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Register a new userReversible Self-Replication of Spatio-Temporal Kerr Cavity Patterns
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Added by
Carles Mili\\'an Enrique
Publication date
2021
fields
Physics
and research's language is
English
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We uncover a novel and robust phenomenon that causes the gradual self-replication of spatiotemporal Kerr cavity patterns in cylindrical microresonators. These patterns are inherently synchronised multi-frequency combs. Under proper conditions, the axially-localized nature of the patterns leads to a fundamental drift instability that induces transitions amongst patterns with a different number of rows. Self-replications, thus, result in the stepwise addition or removal of individual combs along the cylinders axis. Transitions occur in a fully reversible and, consequently, deterministic way. The phenomenon puts forward a novel paradigm for Kerr frequency comb formation and reveals important insights into the physics of multi-dimensional nonlinear patterns.
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We experimentally and numerically study the use of intensity modulation for the controlled addressing of temporal Kerr cavity solitons. Using a coherently driven fiber ring resonator, we demonstrate that a single temporally broad intensity modulation pulse applied on the cavity driving field permits systematic and efficient writing and erasing of ultrashort cavity solitons. We use numerical simulations based on the mean-field Lugiato-Lefever model to investigate the addressing dynamics, and present a simple physical description of the underlying physics.
We study the spatio-temporal patterns of the proportion of influenza B out of laboratory confirmations of both influenza A and B, with data from 139 countries and regions downloaded from the FluNet compiled by the World Health Organization, from January 2006 to October 2015, excluding 2009. We restricted our analysis to 34 countries that reported more than 2000 confirmations for each of types A and B over the study period. We find that Pearsons correlation is 0.669 between effective distance from Mexico and influenza B proportion among the countries from January 2006 to October 2015. In the United States, influenza B proportion in the pre-pandemic period (2003-2008) negatively correlated with that in the post-pandemic era (2010-2015) at the regional level. Our study limitations are the country-level variations in both surveillance methods and testing policies. Influenza B proportion displayed wide variations over the study period. Our findings suggest that even after excluding 2009s data, the influenza pandemic still has an evident impact on the relative burden of the two influenza types. Future studies could examine whether there are other additional factors. This study has potential implications in prioritizing public health control measures.
Dissipative Kerr cavity solitons (CSs) are persisting pulses of light that manifest themselves in driven optical resonators and that have attracted significant attention over the last decade. Whilst the vast majority of studies have revolved around conditions where the resonator exhibits strong anomalous dispersion, recent studies have shown that solitons with unique characteristics and dynamics can arise under conditions of near-zero-dispersion driving. Here we report on experimental studies of the existence and stability dynamics of Kerr CSs under such conditions. In particular, we experimentally probe the solitons range of existence and examine how their breathing instabilities are modified when group-velocity dispersion is close to zero, such that higher-order dispersion terms play a significant role. On the one hand, our experiments directly confirm earlier theoretical works that predict (i) breathing near-zero-dispersion solitons to emit polychromatic dispersive radiation, and (ii) that higher-order dispersion can extend the range over which the solitons are stable. On the other hand, our experiments also reveal a novel cross-over scenario, whereby the influence of higher-order dispersion changes from stabilising to destabilising. Our comprehensive experiments sample soliton dynamics both in the normal and anomalous dispersion regimes, and our results are in good agreement with numerical simulations and theoretical predictions.
We present a simple mathematical model in which a time averaged pattern emerges out of spatio-temporal chaos as a result of the collective action of chaotic fluctuations. Our evolution equation possesses spatial translational symmetry under a periodic boundary condition. Thus the spatial inhomogeneity of the statistical state arises through a spontaneous symmetry breaking. The transition from a state of homogeneous spatio-temporal chaos to one exhibiting spatial order is explained by introducing a collective viscosity which relates the averaged pattern with a correlation of the fluctuations.
Certain two-component reaction-diffusion systems on a finite interval are known to possess mesa (box-like) steadystate patterns in the singularly perturbed limit of small diffusivity for one of the two solution components. As the diffusivity D of the second component is decreased below some critical value Dc, with Dc = O(1), the existence of a steady-state mesa pattern is lost, triggering the onset of a mesa self-replication event that ultimately leads to the creation of additional mesas. The initiation of this phenomena is studied in detail for a particular scaling limit of the Brusselator model. Near the existence threshold Dc of a single steady-state mesa, it is shown that an internal layer forms in the center of the mesa. The structure of the solution within this internal layer is shown to be governed by a certain core problem, comprised of a single non-autonomous second-order ODE. By analyzing this core problem using rigorous and formal asymptotic methods, and by using the Singular Limit Eigenvalue Problem (SLEP) method to asymptotically calculate small eigenvalues, an analytical verification of the conditions of Nishiura and Ueyema [Physica D, 130, No. 1, (1999), pp. 73-104], believed to be responsible for self-replication, is given. These conditions include: (1) The existence of a saddle-node threshold at which the steady-state mesa pattern disappears; (2) the dimple-shaped eigenfunction at the threshold, believed to be responsible for the initiation of the replication process; and (3) the stability of the mesa pattern above the existence threshold. Finally, we show that the core problem is universal in the sense that it pertains to a class of reaction-diffusion systems, including the Gierer-Meinhardt model with saturation, where mesa self-replication also occurs.
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