847 research outputs found
Thresholds for breather solutions on the Discrete Nonlinear Schr\"odinger Equation with saturable and power nonlinearity
We consider the question of existence of periodic solutions (called breather
solutions or discrete solitons) for the Discrete Nonlinear Schr\"odinger
Equation with saturable and power nonlinearity. Theoretical and numerical
results are proved concerning the existence and nonexistence of periodic
solutions by a variational approach and a fixed point argument. In the
variational approach we are restricted to DNLS lattices with Dirichlet boundary
conditions. It is proved that there exists parameters (frequency or
nonlinearity parameters) for which the corresponding minimizers satisfy
explicit upper and lower bounds on the power. The numerical studies performed
indicate that these bounds behave as thresholds for the existence of periodic
solutions. The fixed point method considers the case of infinite lattices.
Through this method, the existence of a threshold is proved in the case of
saturable nonlinearity and an explicit theoretical estimate which is
independent on the dimension is given. The numerical studies, testing the
efficiency of the bounds derived by both methods, demonstrate that these
thresholds are quite sharp estimates of a threshold value on the power needed
for the the existence of a breather solution. This it justified by the
consideration of limiting cases with respect to the size of the nonlinearity
parameters and nonlinearity exponents.Comment: 26 pages, 10 figure
An Evaluation Of The Relationships Between Resilient Safety Culture, Safety Risk Parameters, And Mindfulness In The International Air Show Community
A convergent mixed-methods approach with data triangulation was utilized to assess the strength of relationships between operational risk factors, hazardous attitude, and resilient safety culture when mediated by mindfulness in the international air show community. An anonymous online survey of respondents’ perceptions, semi-structured interviews of air show experts, focus-group on air show performers, field observation at an air show, and a documentary analysis of air show safety event data was used to collect data. The quantitative findings suggest a good fit of a hypothesized structural model showing the relationships between study variables using structural equation modeling (SEM). Mindfulness (MF) significantly mediates the predictive relationship between hazardous attitudes (HA), risk perception (RP), risk tolerance (RT), and resilient safety culture (RSC) with a high effect size. There was significant predictive relationship between MF and RSC with medium effect size. Demographically, married respondents had significantly lower mean scores on MF compared to single and divorced while single respondents had higher mean scores on RT than married or divorced. The qualitative findings indicate that the RSC of air show performers has a negative correlation with RT and HA. The triangulation suggests military air show background was strongly correlated with RSC, MF, and a negative correlation to HA. This study provides a validated measurement model to assess the relationships between the study variables and fills a gap in the literature related to resilient safety culture in the airshow community. Theoretical and practical implications of this study provide a framework for continuous improvement of safety in the air show community
Self trapping transition for a nonlinear impurity within a linear chain
In the present work we revisit the issue of the self-trapping dynamical
transition at a nonlinear impurity embedded in an otherwise linear lattice. For
our Schr\"odinger chain example, we present rigorous arguments that establish
necessary conditions and corresponding parametric bounds for the transition
between linear decay and nonlinear persistence of a defect mode. The proofs
combine a contraction mapping approach applied in the fully dynamical problem
in the case of a 3D-lattice, together with variational arguments for the
derivation of parametric bounds for the creation of stationary states
associated with the expected fate of the self-trapping dynamical transition.
The results are relevant for both power law nonlinearities and saturable ones.
The analytical results are corroborated by numerical computations.Comment: 16 pages, 7 figures. To be published in Journal of Mathematical
Physic
Επίλυση στοχαστικής Μη γραμμικής εξίσωσης με τη μέθοδο του Πολυωνυμικού Χάους
Εθνικό Μετσόβιο Πολυτεχνείο--Μεταπτυχιακή Εργασία. Διεπιστημονικό-Διατμηματικό Πρόγραμμα Μεταπτυχιακών Σπουδών (Δ.Π.Μ.Σ.) “Υπολογιστική Μηχανική
Conservation laws, exact travelling waves and modulation instability for an extended nonlinear Schr\"odinger equation
We study various properties of solutions of an extended nonlinear
Schr\"{o}dinger (ENLS) equation, which arises in the context of geometric
evolution problems -- including vortex filament dynamics -- and governs
propagation of short pulses in optical fibers and nonlinear metamaterials. For
the periodic initial-boundary value problem, we derive conservation laws
satisfied by local in time, weak (distributional) solutions, and
establish global existence of such weak solutions. The derivation is obtained
by a regularization scheme under a balance condition on the coefficients of the
linear and nonlinear terms -- namely, the Hirota limit of the considered ENLS
model. Next, we investigate conditions for the existence of traveling wave
solutions, focusing on the case of bright and dark solitons. The balance
condition on the coefficients is found to be essential for the existence of
exact analytical soliton solutions; furthermore, we obtain conditions which
define parameter regimes for the existence of traveling solitons for various
linear dispersion strengths. Finally, we study the modulational instability of
plane waves of the ENLS equation, and identify important differences between
the ENLS case and the corresponding NLS counterpart. The analytical results are
corroborated by numerical simulations, which reveal notable differences between
the bright and the dark soliton propagation dynamics, and are in excellent
agreement with the analytical predictions of the modulation instability
analysis.Comment: 27 pages, 5 figures. To be published in Journal of Physics A:
Mathematical and Theoretica
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