757 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
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
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
Learning automata with side-effects
Automata learning has been successfully applied in the verification of hardware and software. The size of the automaton model learned is a bottleneck for scalability, and hence optimizations that enable learning of compact representations are important. This paper exploits monads, both as a mathematical structure and a programming construct, to design and prove correct a wide class of such optimizations. Monads enable the development of a new learning algorithm and correctness proofs, building upon a general framework for automata learning based on category theory. The new algorithm is parametric on a monad, which provides a rich algebraic structure to capture non-determinism and other side-effects. We show that this allows us to uniformly capture existing algorithms, develop new ones, and add optimizations
Thermography as a method to detect dental anxiety in oral surgery
(1) Background: the aim of this study was to evaluate if dental anxiety can be measured objectively using thermal infrared imaging. (2) Methods: Patients referred to the Department of Oral Surgery of the University of Naples Federico II and requiring dental extractions were consecutively enrolled in the study. Face thermal distribution images of the patients were acquired before and during their first clinical examination using infrared thermal cameras. The data were analyzed in relation to five regions of interest (ROI) of the patientâs face (nose, ear, forehead, zygoma, chin). The differences in the temperatures assessed between the two measurements for each ROI were evaluated by using paired Tâtest. The Pearson correlation and linear regression were performed to evaluate the association between differences in temperatures and Modified Dental Anxiety Scale (MDAS) questionnaire score, age, and gender; (3) results: sixty participants were enrolled in the study (28 males and 32 females; mean age 57.4 yearâold; age range 18â80 yearâold). Only for nose and ear zone there was a statistically significant difference between measurements at baseline and visit. Correlation between the thermal imaging measurements and the scores of the MDAS questionnaire was found for nose and ear, but not for all of the other regions. (4) Conclusions: the study demonstrated a potential use of thermal infrared imaging to measure dental anxiety
Route to chaos in the weakly stratified Kolmogorov flow
We consider a two-dimensional fluid exposed to Kolmogorovâs forcing cos(ny) and heated from above. The stabilizing effects of temperature are taken into account using the Boussinesq approximation. The fluid with no temperature stratification has been widely studied and, although relying on strong simplifications, it is considered an important tool for the theoretical and experimental study of transition to turbulence. In this paper, we are interested in the set of transitions leading the temperature stratified fluid from the laminar solution [Uâcos(ny),0, T â y] to more complex states until the onset of chaotic states. We will consider Reynolds numbers 0 < Re †30, while the Richardson numbers shall be kept in the regime of weak stratifications (Ri †5 Ă 10 â3 ). We shall first review the non-stratified Kolmogorov flow and find a new period-tripling bifurcation as the precursor of chaotic states. Introducing the stabilizing temperature gradient, we shall observe that higher Re are required to trigger instabilities. More importantly, we shall see new states and phenomena: the newly discovered period-tripling bifurcation is supercritical or subcritical according to Ri; more period-tripling and doubling bifurcations may depart from this new state; strong enough stratifications trigger new regions of chaotic solutions and, on the drifting solution branch, non-chaotic bursting solutions
The Perceived Relationship between Men's Intercollegiate Athletics and General Alumni Giving at Boston College from 1996-2005
Thesis advisor: Philip G. AltbachThis qualitative case study examines the importance of men's intercollegiate athletics for alumni giving at Boston College for a 10-year period, based on the perceptions of 21 Boston College administrators and alumni. This study explores how athletics at Boston College engages alumni in ways that may eventually lead to their financial support of the institution. The findings reveal that study participants perceive football and men's basketball as a major source of engagement for the University's alumni that outrank other alumni activities in terms of reconnecting graduates with the institution. Further, participants support the existence of a relationship between men's intercollegiate athletics and general alumni giving at Boston College, although at varying levels of impact. The findings from this study suggest that engagement with athletic activities and events may serve as the conduit to general alumni giving that supports a host of programs and initiatives that aid the institution in its position as a national research university. Major findings focus on five areas regarding the relationship between men's intercollegiate athletics and general alumni giving at Boston College: the importance of general alumni giving, why alumni give, the importance of men's intercollegiate athletics, what engages alumni, and the influence of men's intercollegiate athletics on general alumni giving.Thesis (PhD) â Boston College, 2010.Submitted to: Boston College. Lynch School of Education.Discipline: Educational Leadership and Higher Education
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