Phase instabilities in hexagonal patterns

The general form of the amplitude equations for a hexagonal pattern including spatial terms is discussed. At the lowest order we obtain the phase equation for such patterns. The general expression of the diffusion coefficients is given and the contributions of the new spatial terms are analysed in this paper. From these coefficients the phase stability regions in a hexagonal pattern are determined. In the case of Benard-Marangoni instability our results agree qualitatively with numerical simulations performed recently.Comment: 6 pages, 6 figures, to appear in Europhys. Let

Superlattice Patterns in Surface Waves

We report novel superlattice wave patterns at the interface of a fluid layer driven vertically. These patterns are described most naturally in terms of two interacting hexagonal sublattices. Two frequency forcing at very large aspect ratio is utilized in this work. A superlattice pattern ("superlattice-I") consisting of two hexagonal lattices oriented at a relative angle of 22^o is obtained with a 6:7 ratio of forcing frequencies. Several theoretical approaches that may be useful in understanding this pattern have been proposed. In another example, the waves are fully described by two superimposed hexagonal lattices with a wavelength ratio of sqrt(3), oriented at a relative angle of 30^o. The time dependence of this "superlattice-II" wave pattern is unusual. The instantaneous patterns reveal a time-periodic stripe modulation that breaks the 6-fold symmetry at any instant, but the stripes are absent in the time average. The instantaneous patterns are not simply amplitude modulations of the primary standing wave. A transition from the superlattice-II state to a 12-fold quasi-crystalline pattern is observed by changing the relative phase of the two forcing frequencies. Phase diagrams of the observed patterns (including superlattices, quasicrystalline patterns, ordinary hexagons, and squares) are obtained as a function of the amplitudes and relative phases of the driving accelerations.Comment: 15 pages, 14 figures (gif), to appear in Physica

Nonlinear Competition Between Small and Large Hexagonal Patterns

Recent experiments by Kudrolli, Pier and Gollub on surface waves, parametrically excited by two-frequency forcing, show a transition from a small hexagonal standing wave pattern to a triangular ``superlattice'' pattern. We show that generically the hexagons and the superlattice wave patterns bifurcate simultaneously from the flat surface state as the forcing amplitude is increased, and that the experimentally-observed transition can be described by considering a low-dimensional bifurcation problem. A number of predictions come out of this general analysis.Comment: 4 pages, RevTex, revised, to appear in Phys. Rev. Let

Conjugating Biotin to Ruthenium(II) Arene Units via Phosphine Ligand Functionalization

Two-step functionalization of 4-diphenylphosphino benzoic acid with biotin afforded 2-(biotinyloxy)ethyl 4-(diphenylphosphanyl)benzoate (LP), that was subsequently used to synthesize the Ru(II) arene complexes [RuCl2(η6-p-cymene)(LP)] (1), [Ru(C2O4)(η6-p-cymene)(LP)] (2) and [Ru(curc)(η6-p-cymene)(LP)]NO3 ([3]NO3), the latter incorporating curcumin (curcH) as an additional bioactive fragment. [Ru(curc)(η6-p-cymene)(PPh3)]NO3 ([4]NO3) was also prepared as a reference compound. Compounds 2 and [3]NO3 exhibited excellent stability in water/DMSO solution while being slowly activated in the cell culture medium over 72 hours. Together with LP, they were therefore assessed for their antiproliferative activity towards a panel of cancer cell lines, with different levels of biotin transporter expression. The apparent affinity of the compounds towards avidin varies, and their antiproliferative activity does not correlate with biotin transporter expression, although it is systematically enhanced when biotin-free cell culture medium is used

Exploring the anticancer potential of diiron bis-cyclopentadienyl complexes with bridging hydrocarbyl ligands: Behavior in aqueous media and in vitro cytotoxicity

A series of diiron complexes based on the [Fe2Cp2(CO)x] skeleton (Cp = \u3b75-C5H5, x = 2, 3; \u3b74-C5H5Ph in place of one Cp in one case) and containing different bridging hydrocarbyl ligands (aminocarbyne, thiocarbyne, allenyl) were preliminarily investigated for their anticancer potential. The water solubility, stability in water and in the presence of a cell culture medium, and octanol/water partition coefficient were evaluated by spectroscopic techniques. The cytotoxicity was assessed in vitro toward the human ovarian carcinoma cell line A2780, the human triple negative breast cancer cell line MDA-MB-231, and the human vascular smooth muscle cell line SMC. Some aminocarbyne complexes exhibited a potent cytotoxicity, with IC50 values in the low micromolar/nanomolar range, and a strong selectivity for the A2780 cells in comparison to the SMC cell line. Several experiments were carried out in order to give insight into the mode of action of selected compounds, including an assessment of catalytic NADH oxidation and ROS production and studies of binding with DNA and with a model protein

Testing geological proxies for deep‐time tidal model simulations

Tides are a key driver of a range of Earth system processes, and we now have the capacity to simulate tidal dynamics on a range of temporal and spatial scales. Deep‐time tidal model simulations have been used to provide insight into past ocean circulation patterns, evolution of life and the developments of the Earth‐Moon system's orbital configuration. However, these tidal model simulations are relatively poorly constrained and validated because of a lack of readily available proxies. The feasibility of using two types of proxy is explored here; (1) sedimentary deposits which can directly estimate palaeotidal ranges, and (2) black shale, to constrain three palaeotidal model simulations for different time slices. Specifically, three palaeotidal range proxies were used for the early Devonian (400 Ma), three palaeotidal range proxies and five black shales for the lower Jurassic (185 Ma), and eight black shales for the early Cretaceous (95 Ma). Both tidal proxies confirm the tidal model results in most locations. The model results for 400 Ma and 185 Ma matched 2/3 of the palaeotidal range proxies for each of these periods. The locations of black shale were compared with tidal front locations predicted by the model outputs based on the Simpson–Hunter parameter and the model results from 95 to 185 Ma agree with the black shale proxies in 10/13 of the locations. In the cases where there is a disagreement, the model resolution is probably too low to fully resolve the details of the coastal topography, or—in one case—the palaeobathymetry is incorrect. Consequently, it is argued that it is worth expanding this type of work, and that such data can be used to validate both models and reconstructions

Spatial correlations in hexagons generated via a Kerr nonlinearity

We consider the hexagonal pattern forming in the cross-section of an optical beam produced by a Kerr cavity, and we study the quantum correlations characterizing this structure. By using arguments related to the symmetry broken by the pattern formation, we identify a complete scenario of six-mode entanglement. Five independent phase quadratures combinations, connecting the hexagonal modes, are shown to exhibit sub-shot-noise fluctuations. By means of a non-linear quantum calculation technique, quantum correlations among the mode photon numbers are demonstrated and calculated.Comment: ReVTeX file, 20 pages, 7 eps figure

Pattern formation in 2-frequency forced parametric waves

We present an experimental investigation of superlattice patterns generated on the surface of a fluid via parametric forcing with 2 commensurate frequencies. The spatio-temporal behavior of 4 qualitatively different types of superlattice patterns is described in detail. These states are generated via a number of different 3--wave resonant interactions. They occur either as symmetry--breaking bifurcations of hexagonal patterns composed of a single unstable mode or via nonlinear interactions between the two primary unstable modes generated by the two forcing frequencies. A coherent picture of these states together with the phase space in which they appear is presented. In addition, we describe a number of new superlattice states generated by 4--wave interactions that arise when symmetry constraints rule out 3--wave resonances.Comment: The paper contains 34 pages and 53 figures and provides an extensive review of both the theoretical and experimental work peformed in this syste