Analytic Determination of the Critical Coupling for Oscillators in a Ring

We study a model of coupled oscillators with bidirectional first nearest neighbours coupling with periodic boundary conditions. We show that a stable phase-locked solution is decided by the oscillators at the borders between the major clusters, which merge to form a larger one of all oscillators at the stage of complete synchronization. We are able to locate these four oscillators as well as the size of major clusters in the vicinity of the stage of full synchronization which we show to depend only on the set of initial frequencies. Using the method presented here, we are able to obtain an analytic form of the critical coupling, at which the complete synchronization state occurs.Comment: 5 pages and 3 figure

Nonlocal synchronization in nearest neighbour coupled oscillators

We investigate a system of nearest neighbor coupled oscillators. We show that the nonlocal frequency synchronization, that might appear in such a system, occurs as a consequence of the nearest neighbor coupling. The power spectra of nonadjacent oscillators show that there is no complete coincidence between all frequency peaks of the oscillators in the nonlocal cluster, while the peaks for neighboring oscillators approximately coincide even if they are not yet in a cluster. It is shown that nonadjacent oscillators closer in frequencies, share slow modes with their adjacent oscillators which are neighbors in space. It is also shown that when a direct coupling between non-neighbors oscillators is introduced explicitly, the peaks of the spectra of the frequencies of those non-neighbors coincide

Transition to complete synchronization in phase coupled oscillators with nearest neighbours coupling

We investigate synchronization in a Kuramoto-like model with nearest neighbour coupling. Upon analyzing the behaviour of individual oscillators at the onset of complete synchronization, we show that the time interval between bursts in the time dependence of the frequencies of the oscillators exhibits universal scaling and blows up at the critical coupling strength. We also bring out a key mechanism that leads to phase locking. Finally, we deduce forms for the phases and frequencies at the onset of complete synchronization.Comment: 6 pages, 4 figures, to appear in CHAO

Range expansion with mutation and selection: dynamical phase transition in a two-species Eden model

The colonization of unoccupied territory by invading species, known as range expansion, is a spatially heterogeneous non-equilibrium growth process. We introduce a two-species Eden growth model to analyze the interplay between uni-directional (irreversible) mutations and selection at the expanding front. While the evolutionary dynamics leads to coalescence of both wild-type and mutant clusters, the non-homogeneous advance of the colony results in a rough front. We show that roughening and domain dynamics are strongly coupled, resulting in qualitatively altered bulk and front properties. For beneficial mutations the front is quickly taken over by mutants and growth proceeds Eden-like. In contrast, if mutants grow slower than wild-types, there is an antagonism between selection pressure against mutants and growth by the merging of mutant domains with an ensuing absorbing state phase transition to an all-mutant front. We find that surface roughening has a marked effect on the critical properties of the absorbing state phase transition. While reference models, which keep the expanding front flat, exhibit directed percolation critical behavior, the exponents of the two-species Eden model strongly deviate from it. In turn, the mutation-selection process induces an increased surface roughness with exponents distinct from that of the classical Eden model

Crossover effects in a discrete deposition model with Kardar-Parisi-Zhang scaling

We simulated a growth model in 1+1 dimensions in which particles are aggregated according to the rules of ballistic deposition with probability p or according to the rules of random deposition with surface relaxation (Family model) with probability 1-p. For any p>0, this system is in the Kardar-Parisi-Zhang (KPZ) universality class, but it presents a slow crossover from the Edwards-Wilkinson class (EW) for small p. From the scaling of the growth velocity, the parameter p is connected to the coefficient of the nonlinear term of the KPZ equation, lambda, giving lambda ~ p^gamma, with gamma = 2.1 +- 0.2. Our numerical results confirm the interface width scaling in the growth regime as W ~ lambda^beta t^beta, and the scaling of the saturation time as tau ~ lambda^(-1) L^z, with the expected exponents beta =1/3 and z=3/2 and strong corrections to scaling for small lambda. This picture is consistent with a crossover time from EW to KPZ growth in the form t_c ~ lambda^(-4) ~ p^(-8), in agreement with scaling theories and renormalization group analysis. Some consequences of the slow crossover in this problem are discussed and may help investigations of more complex models.Comment: 16 pages, 7 figures; to appear in Phys. Rev.

