30,164 research outputs found
Spontaneous spatial fractal pattern formation in absorptive systems
We predict, for the first time to our knowledge, that purely-absorptive nonlinearity can support spontaneous spatial fractal pattern formation. A passive optical ring cavity with a thin slice of saturable absorber is analyzed. Linear stability analysis yields threshold curves for Turing (static) instabilities with features proposed as characteristics of potential fractal pattern formation. Numerical simulations of the fully-nonlinear dynamics, with both one and two transverse dimensions, confirm theoretical predictions
From continuum mechanics to general relativity
Using ideas from continuum mechanics we construct a theory of gravity. We
show that this theory is equivalent to Einstein's theory of general relativity;
it is also a much faster way of reaching general relativity than the
conventional route. Our approach is simple and natural: we form a very general
model and then apply two physical assumptions supported by experimental
evidence. This easily reduces our construction to a model equivalent to general
relativity. Finally, we suggest a simple way of modifying our theory to
investigate non-standard space-time symmetries.Comment: 7 pages, this essay received a honorable mention in the 2014 essay
competition of the Gravity Research Foundatio
Rotational elasticity
We consider an infinite 3-dimensional elastic continuum whose material points
experience no displacements, only rotations. This framework is a special case
of the Cosserat theory of elasticity. Rotations of material points are
described mathematically by attaching to each geometric point an orthonormal
basis which gives a field of orthonormal bases called the coframe. As the
dynamical variables (unknowns) of our theory we choose the coframe and a
density. We write down the general dynamic variational functional for our
rotational theory of elasticity, assuming our material to be physically linear
but the kinematic model geometrically nonlinear. Allowing geometric
nonlinearity is natural when dealing with rotations because rotations in
dimension 3 are inherently nonlinear (rotations about different axes do not
commute) and because there is no reason to exclude from our study large
rotations such as full turns. The main result of the paper is an explicit
construction of a class of time-dependent solutions which we call plane wave
solutions; these are travelling waves of rotations. The existence of such
explicit closed form solutions is a nontrivial fact given that our system of
Euler-Lagrange equations is highly nonlinear. In the last section we consider a
special case of our rotational theory of elasticity which in the stationary
setting (harmonic time dependence and arbitrary dependence on spatial
coordinates) turns out to be equivalent to a pair of massless Dirac equations
Adhesive for polyester films cures at room temperature, has high initial tack
Quick room-temperature-cure adhesive bonds polyester-insulated flat electrical cables to metal surfaces and various other substrates. The bond strength of the adhesive may be considerably increased by first applying a commercially available polyamide primer to the polyester film
An Incentive Theory of Matching
This paper presents a theory explaining the labor market matching process through microeconomic incentives. There are heterogeneous variations in the characteristics of workers and jobs, and firms face adjustment costs in responding to these variations. Matches and separations are described through firms' job offer and firing decisions and workers' job acceptance and quit decisions. This approach obviates the need for a matching function. On this theoretical basis, we argue that the matching function is vulnerable to the Lucas critique. Our calibrated model for the U.S. economy can account for important empirical regularities that the conventional matching model cannot.matching, incentives, adjustment costs, unemployment, employment, quits, firing, job offers, job acceptance
Charge Inversion of Divalent Ionic Solutions in Silica Channels
Recent experiments (F.H.J. Van Der Heyden et al., PRL 96, 224502 (2006)) of
streaming currents in silica nanochannels with divalent ions report charge
inversion, i.e. interfacial charges attracting counterions in excess of their
own nominal charge, in conflict with existing theoretical and simulation
results. We reveal the mechanism of charge inversion by using all-atomic
molecular dynamics simulations. Our results show excellent agreement with
experiments, both qualitatively and quantitatively. We further discuss the
implications of our study for the general problem of ionic correlations in
solutions as well as in regards of the properties of silica-water interfaces.Comment: 5 pages, 5 figure
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