Synchronization in the presence of memory

We study the effect of memory on synchronization of identical chaotic systems driven by common external noises. Our examples show that while in general synchronization transition becomes more difficult to meet when memory range increases, for intermediate ranges the synchronization tendency of systems can be enhanced. Generally the synchronization transition is found to depend on the memory range and the ratio of noise strength to memory amplitude, which indicates on a possibility of optimizing synchronization by memory. We also point out on a close link between dynamics with memory and noise, and recently discovered synchronizing properties of networks with delayed interactions

Tetrahedratic mesophases, chiral order, and helical domains induced by quadrupolar and octupolar interactions

We present an exhaustive account of phases and phase transitions that can be stabilized in the recently introduced generalized Lebwohl-Lasher model with quadrupolar and octupolar microscopic interactions [ L. Longa, G. Pająk and T. Wydro Phys. Rev. E 79 040701 (2009)]. A complete mean-field analysis of the model, along with Monte Carlo simulations allows us to identify four distinct classes of the phase diagrams with a number of multicritical points where, in addition to the standard uniaxial and biaxial nematic phases, the other nematic like phases are stabilized. These involve, among the others, tetrahedratic (T), nematic tetrahedratic (NT), and chiral nematic tetrahedratic (NT*) phases of global Td, D2d, and D2 symmetry, respectively. Molecular order parameters and correlation functions in these phases are determined. We conclude with generalizations of the model that give a simple molecular interpretation of macroscopic regions with opposite optical activity (ambidextrous chirality), observed, e.g., in bent-core systems. An estimate of the helical pitch in the NT* phase is also given

Roundoff-induced Coalescence of Chaotic Trajectories

Numerical experiments recently discussed in the literature show that identical nonlinear chaotic systems linked by a common noise term (or signal) may synchronize after a finite time. We study the process of synchronization as function of precision of calculations. Two generic behaviors of the average coalescence time are identified: exponential or linear. In both cases no synchronization occurs if iterations are done with {\em infinite} precision.Comment: 6 pages, 3 postscript figures, to be published in Phys. Rev.

Close companions around young stars

Multiplicity is a fundamental property that is set early during stellar lifetimes, and it is a stringent probe of the physics of star formation. The distribution of close companions around young stars is still poorly constrained by observations. We present an analysis of stellar multiplicity derived from APOGEE-2 spectra obtained in targeted observations of nearby star-forming regions. This is the largest homogeneously observed sample of high-resolution spectra of young stars. We developed an autonomous method to identify double lined spectroscopic binaries (SB2s). Out of 5007 sources spanning the mass range of $\sim$0.05--1.5 \msun, we find 399 binaries, including both RV variables and SB2s. The mass ratio distribution of SB2s is consistent with a uniform for $q0.95$. The period distribution is consistent with what has been observed in close binaries ($<10$ AU) in the evolved populations. Three systems are found to have $q\sim$0.1, with a companion located within the brown dwarf desert. There are not any strong trends in the multiplicity fraction (MF) as a function of cluster age from 1 to 100 Myr. There is a weak dependence on stellar density, with companions being most numerous at $\Sigma_*\sim30$ stars/pc$^{-2}$, and decreasing in more diffuse regions. Finally, disk-bearing sources are deficient in SB2s (but not RV variables) by a factor of $\sim$2; this deficit is recovered by the systems without disks. This may indicate a quick dispersal of disk material in short-period equal mass systems that is less effective in binaries with lower $q$.Comment: 25 pages, 20 figures. Accepted to A

Bi-modality in the wakes of simplified road vehicles: simulation and feedback control

Large Eddy Simulations are performed to investigate the bi-modal behavior of the flow past three-dimensional square - back bluff bodies. We consider two simplified road vehicle geometries: (i) the squareback Ahmed body and (ii) a simplified square -back truck geometry, with height greater than its width. The Reynolds numbers based on body height is chosen in the range 20,000 - 33,000, such that turbulent separation occurs for both. It is characteristic of such wakes to exhibit slow random switching between asymmetric states. The accessibility of full flow - field data allows us to extract wake flow features that offer new insights. Finally we apply a single-input single - output linear feedback control strategy to the flow. This consists of sensing the base pressure force fluctuations, and actuating a zero- net-mass-flux slot jet just ahead of separation to attenuate base pressure force fluctuations. Its effects on the symmetry of the wake and the mean pressure drag are investigated

Landau-deGennes Theory of Biaxial Nematics Re-examined

Recent experiments report that the long looked for thermotropic biaxial nematic phase has been finally detected in some thermotropic liquid crystalline systems. Inspired by these experimental observations we concentrate on some elementary theoretical issues concerned with the classical sixth-order Landau-deGennes free energy expansion in terms of the symmetric and traceless tensor order parameter $Q_{\alpha\beta}$. In particular, we fully explore the stability of the biaxial nematic phase giving analytical solutions for all distinct classes of the phase diagrams that theory allows. This includes diagrams with triple- and (tri-)critical points and with multiple (reentrant) biaxial- and uniaxial phase transitions. A brief comparison with predictions of existing molecular theories is also given.Comment: 12 pages, 14 figure