7,526 research outputs found
Pattern formation driven by cross--diffusion in a 2D domain
In this work we investigate the process of pattern formation in a two
dimensional domain for a reaction-diffusion system with nonlinear diffusion
terms and the competitive Lotka-Volterra kinetics. The linear stability
analysis shows that cross-diffusion, through Turing bifurcation, is the key
mechanism for the formation of spatial patterns. We show that the bifurcation
can be regular, degenerate non-resonant and resonant. We use multiple scales
expansions to derive the amplitude equations appropriate for each case and show
that the system supports patterns like rolls, squares, mixed-mode patterns,
supersquares, hexagonal patterns
Untenable nonstationarity: An assessment of the fitness for purpose of trend tests in hydrology
The detection and attribution of long-term patterns in hydrological time series have been important research topics for decades. A significant portion of the literature regards such patterns as ‘deterministic components’ or ‘trends’ even though the complexity of hydrological systems does not allow easy deterministic explanations and attributions. Consequently, trend estimation techniques have been developed to make and justify statements about tendencies in the historical data, which are often used to predict future events. Testing trend hypothesis on observed time series is widespread in the hydro-meteorological literature mainly due to the interest in detecting consequences of human activities on the hydrological cycle. This analysis usually relies on the application of some null hypothesis significance tests (NHSTs) for slowly-varying and/or abrupt changes, such as Mann-Kendall, Pettitt, or similar, to summary statistics of hydrological time series (e.g., annual averages, maxima, minima, etc.). However, the reliability of this application has seldom been explored in detail. This paper discusses misuse, misinterpretation, and logical flaws of NHST for trends in the analysis of hydrological data from three different points of view: historic-logical, semantic-epistemological, and practical. Based on a review of NHST rationale, and basic statistical definitions of stationarity, nonstationarity, and ergodicity, we show that even if the empirical estimation of trends in hydrological time series is always feasible from a numerical point of view, it is uninformative and does not allow the inference of nonstationarity without assuming a priori additional information on the underlying stochastic process, according to deductive reasoning. This prevents the use of trend NHST outcomes to support nonstationary frequency analysis and modeling. We also show that the correlation structures characterizing hydrological time series might easily be underestimated, further compromising the attempt to draw conclusions about trends spanning the period of records. Moreover, even though adjusting procedures accounting for correlation have been developed, some of them are insufficient or are applied only to some tests, while some others are theoretically flawed but still widely applied. In particular, using 250 unimpacted stream flow time series across the conterminous United States (CONUS), we show that the test results can dramatically change if the sequences of annual values are reproduced starting from daily stream flow records, whose larger sizes enable a more reliable assessment of the correlation structures
Photon localization versus population trapping in a coupled-cavity array
We consider a coupled-cavity array (CCA), where one cavity interacts with a
two-level atom under the rotating-wave approximation. We investigate the
excitation transport dynamics across the array, which arises in the atom's
emission process into the CCA vacuum. Due to the known formation of atom-photon
bound states, partial field localization and atomic population trapping in
general take place. We study the functional dependance on the coupling strength
of these two phenomena and show that the threshold values beyond which they
become significant are different. As the coupling strength grows from zero,
field localization is exhibited first.Comment: 9 pages, 5 figures. Replaced one plot in Fig.
