Anomalies of ac driven solitary waves with internal modes: Nonparametric resonances induced by parametric forces

We study the dynamics of kinks in the $\phi^4$ model subjected to a parametric ac force, both with and without damping, as a paradigm of solitary waves with internal modes. By using a collective coordinate approach, we find that the parametric force has a non-parametric effect on the kink motion. Specifically, we find that the internal mode leads to a resonance for frequencies of the parametric driving close to its own frequency, in which case the energy of the system grows as well as the width of the kink. These predictions of the collective coordinate theory are verified by numerical simulations of the full partial differential equation. We finally compare this kind of resonance with that obtained for non-parametric ac forces and conclude that the effect of ac drivings on solitary waves with internal modes is exactly the opposite of their character in the partial differential equation.Comment: To appear in Phys Rev

Polynomial iterative algorithms for coloring and analyzing random graphs

We study the graph coloring problem over random graphs of finite average connectivity $c$. Given a number $q$ of available colors, we find that graphs with low connectivity admit almost always a proper coloring whereas graphs with high connectivity are uncolorable. Depending on $q$, we find the precise value of the critical average connectivity $c_q$. Moreover, we show that below $c_q$ there exist a clustering phase $c\in [c_d,c_q]$ in which ground states spontaneously divide into an exponential number of clusters. Furthermore, we extended our considerations to the case of single instances showing consistent results. This lead us to propose a new algorithm able to color in polynomial time random graphs in the hard but colorable region, i.e when $c\in [c_d,c_q]$.Comment: 23 pages, 10 eps figure

Breathing Current Domains in Globally Coupled Electrochemical Systems: A Comparison with a Semiconductor Model

Spatio-temporal bifurcations and complex dynamics in globally coupled intrinsically bistable electrochemical systems with an S-shaped current-voltage characteristic under galvanostatic control are studied theoretically on a one-dimensional domain. The results are compared with the dynamics and the bifurcation scenarios occurring in a closely related model which describes pattern formation in semiconductors. Under galvanostatic control both systems are unstable with respect to the formation of stationary large amplitude current domains. The current domains as well as the homogeneous steady state exhibit oscillatory instabilities for slow dynamics of the potential drop across the double layer, or across the semiconductor device, respectively. The interplay of the different instabilities leads to complex spatio-temporal behavior. We find breathing current domains and chaotic spatio-temporal dynamics in the electrochemical system. Comparing these findings with the results obtained earlier for the semiconductor system, we outline bifurcation scenarios leading to complex dynamics in globally coupled bistable systems with subcritical spatial bifurcations.Comment: 13 pages, 11 figures, 70 references, RevTex4 accepted by PRE http://pre.aps.or

Resonances in the dynamics of ϕ4\phi^4 kinks perturbed by ac forces

We study the dynamics of $\phi^4$ kinks perturbed by an ac force, both with and without damping. We address this issue by using a collective coordinate theory, which allows us to reduce the problem to the dynamics of the kink center and width. We carry out a careful analysis of the corresponding ordinary differential equations, of Mathieu type in the undamped case, finding and characterizing the resonant frequencies and the regions of existence of resonant solutions. We verify the accuracy of our predictions by numerical simulation of the full partial differential equation, showing that the collective coordinate prediction is very accurate. Numerical simulations for the damped case establish that the strongest resonance is the one at half the frequency of the internal mode of the kink. In the conclusion we discuss on the possible relevance of our results for other systems, especially the sine-Gordon equation. We also obtain additional results regarding the equivalence between different collective coordinate methods applied to this problem.Comment: 23 pages, 7 figures, REVTeX, accepted for publication in Phys. Rev.

Extent of coronary artery disease in patients with stenotic bicuspid versus tricuspid aortic valves

Background Bicuspid aortic valve (BAV) is the most common congenital cardiac malformation, which is often complicated by aortic valve stenosis (AoS). In tricuspid aortic valve (TAV), AoS strongly associates with coronary artery disease (CAD) with common pathophysiological factors. Yet, it remains unclear whether AoS in patients with BAV is also associated with CAD. This study investigated the association between the aortic valve morphological features and the extent of CAD.Methods and Results A single-center study was performed, including all patients who underwent an aortic valve replacement attributable to AoS between 2006 and 2019. Coronary sclerosis was graded on preoperative coronary angiographies using the coronary artery greater even than scoring method, which divides the coronaries in 28 segments and scores nonobstructive (20%-49% sclerosis) and obstructive coronary sclerosis (>49% sclerosis) in each segment. Multivariate analyses were performed, controlling for age, sex, and CAD risk factors. A total of 1296 patients (931 TAV and 365 BAV) were included, resulting in 548 matched patients. Patients with TAV exhibited more CAD risk factors (odds ratio [OR], 2.66; 95% CI, 1.79-3.96; PCardiolog