Existence threshold for the ac-driven damped nonlinear Schr\"odinger solitons

It has been known for some time that solitons of the externally driven, damped nonlinear Schr\"odinger equation can only exist if the driver's strength, $h$, exceeds approximately $(2/ \pi) \gamma$, where $\gamma$ is the dissipation coefficient. Although this perturbative result was expected to be correct only to the leading order in $\gamma$, recent studies have demonstrated that the formula $h_{thr}= (2 /\pi) \gamma$ gives a remarkably accurate description of the soliton's existence threshold prompting suggestions that it is, in fact, exact. In this note we evaluate the next order in the expansion of $h_{thr}(\gamma)$ showing that the actual reason for this phenomenon is simply that the next-order coefficient is anomalously small: $h_{thr}=(2/ \pi) \gamma + 0.002 \gamma^3$. Our approach is based on a singular perturbation expansion of the soliton near the turning point; it allows to evaluate $h_{thr}(\gamma)$ to all orders in $\gamma$ and can be easily reformulated for other perturbed soliton equations.Comment: 8 pages in RevTeX; 5 figures in ps format included in the text. To be published in Physica

Effect of Disorder on Synchronization in Prototype 2-Dimensional Josephson Arrays

We study the effects of quenched disorder on the dynamics of two-dimensional arrays of overdamped Josephson junctions. Disorder in both the junction critical currents and resistances is considered. Analytical results for small arrays are used to identify a physical mechanism which promotes frequency locking across each row of the array, and to show that no such locking mechanism exists between rows. The intrarow locking mechanism is surprisingly strong, so that a row can tolerate large amounts of disorder before frequency locking is destroyed

The Mechanism of Ciliary Stimulation by Acetylcholine: Roles of Calcium, PKA, and PKG

Stimulation of ciliary cells through muscarinic receptors leads to a strong biphasic enhancement of ciliary beat frequency (CBF). The main goal of this work is to delineate the chain of molecular events that lead to the enhancement of CBF induced by acetylcholine (ACh). Here we show that the Ca2+, cGMP, and cAMP signaling pathways are intimately interconnected in the process of cholinergic ciliary stimulation. ACh induces profound time-dependent increase in cGMP and cAMP concentrations mediated by the calcium–calmodulin complex. The initial strong CBF enhancement in response to ACh is mainly governed by PKG and elevated calcium. The second phase of CBF enhancement induced by ACh, a stable moderately elevated CBF, is mainly regulated by PKA in a Ca2+-independent manner. Inhibition of either guanylate cyclase or of PKG partially attenuates the response to ACh of [Ca2+]i, but completely abolishes the response of CBF. Inhibition of PKA moderately attenuates and significantly shortens the responses to ACh of both [Ca2+]i and CBF. In addition, PKA facilitates the elevation in [Ca2+]i and cGMP levels induced by ACh, whereas an unimpeded PKG activity is essential for CBF enhancement mediated by either Ca2+ or PKA

Properties of Shannon and R\'{e}nyi entropies of the Poisson distribution as the functions of intensity parameter

We consider two types of entropy, namely, Shannon and R\'{e}nyi entropies of the Poisson distribution, and establish their properties as the functions of intensity parameter. More precisely, we prove that both entropies increase with intensity. While for Shannon entropy the proof is comparatively simple, for R\'{e}nyi entropy, which depends on additional parameter $\alpha>0$, we can characterize it as nontrivial. The proof is based on application of Karamata's inequality to the terms of Poisson distribution.Comment: 23 pages, 8 figure