The Effect of On-Site Potentials on Supratransmission in One-Dimensional Hamiltonian Lattices.

We investigated a class of one-dimensional (1D) Hamiltonian N-particle lattices whose binary interactions are quadratic and/or quartic in the potential. We also included on-site potential terms, frequently considered in connection with localization phenomena, in this class. Applying a sinusoidal perturbation at one end of the lattice and an absorbing boundary on the other, we studied the phenomenon of supratransmission and its dependence on two ranges of interactions, 0<α<∞ and 0<ß<∞, as the effect of the on-site potential terms of the Hamiltonian varied. In previous works, we studied the critical amplitude As(α,Ω) at which supratransmission occurs, for one range parameter α, and showed that there was a sharp threshold above which energy was transmitted in the form of large-amplitude nonlinear modes, as long as the driving frequency Ω lay in the forbidden band-gap of the system. In the absence of on-site potentials, it is known that As(α,Ω) increases monotonically the longer the range of interactions is (i.e., as α⟶0). However, when on-site potential terms are taken into account, As(α,Ω) reaches a maximum at a low value of α that depends on Ω, below which supratransmission thresholds decrease sharply to lower values. In this work, we studied this phenomenon further, as the contribution of the on-site potential terms varied, and we explored in detail their effect on the supratransmission thresholds.

Prediction of individual implant bone levels and the existence of implant "phenotypes".

OBJECTIVES: To cluster implants placed in patients of a private practice and identify possible implant "phenotypes" and predictors of individual implant mean bone levels (IIMBL). MATERIALS AND METHODS: Clinical and radiographical variables were collected from 72 implant-treated patients with 237 implants and a mean 7.4 ± 3.5 years of function. We clustered implants using the k-means method guided by multidimensional unfolding. For predicting IIMBL, we used principal component analysis (PCA) as a variable reduction method for an ensemble selection (ES) and a support vector machines models (SVMs). Network analysis investigated variable interactions. RESULTS: We identified a cluster of implants susceptible to peri-implantitis (96% of the implants in the cluster were affected by peri-implantitis) and two overlapping clusters of implants resistant to peri-implantitis. The cluster susceptible to peri-implantitis showed a mean IIMBL of 5.2 mm and included implants placed mainly in the lower front jaw and in mouths having a mean of eight teeth. PCA extracted the parameters such as number of teeth, full-mouth plaque scores, implant surface, periodontitis severity, age and diabetes as significant in explaining the data variability. ES and SVMs showed good results in predicting IIMBL (root-mean-squared error of 0.133 and 0.149, 10-fold cross-validation error of 0.147 and 0.150, respectively). Network analysis revealed limited interdependencies of variables among peri-implantitis-affected and non-affected implants and supported the hypothesis of the existence of distinct implant "phenotypes." CONCLUSION: Two implant "phenotypes" were identified, one with susceptibility and another with resistance to peri-implantitis. Prediction of IIMBL could be achieved by using six variables.

Peri-implantitis: a complex condition with non-linear characteristics.

AIM: To cluster peri-implantitis patients and explore non-linear patterns in peri-implant bone levels. MATERIALS AND METHODS: Clinical and radiographic variables were retrieved from 94 implant-treated patients (340 implants, mean 7.1 ± 4.1 years in function). Kernel probability density estimations on patient mean peri-implant bone levels were used to identify patient clusters. Inter-relationships of all variables were evaluated by principal component analysis; a k-nearest neighbours method was performed for supervised prediction of implant bone levels at the patient level. Self-similar patterns of mean bone level per implant from different jaw bone sites were examined and their associated fractal dimensions were estimated. RESULTS: Two clusters of implant-treated patients were identified, one at patient mean bone levels of 1.7 mm and another at 4.0 mm. Five of thirteen available variables (number of teeth, age, gender, periodontitis severity, years of implant service), were predictive for peri-implant bone levels. A high jaw bone fractal dimension was associated with less severe peri-implantitis. CONCLUSIONS: Non-linearity of peri-implantitis was evidenced by finding different peri-implant bone levels between two main clusters of implant-treated patients and among six different jaw bone sites. The patient mean peri-implant bone levels were predicted from five variables and confirmed complexity for peri-implantitis.

Stability of simple periodic orbits and chaos in a Fermi-Pasta-Ulam lattice.

