6,086 research outputs found
Duality between Ahlfors-Liouville and Khas'minskii properties for nonlinear equations
In recent years, the study of the interplay between (fully) non-linear
potential theory and geometry received important new impulse. The purpose of
this work is to move a step further in this direction by investigating
appropriate versions of parabolicity and maximum principles at infinity for
large classes of non-linear (sub)equations on manifolds. The main goal is
to show a unifying duality between such properties and the existence of
suitable -subharmonic exhaustions, called Khas'minskii potentials, which is
new even for most of the "standard" operators arising from geometry, and
improves on partial results in the literature. Applications include new
characterizations of the classical maximum principles at infinity (Ekeland,
Omori-Yau and their weak versions by Pigola-Rigoli-Setti) and of conservation
properties for stochastic processes (martingale completeness). Applications to
the theory of submanifolds and Riemannian submersions are also discussed.Comment: 67 pages. Final versio
The Impact of Paternity Leave on Long-term Father Involvement
Using Norwegian registry data we investigate how paternity leave affects fathersâ long-term earnings. In 1993 Norway introduced a paternity quota of the paid parental leave. We estimate a difference-in-differences model which exploits differences in fathers' exposure to the paternity quota. Our analysis suggests that four weeks paternity leave during the childâs first year decreases fathersâ future earnings by 2.1 percent. Importantly, this effect persists up until our last point of observation when the child is five years old. The earnings effect is consistent with increased long-term father involvement, as fathers shift time and effort from market to home production. In an investigation of Norwegian time use data we find additional evidence for this hypothesis.father involvement, household production, parental leave
The impact of paternity leave on long-term father involvement
.Household production; Father involvement; paternal leave
A general theorem on the divergence of vortex beams
The propagation and divergence properties of beams carrying orbital angular
momentum (OAM) play a crucial role in many applications. Here we present a
general study on the divergence of optical beams with OAM. We show that the
mean absolute value of the OAM imposes a lower bound on the value of the beam
divergence. We discuss our results for two different definitions of the
divergence, the so called rms or encircled-energy. The bound on the rms
divergence can be expressed as a generalized uncertainty principle, with
applications in long-range communication, microscopy and 2D quantum systems.Comment: RevTex, published versio
A Map-Reduce Parallel Approach to Automatic Synthesis of Control Software
Many Control Systems are indeed Software Based Control Systems, i.e. control
systems whose controller consists of control software running on a
microcontroller device. This motivates investigation on Formal Model Based
Design approaches for automatic synthesis of control software.
Available algorithms and tools (e.g., QKS) may require weeks or even months
of computation to synthesize control software for large-size systems. This
motivates search for parallel algorithms for control software synthesis.
In this paper, we present a Map-Reduce style parallel algorithm for control
software synthesis when the controlled system (plant) is modeled as discrete
time linear hybrid system. Furthermore we present an MPI-based implementation
PQKS of our algorithm. To the best of our knowledge, this is the first parallel
approach for control software synthesis.
We experimentally show effectiveness of PQKS on two classical control
synthesis problems: the inverted pendulum and the multi-input buck DC/DC
converter. Experiments show that PQKS efficiency is above 65%. As an example,
PQKS requires about 16 hours to complete the synthesis of control software for
the pendulum on a cluster with 60 processors, instead of the 25 days needed by
the sequential algorithm in QKS.Comment: To be submitted to TACAS 2013. arXiv admin note: substantial text
overlap with arXiv:1207.4474, arXiv:1207.409
A constitutive model for simple shear of dense frictional suspensions
Discrete particle simulations are used to study the shear rheology of dense,
stabilized, frictional particulate suspensions in a viscous liquid, toward
development of a constitutive model for steady shear flows at arbitrary stress.
These suspensions undergo increasingly strong continuous shear thickening (CST)
as solid volume fraction increases above a critical volume fraction, and
discontinuous shear thickening (DST) is observed for a range of . When
studied at controlled stress, the DST behavior is associated with non-monotonic
flow curves of the steady-state stress as a function of shear rate. Recent
studies have related shear thickening to a transition between mostly lubricated
to predominantly frictional contacts with the increase in stress. In this
study, the behavior is simulated over a wide range of the dimensionless
parameters , and , with the dimensionless shear stress and the coefficient of
interparticle friction: the dimensional stress is , and , where is the magnitude of repulsive force at contact
and is the particle radius. The data have been used to populate the model
of the lubricated-to-frictional rheology of Wyart and Cates [Phys. Rev.
Lett.{\bf 112}, 098302 (2014)], which is based on the concept of two viscosity
divergences or \textquotedblleft jamming\textquotedblright\ points at volume
fraction (random close packing) for the
low-stress lubricated state, and at for
any nonzero in the frictional state; a generalization provides the normal
stress response as well as the shear stress. A flow state map of this material
is developed based on the simulation results.Comment: 12 pages, 10 figure
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