Turing Instability and Pattern Formation in an Activator-Inhibitor System with Nonlinear Diffusion
In this work we study the effect of density dependent nonlinear diffusion on
pattern formation in the Lengyel--Epstein system. Via the linear stability
analysis we determine both the Turing and the Hopf instability boundaries and
we show how nonlinear diffusion intensifies the tendency to pattern formation;
%favors the mechanism of pattern formation with respect to the classical linear
diffusion case; in particular, unlike the case of classical linear diffusion,
the Turing instability can occur even when diffusion of the inhibitor is
significantly slower than activator's one. In the Turing pattern region we
perform the WNL multiple scales analysis to derive the equations for the
amplitude of the stationary pattern, both in the supercritical and in the
subcritical case. Moreover, we compute the complex Ginzburg-Landau equation in
the vicinity of the Hopf bifurcation point as it gives a slow spatio-temporal
modulation of the phase and amplitude of the homogeneous oscillatory solution.Comment: Accepted for publication in Acta Applicandae Mathematica
Isospin singlet (pn) pairing and quartetting contribution to the binding energy of nuclei
Isospin singlet (pn) pairing as well as quartetting in nuclei is expected to
arise near the symmetry line . Empirical values can be deduced from the
nuclear binding energies applying special filters. Within the local density
approximation, theoretical estimates for finite nuclei are obtained from
results for the condensation energy of asymmetric nuclear matter. It is shown
that the isospin singlet condensation energy drops down abruptly for |N-Z|~4
for medium nuclei in the region A=40. Furthermore, alpha-like quartetting and
the influence of excitations are discussed.Comment: 19 pages, 19 figures, submitted to PR
Depression and Anxiety in Roman Catholic Secular Clergy
A nationally selected random sample of Roman Catholic secular priests was investigated using the Center for Epidemiological Studies-Depression scale and the State-Trait Anxiety Inventory Form Y. Additionally, a Self-Report Inventory requested information regarding participants\u27 demographics as well as four categories of predictor variables (i.e., Vocational Satisfaction, Social Support, Spiritual Activities, Physical Environment) potentially associated with depression and anxiety. The study yielded a return rate of 64%. Secular clergy reported significantly greater depression and anxiety (both state and trait) than are reported in the general population. Low Vocational Satisfaction was found to be predictive of depression as well as both state and trait anxiety. Additionally, low Social Support was found to be predictive of state and trait anxiety. When the significant predictor variables were conceptually collapsed, it appeared that both people and place were significantly related to Roman Catholic secular priests\u27 experience of depression and anxiety
Screening Effects in Superfluid Nuclear and Neutron Matter within Brueckner Theory
Effects of medium polarization are studied for pairing in neutron and
nuclear matter. The screening potential is calculated in the RPA limit,
suitably renormalized to cure the low density mechanical instability of nuclear
matter. The selfenergy corrections are consistently included resulting in a
strong depletion of the Fermi surface. All medium effects are calculated based
on the Brueckner theory. The gap is determined from the generalized gap
equation. The selfenergy corrections always lead to a quenching of the gap,
which is enhanced by the screening effect of the pairing potential in neutron
matter, whereas it is almost completely compensated by the antiscreening effect
in nuclear matter.Comment: 8 pages, 6 Postscript figure
Energy-momentum tensor for scalar fields coupled to the dilaton in two dimensions
We clarify some issues related to the evaluation of the mean value of the
energy-momentum tensor for quantum scalar fields coupled to the dilaton field
in two-dimensional gravity. Because of this coupling, the energy-momentum
tensor for the matter is not conserved and therefore it is not determined by
the trace anomaly. We discuss different approximations for the calculation of
the energy-momentum tensor and show how to obtain the correct amount of Hawking
radiation. We also compute cosmological particle creation and quantum
corrections to the Newtonian potential.Comment: 18 pages, RevTex, no figures. Some changes have been added. To appear
in Physical Review
Turing pattern formation in the Brusselator system with nonlinear diffusion
In this work we investigate the effect of density dependent nonlinear
diffusion on pattern formation in the Brusselator system. Through linear
stability analysis of the basic solution we determine the Turing and the
oscillatory instability boundaries. A comparison with the classical linear
diffusion shows how nonlinear diffusion favors the occurrence of Turing pattern
formation. We study the process of pattern formation both in 1D and 2D spatial
domains. Through a weakly nonlinear multiple scales analysis we derive the
equations for the amplitude of the stationary patterns. The analysis of the
amplitude equations shows the occurrence of a number of different phenomena,
including stable supercritical and subcritical Turing patterns with multiple
branches of stable solutions leading to hysteresis. Moreover we consider
traveling patterning waves: when the domain size is large, the pattern forms
sequentially and traveling wavefronts are the precursors to patterning. We
derive the Ginzburg-Landau equation and describe the traveling front enveloping
a pattern which invades the domain. We show the emergence of radially symmetric
target patterns, and through a matching procedure we construct the outer
amplitude equation and the inner core solution.Comment: Physical Review E, 201
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