23,098 research outputs found
Logarithmic coarsening and glassy behavior in a polymer model with mass-dependent diffusion
We present a model of polymer growth and diffusion with frustration
mechanisms for density increase and with diffusion rates of Arrhenius form with
mass-dependent energy barriers Gamma(m) ~ (m-1)^gamma. It shows non-universal
logarithmic coarsening involving the exponent gamma. Strong-glass behavior is
found in the typical times for disappearance of all polymers up to a given
length, without reference to the equilibrium states of the macroscopic system.
These features are predicted by numerical simulations, scaling theories and an
analytic solution of the master equation within an independent interval
approximation, which also provides the cluster size distribution.Comment: 16 pages, including 7 figures. To be published in Phys. Rev.
Non-universal coarsening and universal distributions in far-from equilibrium systems
Anomalous coarsening in far-from equilibrium one-dimensional systems is
investigated by simulation and analytic techniques. The minimal hard core
particle (exclusion) models contain mechanisms of aggregated particle
diffusion, with rates epsilon<<1, particle deposition into cluster gaps, but
suppressed for the smallest gaps, and breakup of clusters which are adjacent to
large gaps. Cluster breakup rates vary with the cluster length x as kx^alpha.
The domain growth law x ~ (epsilon t)^z, with z=1/(2+alpha) for alpha>0, is
explained by a scaling picture, as well as the scaling of the density of double
vacancies (at which deposition and cluster breakup are allowed) as 1/[t(epsilon
t)^z]. Numerical simulations for several values of alpha and epsilon confirm
these results. An approximate factorization of the cluster configuration
probability is performed within the master equation resulting from the mapping
to a column picture. The equation for a one-variable scaling function explains
the above results. The probability distributions of cluster lengths scale as
P(x)= 1/(epsilon t)^z g(y), with y=x/(epsilon t)^z. However, those
distributions show a universal tail with the form g(y) ~ exp(-y^{3/2}), which
disagrees with the prediction of the independent cluster approximation. This
result is explained by the connection of the vacancy dynamics with the problem
of particle trapping in an infinite sea of traps and is confirmed by
simulation.Comment: 30 pages (10 figures included), to appear in Phys. Rev.
Modeling one-dimensional island growth with mass-dependent detachment rates
We study one-dimensional models of particle diffusion and
attachment/detachment from islands where the detachment rates gamma(m) of
particles at the cluster edges increase with cluster mass m. They are expected
to mimic the effects of lattice mismatch with the substrate and/or long-range
repulsive interactions that work against the formation of long islands.
Short-range attraction is represented by an overall factor epsilon<<1 in the
detachment rates relatively to isolated particle hopping rates [epsilon ~
exp(-E/T), with binding energy E and temperature T]. We consider various
gamma(m), from rapidly increasing forms such as gamma(m) ~ m to slowly
increasing ones, such as gamma(m) ~ [m/(m+1)]^b. A mapping onto a column
problem shows that these systems are zero-range processes, whose steady states
properties are exactly calculated under the assumption of independent column
heights in the Master equation. Simulation provides island size distributions
which confirm analytic reductions and are useful whenever the analytical tools
cannot provide results in closed form. The shape of island size distributions
can be changed from monomodal to monotonically decreasing by tuning the
temperature or changing the particle density rho. Small values of the scaling
variable X=epsilon^{-1}rho/(1-rho) favour the monotonically decreasing ones.
However, for large X, rapidly increasing gamma(m) lead to distributions with
peaks very close to and rapidly decreasing tails, while slowly increasing
gamma(m) provide peaks close to /2$ and fat right tails.Comment: 16 pages, 6 figure
Decentering the cold war in Southern Africa: the portuguese policy of decolonization and détente in Angola and Mozambique (1974–1984)
Contrary to the expectations of many, the break between Portugal and its former colonies in southern Africa was far from complete after decolonization. This article points to three major reasons. First, the impact on relations with Angola and Mozambique of the fragmentation of Portuguese state power and tense polarization in the Portuguese polity after the military coup of 24 April 1974 has been overstated and was far from entirely negative. Second, diplomatic relations were normalized between Portugal, Angola, and Mozambique during the Cold War in a way that has significant parallels with West Germany's Ostpolitik. Portugal's Südpolitik saw a cultural identity worth preserving despite geopolitical divisions and pushed for better relations and deepened ties with these states to help move them away from strict alignment with the Soviet bloc. Third, officers of the Armed Forces Movement that carried out the April 1974 coup exercised a fundamental, positive influence in Portuguese policies toward Angola and Mozambique during decolonization and for years afterward.info:eu-repo/semantics/publishedVersio
High harmonic generation from Bloch electrons in solids
We study the generation of high harmonic radiation by Bloch electrons in a
model transparent solid driven by a strong mid-infrared laser field. We solve
the single-electron time-dependent Schr\"odinger equation (TDSE) using a
velocity-gauge method [New J. Phys. 15, 013006 (2013)] that is numerically
stable as the laser intensity and number of energy bands are increased. The
resulting harmonic spectrum exhibits a primary plateau due to the coupling of
the valence band to the first conduction band, with a cutoff energy that scales
linearly with field strength and laser wavelength. We also find a weaker second
plateau due to coupling to higher-lying conduction bands, with a cutoff that is
also approximately linear in the field strength. To facilitate the analysis of
the time-frequency characteristics of the emitted harmonics, we also solve the
TDSE in a time-dependent basis set, the Houston states [Phys. Rev. B 33, 5494
(1986)], which allows us to separate inter-band and intra-band contributions to
the time-dependent current. We find that the inter-band and intra-band
contributions display very different time-frequency characteristics. We show
that solutions in these two bases are equivalent under an unitary
transformation but that, unlike the velocity gauge method, the Houston state
treatment is numerically unstable when more than a few low lying energy bands
are used
Cluster growth in far-from-equilibrium particle models with diffusion, detachment, reattachment and deposition
Monolayer cluster growth in far-from-equilibrium systems is investigated by
applying simulation and analytic techniques to minimal hard core particle
(exclusion) models. The first model (I), for post-deposition coarsening
dynamics, contains mechanisms of diffusion, attachment, and slow activated
detachment (at rate epsilon<<1) of particles on a line. Simulation shows three
successive regimes of cluster growth: fast attachment of isolated particles;
detachment allowing further (epsilon t)^(1/3) coarsening of average cluster
size; and t^(-1/2) approach to a saturation size going like epsilon^(-1/2).
Model II generalizes the first one in having an additional mechanism of
particle deposition into cluster gaps, suppressed for the smallest gaps. This
model exhibits early rapid filling, leading to slowing deposition due to the
increasing scarcity of deposition sites, and then continued power law (epsilon
t)^(1/2) cluster size coarsening through the redistribution allowed by slow
detachment. The basic (epsilon t)^(1/3) domain growth laws and epsilon^(-1/2)
saturation in model I are explained by a simple scaling picture. A second,
fuller approach is presented which employs a mapping of cluster configurations
to a column picture and an approximate factorization of the cluster
configuration probability within the resulting master equation. This allows
quantitative results for the saturation of model I in excellent agreement with
the simulation results. For model II, it provides a one-variable scaling
function solution for the coarsening probability distribution, and in
particular quantitative agreement with the cluster length scaling and its
amplitude.Comment: Accepted in Phys. Rev. E; 9 pages with figure
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