and measurements. The streamwise scalar flux is
found to be in good agreement with the results of atmospheric measurements.
However, both the model results and the atmospheric measurements disagree with
classical predictions. A detailed analysis of the different terms in the
evolution equation for the streamwise scalar flux spectrum shows that nonlinear
contributions are governing the inertial subrange of this spectrum and that
these contributions are relatively more important than for the cross-stream
flux. A new expression for the scalar flux spectra is proposed. It allows us to
unify the description of the components in one single expression, leading to a
classical K^-7/3 inertial range for the cross-stream component and to a new
K^-23/9 scaling for the streamwise component that agrees better with
atmospheric measurements than the K^-3 prediction of J. C. Wyngaard and O. R.
Cot\'e [Quart. J. R. Met. Soc. 98, 590 (1972)]
Nonlocal Form of the Rapid Pressure-Strain Correlation in Turbulent Flows
A new fundamentally-based formulation of nonlocal effects in the rapid
pressure-strain correlation in turbulent flows has been obtained. The resulting
explicit form for the rapid pressure-strain correlation accounts for nonlocal
effects produced by spatial variations in the mean-flow velocity gradients, and
is derived through Taylor expansion of the mean velocity gradients appearing in
the exact integral relation for the rapid pressure-strain correlation. The
integrals in the resulting series expansion are solved for high- and
low-Reynolds number forms of the longitudinal correlation function , and
the resulting nonlocal rapid pressure-strain correlation is expressed as an
infinite series in terms of Laplacians of the mean strain rate tensor. The new
formulation is used to obtain a nonlocal transport equation for the turbulence
anisotropy that is expected to provide improved predictions of the anisotropy
in strongly inhomogeneous flows.Comment: 11 pages, submitted to Phys. Rev.
Continuous, Semi-discrete, and Fully Discretized Navier-Stokes Equations
The Navier--Stokes equations are commonly used to model and to simulate flow
phenomena. We introduce the basic equations and discuss the standard methods
for the spatial and temporal discretization. We analyse the semi-discrete
equations -- a semi-explicit nonlinear DAE -- in terms of the strangeness index
and quantify the numerical difficulties in the fully discrete schemes, that are
induced by the strangeness of the system. By analyzing the Kronecker index of
the difference-algebraic equations, that represent commonly and successfully
used time stepping schemes for the Navier--Stokes equations, we show that those
time-integration schemes factually remove the strangeness. The theoretical
considerations are backed and illustrated by numerical examples.Comment: 28 pages, 2 figure, code available under DOI: 10.5281/zenodo.998909,
https://doi.org/10.5281/zenodo.99890
The stochastic gravitational wave background from turbulence and magnetic fields generated by a first-order phase transition
We analytically derive the spectrum of gravitational waves due to
magneto-hydrodynamical turbulence generated by bubble collisions in a
first-order phase transition. In contrast to previous studies, we take into
account the fact that turbulence and magnetic fields act as sources of
gravitational waves for many Hubble times after the phase transition is
completed. This modifies the gravitational wave spectrum at large scales. We
also model the initial stirring phase preceding the Kolmogorov cascade, while
earlier works assume that the Kolmogorov spectrum sets in instantaneously. The
continuity in time of the source is relevant for a correct determination of the
peak position of the gravitational wave spectrum. We discuss how the results
depend on assumptions about the unequal-time correlation of the source and
motivate a realistic choice for it. Our treatment gives a similar peak
frequency as previous analyses but the amplitude of the signal is reduced due
to the use of a more realistic power spectrum for the magneto-hydrodynamical
turbulence. For a strongly first-order electroweak phase transition, the signal
is observable with the space interferometer LISA.Comment: 46 pages, 17 figures. Replaced with revised version accepted for
publication in JCA
Solidity of Viscous Liquids
Recent NMR experiments on supercooled toluene and glycerol by Hinze and
Bohmer show that small rotation angles dominate with only few large molecular
rotations. These results are here interpreted by assuming that viscous liquids
are solid-like on short length scales. A characteristic length, the "solidity
length", separates solid-like behavior from liquid-like behavior.Comment: Plain RevTex file, no figure
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