We investigate the connection between local and global dynamics in the Fermi-Pasta-Ulam (FPU) beta model from the point of view of stability of its simplest periodic orbits (SPO's). In particular, we show that there is a relatively high-q mode [q = 2(N + 1)/3] of the linear lattice, having one particle fixed every two oppositely moving ones (called SPO2 here), which can be exactly continued to the nonlinear case for N = 5 + 3m, m = 0,1,2,, and whose first destabilization E(2u), as the energy (or beta) increases for any fixed N, practically coincides with the onset of a "weak" form of chaos preceding the breakdown of FPU recurrences, as predicted recently in a similar study of the continuation of a very low (q = 3) mode of the corresponding linear chain. This energy threshold per particle behaves like E(2u)/N alpha N(-2). We also follow exactly the properties of another SPO [with q = (N + 1)/2] in which fixed and moving particles are interchanged (called SPO1 here) and which destabilizes at higher energies than SPO2, since E(1u)/N alpha N(-1). We find that, immediately after their first destabilization, these SPO's have different (positive) Lyapunov spectra in their vicinity. However, as the energy increases further (at fixed N), these spectra converge to the same exponentially decreasing function, thus providing strong evidence that the chaotic regions around SPO1 and SPO2 have "merged" and large-scale chaos has spread throughout the lattice. Since these results hold for N arbitrarily large, they suggest a direct approach by which one can use local stability analysis of SPO's to estimate the energy threshold at which a transition to ergodicity occurs and thermodynamic properties such as Kolmogorov-Sinai entropies per particle can be computed for similar one-dimensional lattices.

The Asymmetric Active Coupler: Stable Nonlinear Supermodes and Directed Transport.

We consider the asymmetric active coupler (AAC) consisting of two coupled dissimilar waveguides with gain and loss. We show that under generic conditions, not restricted by parity-time symmetry, there exist finite-power, constant-intensity nonlinear supermodes (NS), resulting from the balance between gain, loss, nonlinearity, coupling and dissimilarity. The system is shown to possess non-reciprocal dynamics enabling directed power transport functionality.

Stability and dynamics of nonautonomous systems with pulsed nonlinearity.

We study the dynamics of a class of nonautonomous systems with pulsed nonlinearity that consist of a periodic sequence of linear and nonlinear autonomous systems, each one acting alone in a different time or space interval. We focus on the investigation of control capabilities of such systems in terms of altering their fundamental dynamical properties by appropriate parameter selections. For the case of single oscillators, the stability of the zero solution as well as the phase space topology is shown to drastically depend on parameters such as the frequency of the linear oscillations and the durations of the linear and nonlinear intervals. In cases of chain of coupled oscillators with pulsed onsite nonlinearity, it is shown that appropriate parameter selections can stabilize an otherwise unstable zero background allowing for the existence of dynamically robust localized excitations, whose evolution properties can now be explicitly determined and controlled.

Weak chaos and the "melting transition" in a confined microplasma system.

We present results demonstrating the occurrence of changes in the collective dynamics of a Hamiltonian system which describes a confined microplasma characterized by long-range Coulomb interactions. In its lower energy regime, we first detect macroscopically the transition from a "crystallinelike" to a "liquidlike" behavior, which we call the "melting transition." We then proceed to study this transition using a microscopic chaos indicator called the smaller alignment index (SALI), which utilizes two deviation vectors in the tangent dynamics of the flow and is nearly constant for ordered (quasiperiodic) orbits, while it decays exponentially to zero for chaotic orbits as exp[-(lambda(1)-lambda(2))t], where lambda(1)>lambda(2)>0 are the two largest Lyapunov exponents. During the melting phase, SALI exhibits a peculiar stairlike decay to zero, reminiscent of "sticky" orbits of Hamiltonian systems near the boundaries of resonance islands. This alerts us to the importance of the Deltalambda=lambda(1)-lambda(2) variations in that regime and helps us identify the energy range over which "melting" occurs as a multistage diffusion process through weakly chaotic layers in the phase space of the microplasma. Additional evidence supporting further the above findings is given by examining the GALI(k) indices, which generalize SALI (=GALI(2)) to the case of k>2 deviation vectors and depend on the complete spectrum of Lyapunov exponents of the tangent flow about the reference orbit.

An adaptive way for improving noise reduction using local geometric projection.

We propose an adaptive way to improve noise reduction by local geometric projection. From the neighborhood of each candidate point in phase space, we identify the best subspace that the point will be orthogonally projected to. The signal subspace is formed by the most significant eigendirections of the neighborhood, while the less significant ones define the noise subspace. We provide a simple criterion to separate the most significant eigendirections from the less significant ones. This criterion is based on the maximum logarithmic difference between the neighborhood eigendirection lengths, and the assumption that there is at least one eigendirection that corresponds to the noise subspace. In this way, we take into account the special characteristics of each neighborhood and introduce a more successful noise reduction technique. Results are presented for a chaotic time series of the Henon map and Ikeda map, as well as on the Nasdaq Composite index.