2,052 research outputs found
Quasi-periodic solutions of completely resonant forced wave equations
We prove existence of quasi-periodic solutions with two frequencies of
completely resonant, periodically forced nonlinear wave equations with periodic
spatial boundary conditions. We consider both the cases the forcing frequency
is: (Case A) a rational number and (Case B) an irrational number.Comment: 25 pages, 1 figur
Phase separation in quasi incompressible fluids: Cahn-Hilliard model in the Cattaneo-Maxwell framework
In this paper we propose a mathematical model of phase separation for a
quasi-incompressible binary mixture where the spinodal decomposition is induced
by an heat flux governed by the Cattaneo-Maxwell equation. As usual, the phase
separation is considered in the framework of phase field modeling so that the
transition is described by an additional field, the concentration c. The
evolution of concentration is described by the Cahn-Hilliard equation and in
our model is coupled with the Navier-Stokes equation. Since thermal effect are
included, the whole set of evolution equations is set up for the velocity, the
concentration, the temperature and the heat flux. The model is compatible with
thermodynamics and a maximum theorem holds.Comment: Submitted to ZAM
Elastic waves and transition to elastic turbulence in a two-dimensional viscoelastic Kolmogorov flow
We investigate the dynamics of the two-dimensional periodic Kolmogorov flow
of a viscoelastic fluid, described by the Oldroyd-B model, by means of direct
numerical simulations. Above a critical Weissenberg number the flow displays a
transition from stationary to randomly fluctuating states, via periodic ones.
The increasing complexity of the flow in both time and space at progressively
higher values of elasticity accompanies the establishment of mixing features.
The peculiar dynamical behavior observed in the simulations is found to be
related to the appearance of filamental propagating patterns, which develop
even in the limit of very small inertial non-linearities, thanks to the
feedback of elastic forces on the flow.Comment: 10 pages, 14 figure
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Double Compact Objects III: Gravitational Wave Detection Rates
The unprecedented range of second-generation gravitational-wave (GW)
observatories calls for refining the predictions of potential sources and
detection rates. The coalescence of double compact objects (DCOs)---i.e.,
neutron star-neutron star (NS-NS), black hole-neutron star (BH-NS), and black
hole-black hole (BH-BH) binary systems---is the most promising source of GWs
for these detectors. We compute detection rates of coalescing DCOs in
second-generation GW detectors using the latest models for their cosmological
evolution, and implementing inspiral-merger-ringdown (IMR) gravitational
waveform models in our signal-to-noise ratio calculations. We find that: (1)
the inclusion of the merger/ringdown portion of the signal does not
significantly affect rates for NS-NS and BH-NS systems, but it boosts rates by
a factor for BH-BH systems; (2) in almost all of our models BH-BH
systems yield by far the largest rates, followed by NS-NS and BH-NS systems,
respectively, and (3) a majority of the detectable BH-BH systems were formed in
the early Universe in low-metallicity environments. We make predictions for the
distributions of detected binaries and discuss what the first GW detections
will teach us about the astrophysics underlying binary formation and evolution.Comment: published in ApJ, 19 pages, 11 figure
Child Labor and Resistance to Change
We study the interactions between technological innovation, investment in human capital and child labor. In our setting new technologies require new skills and new skills can be developed only through schooling. In a two-stage game, first firms decide on innovation, then households decide on education. In equilibrium the presence of inefficient child labor depends on parameters related to technology, parents’ altruism and the diffusion of firm property. When child labor exists, it is due to either firms reluctance to innovate or households’ unwillingness to educate or both. The optimal policy to eliminate child labor depends crucially on its underlying cause. We show that, in some cases, compulsory schooling laws or a ban on child labor are welfare reducing, while a subsidy to innovation is the right tool to eliminate child labor and increase welfare
Two-dimensional elastic turbulence
We investigate the effect of polymer additives on a two-dimensional
Kolmogorov flow at very low Reynolds numbers by direct numerical simulations of
the Oldroyd-B viscoelastic model. We find that above the elastic instability
threshold the flow develops the elastic turbulence regime recently observed in
experiments. We observe that both the turbulent drag and the Lyapunov exponent
increase with Weissenberg, indicating the presence of a disordered,
turbulent-like mixing flow. The energy spectrum develops a power-law scaling
range with an exponent close to the experimental and theoretical expectations
Horizon Formation in High-Energy Particles Collision
We investigate a classical formation of a trapped surface in 4-dimensional
flat space-time in a process of a non-head-on collision of two high-energy
particles which are treated as Aichelburg-Sexl shock waves. From the condition
of the horizon volume local maximality an equation for the trapped surface is
deduced. Using a known solution on the shocks we find a time-dependent solution
describing the trapped surface between the shocks. We analyze the horizon
appearance and evolution. Obtained results may describe qualitatively the
horizon formation in higher dimensional space-time.Comment: Latex2e, 8 pages, 6 figures, references adde
Combustion dynamics in steady compressible flows
We study the evolution of a reactive field advected by a one-dimensional
compressible velocity field and subject to an ignition-type nonlinearity. In
the limit of small molecular diffusivity the problem can be described by a
spatially discretized system, and this allows for an efficient numerical
simulation. If the initial field profile is supported in a region of size l <
lc one has quenching, i.e., flame extinction, where lc is a characteristic
length-scale depending on the system parameters (reacting time, molecular
diffusivity and velocity field). We derive an expression for lc in terms of
these parameters and relate our results to those obtained by other authors for
different flow settings.Comment: 6 pages, 5 figure
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