Phase correlation and clustering of a nearest neighbour coupled oscillators system

We investigated the phases in a system of nearest neighbour coupled oscillators before complete synchronization in frequency occurs. We found that when oscillators under the influence of coupling form a cluster of the same time-average frequency, their phases start to correlate. An order parameter, which measures this correlation, starts to grow at this stage until it reaches maximum. This means that a time-average phase locked state is reached between the oscillators inside the cluster of the same time-average frequency. At this strength the cluster attracts individual oscillators or a cluster to join in. We also observe that clustering in averaged frequencies orders the phases of the oscillators. This behavior is found at all the transition points studied

Mechanism of action of the intrauterine contraceptive device: evidence for a specific biochemical deficiency in the endometrium.

The precise mechanism of action of the intrauterine contraceptive device (IUCD) is uncertain. In this study we compared the circulating concentrations of a specific endometrial protein, placental protein 14 (PP14), in 62 women with an IUCD and 16 controls. The concentrations of PP14 were substantially lower in IUCD users. There was no difference in the concentrations of another and less specific endometrial protein, insulin-like growth factor binding protein-1 (IGFBP-1). There was no difference in PP14 concentrations between those women with and without intermenstrual bleeding. We conclude that the reduced concentrations of PP14 in IUCD users reflect defective endometrial function in these women, probably related to the contraceptive effect We propose that the measurement of PP14 might be a means of comparing the efficiency of different devices

Nonlocal synchronization in nearest neighbor coupled oscillators

We investigate a system of nearest neighbor coupled oscillators. We show that the nonlocal frequency synchronization, that might appear in such a system, occurs as a consequence of the nearest neighbor coupling. The power spectra of nonadjacent oscillators show that there is no complete coincidence between all frequency peaks of the oscillators in the nonlocal cluster, while the peaks for neighboring oscillators approximately coincide even if they are not yet in a cluster. It is shown that nonadjacent oscillators closer in frequencies, share slow modes with their adjacent oscillators which are neighbors in space. It is also shown that when a direct coupling between non-neighbors oscillators is introduced explicitly, the peaks of the spectra of the frequencies of those non-neighbors coincide

Raised circulating levels of interleukin-6 in women with an intrauterine contraceptive device.

The aim of this study was to determine whether the presence of an intrauterine contraceptive device (IUCD) causes a systemic elevation of interleukin-6 (IL-6). The control group comprised 29 women with normal cycles and who were not using any form of contraception and the study group comprised 74 women who had had an IUCD in place for 10-24 months. Of these, 45 had intermenstrual bleeding. Systemic IL-6 was undetectable (minimum detection limit of the assay is 5 pg/ml) in the control but was raised in 20% of the women fitted with an IUCD (p < 0.01). There was no difference between IL-6 levels in IUCD users who had intermenstrual bleeding and those who did not. These results suggest that the effects of chronic IUCD usage may not be limited to the endometrium. PIP: A case-control study indicated that IUD use causes a systemic elevation of interleukin-6 (IL-6) comparable to that observed in acute and chronic inflammatory conditions. The study group was comprised of 74 women who had had a Copper T-380A device in place for 10-24 months; 45 of these women reported IUD-related intermenstrual bleeding. 29 women with normal cycles who were not using any form of contraception served as controls. IL-6 levels were assessed through immunoradiometric assay. All 29 controls had undetectable circulating IL-6 levels, while 15 (20%) of cases had raised systemic levels of this cytokine. There were no differences in circulating IL-6 levels between cases who did and did not experience intermenstrual bleeding, nor was there a correlation between IL-6 levels and the day of the cycle on which a blood sample was randomly collected. It is unclear whether the circulating IL-6 observed in this study is an "overspill" from locally produced IL-6 or indicative of a more generalized systemic immunoactivation. Recommended are studies that monitor local and systemic production of IL-6 in IUD users in conjunction with other parameters of an inflammatory response, including C-reactive protein