Broken symmetries and pattern formation in two-frequency forced Faraday waves

We exploit the presence of approximate (broken) symmetries to obtain general scaling laws governing the process of pattern formation in weakly damped Faraday waves. Specifically, we consider a two-frequency forcing function and trace the effects of time translation, time reversal and Hamiltonian structure for three illustrative examples: hexagons, two-mode superlattices, and two-mode rhomboids. By means of explicit parameter symmetries, we show how the size of various three-wave resonant interactions depends on the frequency ratio m:n and on the relative temporal phase of the two driving terms. These symmetry-based predictions are verified for numerically calculated coefficients, and help explain the results of recent experiments.Comment: 4 pages, 6 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

Faraday instability on viscous ferrofluids in a horizontal magnetic field: Oblique rolls of arbitrary orientation

A linear stability analysis of the free surface of a horizontally unbounded ferrofluid layer of arbitrary depth subjected to vertical vibrations and a horizontal magnetic field is performed. A nonmonotonic dependence of the stability threshold on the magnetic field is found at high frequencies of the vibrations. The reasons of the decrease of the critical acceleration amplitude caused by a horizontal magnetic field are discussed. It is revealed that the magnetic field can be used to select the first unstable pattern of Faraday waves. In particular, a rhombic pattern as a superposition of two different oblique rolls can occur. A scaling law is presented which maps all data into one graph for the tested range of viscosities, frequencies, magnetic fields and layer thicknesses.Comment: 8 pages, 6 figures, RevTex

Super-lattice, rhombus, square, and hexagonal standing waves in magnetically driven ferrofluid surface

Standing wave patterns that arise on the surface of ferrofluids by (single frequency) parametric forcing with an ac magnetic field are investigated experimentally. Depending on the frequency and amplitude of the forcing, the system exhibits various patterns including a superlattice and subharmonic rhombuses as well as conventional harmonic hexagons and subharmonic squares. The superlattice arises in a bicritical situation where harmonic and subharmonic modes collide. The rhombic pattern arises due to the non-monotonic dispersion relation of a ferrofluid

Parametrically Excited Surface Waves: Two-Frequency Forcing, Normal Form Symmetries, and Pattern Selection

Motivated by experimental observations of exotic standing wave patterns in the two-frequency Faraday experiment, we investigate the role of normal form symmetries in the pattern selection problem. With forcing frequency components in ratio m/n, where m and n are co-prime integers, there is the possibility that both harmonic and subharmonic waves may lose stability simultaneously, each with a different wavenumber. We focus on this situation and compare the case where the harmonic waves have a longer wavelength than the subharmonic waves with the case where the harmonic waves have a shorter wavelength. We show that in the former case a normal form transformation can be used to remove all quadratic terms from the amplitude equations governing the relevant resonant triad interactions. Thus the role of resonant triads in the pattern selection problem is greatly diminished in this situation. We verify our general results within the example of one-dimensional surface wave solutions of the Zhang-Vinals model of the two-frequency Faraday problem. In one-dimension, a 1:2 spatial resonance takes the place of a resonant triad in our investigation. We find that when the bifurcating modes are in this spatial resonance, it dramatically effects the bifurcation to subharmonic waves in the case of forcing frequencies are in ratio 1/2; this is consistent with the results of Zhang and Vinals. In sharp contrast, we find that when the forcing frequencies are in ratio 2/3, the bifurcation to (sub)harmonic waves is insensitive to the presence of another spatially-resonant bifurcating mode.Comment: 22 pages, 6 figures, late

Amplitude measurements of Faraday waves

A light reflection technique is used to measure quantitatively the surface elevation of Faraday waves. The performed measurements cover a wide parameter range of driving frequencies and sample viscosities. In the capillary wave regime the bifurcation diagrams exhibit a frequency independent scaling proportional to the wavelength. We also provide numerical simulations of the full Navier-Stokes equations, which are in quantitative agreement up to supercritical drive amplitudes of 20%. The validity of an existing perturbation analysis is found to be limited to 2.5% overcriticaly.Comment: 7 figure

Derivation of Xeno-Free and GMP-Grade Human Embryonic Stem Cells – Platforms for Future Clinical Applications

Clinically compliant human embryonic stem cells (hESCs) should be developed in adherence to ethical standards, without risk of contamination by adventitious agents. Here we developed for the first time animal-component free and good manufacturing practice (GMP)-compliant hESCs. After vendor and raw material qualification, we derived xeno-free, GMP-grade feeders from umbilical cord tissue, and utilized them within a novel, xeno-free hESC culture system. We derived and characterized three hESC lines in adherence to regulations for embryo procurement, and good tissue, manufacturing and laboratory practices. To minimize freezing and thawing, we continuously expanded the lines from initial outgrowths and samples were cryopreserved as early stocks and banks. Batch release criteria included DNA-fingerprinting and HLA-typing for identity, characterization of pluripotency-associated marker expression, proliferation, karyotyping and differentiation in-vitro and in-vivo. These hESCs may be valuable for regenerative therapy. The ethical, scientific and regulatory methodology presented here may serve for development of additional clinical-grade hESCs

The contribution of storage medium and membranes in the microwave dielectric response of packed red blood cells suspension

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. During cold storage, packed red blood cells (PRBCs) undergo slow detrimental changes that are collectively termed storage lesion. The aging of the cells causes alterations in the composition of the storage-medium in the PRBC unit. In this paper, we present the comparison of the dielectric response of water in the primary (fresh) storage medium (citrate phosphate dextrose adenine solution, CPDA-1) versus the storage medium from three expired units of PRBCs. Dielectric response of the water molecules has been characterized by dielectric spectroscopy technique in the microwave frequency band (0.5-40 GHz). The dominant phenomenon is the significant increase of the dielectric strength and decrease the relaxation time τ for the samples of the stored medium in comparison with the fresh medium CPDA-1. Furthermore, we demonstrated that removing the ghosts from PRBC hemolysate did not cause the alteration of the dielectric spectrum of water. Thus, the contribution associated with water located near the cell membrane can be neglected in microwave dielectric measurements

On the Existence of Quasipattern Solutions of the Swift-Hohenberg Equation

Quasipatterns (two-dimensional patterns that are quasiperiodic in any spatial direction) remain one of the outstanding problems of pattern formation. As with problems involving quasiperiodicity, there is a small divisor problem. In this paper, we consider 8-fold, 10-fold, 12-fold, and higher order quasipattern solutions of the Swift-Hohenberg equation. We prove that a formal solution, given by a divergent series, may be used to build a smooth quasiperiodic function which is an approximate solution of the pattern-forming partial differential equation (PDE) up to an exponentially small error