Perturbation hydrogen-atom spectrum in deformed space with minimal length

We study energy spectrum for hydrogen atom with deformed Heisenberg algebra leading to minimal length. We develop correct perturbation theory free of divergences. It gives a possibility to calculate analytically in the 3D case the corrections to $s$-levels of hydrogen atom caused by the minimal length. Comparing our result with experimental data from precision hydrogen spectroscopy an upper bound for the minimal length is obtained.Comment: 9 pages, 3 figure

Hopf bifurcation in a gene regulatory network model: Molecular movement causes oscillations

Gene regulatory networks, i.e. DNA segments in a cell which interact with each other indirectly through their RNA and protein products, lie at the heart of many important intracellular signal transduction processes. In this paper we analyse a mathematical model of a canonical gene regulatory network consisting of a single negative feedback loop between a protein and its mRNA (e.g. the Hes1 transcription factor system). The model consists of two partial differential equations describing the spatio-temporal interactions between the protein and its mRNA in a 1-dimensional domain. Such intracellular negative feedback systems are known to exhibit oscillatory behaviour and this is the case for our model, shown initially via computational simulations. In order to investigate this behaviour more deeply, we next solve our system using Greens functions and then undertake a linearized stability analysis of the steady states of the model. Our results show that the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf bifurcation. This shows that the spatial movement of the mRNA and protein molecules alone is sufficient to cause the oscillations. This has implications for transcription factors such as p53, NF-$kappa$B and heat shock proteins which are involved in regulating important cellular processes such as inflammation, meiosis, apoptosis and the heat shock response, and are linked to diseases such as arthritis and cancer

A Wideband Direct Data Domain Genetic Algorithm Beamforming

In this paper, a wideband direct data-domain genetic algorithm beamforming is presented. Received wideband signals are decomposed to a set of narrow sub-bands using fast Fourier transform. Each sub-band is transformed to a reference frequency using the steering vector transformation. So, narrowband approaches could be used for any of these sub-bands. Hence, the direct data-domain genetic algorithm beamforming can be used to form a single ‘hybrid’ beam pattern with sufficiently deep nulls in order to separate and reconstruct frequency components of the signal of interest efficiently. The proposed approach avoids most of drawbacks of already-existing statistical and gradient-based approaches since formation of a covariance matrix is not needed, and a genetic algorithm is used to solve the beamforming problem

Quantization and 2π2\pi Periodicity of the Axion Action in Topological Insulators

The Lagrangian describing the bulk electromagnetic response of a three-dimensional strong topological insulator contains a topological `axion' term of the form '\theta E dot B'. It is often stated (without proof) that the corresponding action is quantized on periodic space-time and therefore invariant under '\theta -> \theta +2\pi'. Here we provide a simple, physically motivated proof of the axion action quantization on the periodic space-time, assuming only that the vector potential is consistent with single-valuedness of the electron wavefunctions in the underlying insulator.Comment: 4 pages, 1 figure, version2 (section on axion action quantization of non-periodic systems added

State Vector Reduction as a Shadow of a Noncommutative Dynamics

A model, based on a noncommutative geometry, unifying general relativity with quantum mechanics, is further develped. It is shown that the dynamics in this model can be described in terms of one-parameter groups of random operators. It is striking that the noncommutative counterparts of the concept of state and that of probability measure coincide. We also demonstrate that the equation describing noncommutative dynamics in the quantum gravitational approximation gives the standard unitary evolution of observables, and in the "space-time limit" it leads to the state vector reduction. The cases of the spin and position operators are discussed in details.Comment: 20 pages, LaTex, no figure

Infrared spectroscopy of circumstellar dust: signs of differentiated materials?

Mid-infrared absorption spectra of powdered achondrites are compared with the astronomical spectra of dust around young, evolving stars, to find evidence (or not) of dust formed in collisional cascades of material from planetesimals