A Variational Principle for Eigenvalue Problems of Hamiltonian Systems

We consider the bifurcation problem $u'' + \lambda u = N(u)$ with two point boundary conditions where $N(u)$ is a general nonlinear term which may also depend on the eigenvalue $\lambda$. We give a variational characterization of the bifurcating branch $\lambda$ as a function of the amplitude of the solution. As an application we show how it can be used to obtain simple approximate closed formulae for the period of large amplitude oscillations.Comment: 10 pages Revtex, 2 figures include

Rotary bistable and Parametrically Excited Vibration Energy Harvesting

Parametric resonance is a type of nonlinear vibration phenomenon [1], [2] induced from the periodic modulation of at least one of the system parameters and has the potential to exhibit interesting higher order nonlinear behaviour [3]. Parametrically excited vibration energy harvesters have been previously shown to enhance both the power amplitude [4] and the frequency bandwidth [5] when compared to the conventional direct resonant approach. However, to practically activate the more profitable regions of parametric resonance, additional design mechanisms [6], [7] are required to overcome a critical initiation threshold amplitude. One route is to establish an autoparametric system where external direct excitation is internally coupled to parametric excitation [8]. For a coupled two degrees of freedom (DoF) oscillatory system, principal autoparametric resonance can be achieved when the natural frequency of the first DoF f1 is twice that of the second DoF f2 and the external excitation is in the vicinity of f1. This paper looks at combining rotary and translatory motion and use autoparametric resonance phenomena

Geometric Resonances in Bose-Einstein Condensates with Two- and Three-Body Interactions

We investigate geometric resonances in Bose-Einstein condensates by solving the underlying time-dependent Gross-Pitaevskii equation for systems with two- and three-body interactions in an axially-symmetric harmonic trap. To this end, we use a recently developed analytical method [Phys. Rev. A 84, 013618 (2011)], based on both a perturbative expansion and a Poincar\'e-Lindstedt analysis of a Gaussian variational approach, as well as a detailed numerical study of a set of ordinary differential equations for variational parameters. By changing the anisotropy of the confining potential, we numerically observe and analytically describe strong nonlinear effects: shifts in the frequencies and mode coupling of collective modes, as well as resonances. Furthermore, we discuss in detail the stability of a Bose-Einstein condensate in the presence of an attractive two-body interaction and a repulsive three-body interaction. In particular, we show that a small repulsive three-body interaction is able to significantly extend the stability region of the condensate.Comment: 27 pages, 13 figure

Negative Resistance in Brownian Transport

We prove that negative incremental resistance cannot occur on 1D spaces like the circle or the line; we construct an explicit two-dimensional model on the cylinder, and its collapse into a branched 1D backbone. We derive an accurate numerical method for solving our 2D model, and discuss the relevance of the model to biological ion channels.Comment: 3 separate figure

Arabidopsis thaliana POLYOL/MONOSACCHARIDE TRANSPORTERS 1 and 2: fructose and xylitol/H+ symporters in pollen and young xylem cells

The genome of Arabidopsis thaliana contains six genes, AtPMT1 to AtPMT6 (Arabidopsis thaliana POLYOL/MONOSACCHARIDE TRANSPORTER 1–6), which form a distinct subfamily within the large family of more than 50 monosaccharide transporter-like (MST-like) genes. So far, only AtPMT5 [formerly named AtPLT5 (At3g18830)] has been characterized and was shown to be a plasma membrane-localized H+-symporter with broad substrate specificity. The characterization of AtPMT1 (At2g16120) and AtPMT2 (At2g16130), two other, almost identical, members of this transporter subfamily, are presented here. Expression of the AtPMT1 and AtPMT2 cDNAs in baker's yeast (Saccharomyces cerevisiae) revealed that these proteins catalyse the energy-dependent, high-capacity transport of fructose and xylitol, and the transport of several other compounds with lower rates. Expression of their cRNAs in Xenopus laevis oocytes showed that both proteins are voltage-dependent and catalyse the symport of their substrates with protons. Fusions of AtPMT1 or AtPMT2 with the green fluorescent protein (GFP) localized to Arabidopsis plasma membranes. Analyses of reporter genes performed with AtPMT1 or AtPMT2 promoter sequences showed expression in mature (AtPMT2) or germinating (AtPMT1) pollen grains, as well as in growing pollen tubes, hydathodes, and young xylem cells (both genes). The expression was confirmed with an anti-AtPMT1/AtPMT2 antiserum (αAtPMT1/2) raised against peptides conserved in AtPMT1 and AtPMT2. The physiological roles of the proteins are discussed and related to plant cell wall modifications

The Yin and Yang of Yeast Transcription: Elements of a Global Feedback System between Metabolism and Chromatin

When grown in continuous culture, budding yeast cells tend to synchronize their respiratory activity to form a stable oscillation that percolates throughout cellular physiology and involves the majority of the protein-coding transcriptome. Oscillations in batch culture and at single cell level support the idea that these dynamics constitute a general growth principle. The precise molecular mechanisms and biological functions of the oscillation remain elusive. Fourier analysis of transcriptome time series datasets from two different oscillation periods (0.7 h and 5 h) reveals seven distinct co-expression clusters common to both systems (34% of all yeast ORF), which consolidate into two superclusters when correlated with a compilation of 1,327 unrelated transcriptome datasets. These superclusters encode for cell growth and anabolism during the phase of high, and mitochondrial growth, catabolism and stress response during the phase of low oxygen uptake. The promoters of each cluster are characterized by different nucleotide contents, promoter nucleosome configurations, and dependence on ATP-dependent nucleosome remodeling complexes. We show that the ATP:ADP ratio oscillates, compatible with alternating metabolic activity of the two superclusters and differential feedback on their transcription via activating (RSC) and repressive (Isw2) types of promoter structure remodeling. We propose a novel feedback mechanism, where the energetic state of the cell, reflected in the ATP:ADP ratio, gates the transcription of large, but functionally coherent groups of genes via differential effects of ATP-dependent nucleosome remodeling machineries. Besides providing a mechanistic hypothesis for the delayed negative feedback that results in the oscillatory phenotype, this mechanism may underpin the continuous adaptation of growth to environmental conditions