16,916 research outputs found
On the Executability of Interactive Computation
The model of interactive Turing machines (ITMs) has been proposed to
characterise which stream translations are interactively computable; the model
of reactive Turing machines (RTMs) has been proposed to characterise which
behaviours are reactively executable. In this article we provide a comparison
of the two models. We show, on the one hand, that the behaviour exhibited by
ITMs is reactively executable, and, on the other hand, that the stream
translations naturally associated with RTMs are interactively computable. We
conclude from these results that the theory of reactive executability subsumes
the theory of interactive computability. Inspired by the existing model of ITMs
with advice, which provides a model of evolving computation, we also consider
RTMs with advice and we establish that a facility of advice considerably
upgrades the behavioural expressiveness of RTMs: every countable transition
system can be simulated by some RTM with advice up to a fine notion of
behavioural equivalence.Comment: 15 pages, 0 figure
Skating on slippery ice
The friction of a stationary moving skate on smooth ice is investigated, in
particular in relation to the formation of a thin layer of water between skate
and ice. It is found that the combination of ploughing and sliding gives a
friction force that is rather insensitive for parameters such as velocity and
temperature. The weak dependence originates from the pressure adjustment inside
the water layer. For instance, high velocities, which would give rise to high
friction, also lead to large pressures, which, in turn, decrease the contact
zone and so lower the friction. The theory is a combination and completion of
two existing but conflicting theories on the formation of the water layer.Comment: 26 pages, 8 figures Posted at SciPos
Reptation in the Rubinstein-Duke model: the influence of end-reptons dynamics
We investigate the Rubinstein-Duke model for polymer reptation by means of
density-matrix renormalization group techniques both in absence and presence of
a driving field. In the former case the renewal time \tau and the diffusion
coefficient D are calculated for chains up to N=150 reptons and their scaling
behavior in N is analyzed. Both quantities scale as powers of N: and with the asymptotic exponents z=3 and x=2, in agreement
with the reptation theory. For an intermediate range of lengths, however, the
data are well-fitted by some effective exponents whose values are quite
sensitive to the dynamics of the end reptons. We find 2.7 <z< 3.3 and 1.8 <x<
2.1 for the range of parameters considered and we suggest how to influence the
end reptons dynamics in order to bring out such a behavior. At finite and not
too small driving field, we observe the onset of the so-called band inversion
phenomenon according to which long polymers migrate faster than shorter ones as
opposed to the small field dynamics. For chains in the range of 20 reptons we
present detailed shapes of the reptating chain as function of the driving field
and the end repton dynamics.Comment: RevTeX 12 Pages and 14 figure
A penalty method for PDE-constrained optimization in inverse problems
Many inverse and parameter estimation problems can be written as
PDE-constrained optimization problems. The goal, then, is to infer the
parameters, typically coefficients of the PDE, from partial measurements of the
solutions of the PDE for several right-hand-sides. Such PDE-constrained
problems can be solved by finding a stationary point of the Lagrangian, which
entails simultaneously updating the paramaters and the (adjoint) state
variables. For large-scale problems, such an all-at-once approach is not
feasible as it requires storing all the state variables. In this case one
usually resorts to a reduced approach where the constraints are explicitly
eliminated (at each iteration) by solving the PDEs. These two approaches, and
variations thereof, are the main workhorses for solving PDE-constrained
optimization problems arising from inverse problems. In this paper, we present
an alternative method that aims to combine the advantages of both approaches.
Our method is based on a quadratic penalty formulation of the constrained
optimization problem. By eliminating the state variable, we develop an
efficient algorithm that has roughly the same computational complexity as the
conventional reduced approach while exploiting a larger search space. Numerical
results show that this method indeed reduces some of the non-linearity of the
problem and is less sensitive the initial iterate
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