Intrinsic ergodicity beyond specification: β-shifts, S-gap shifts, and their factors

We give sufficient conditions for a shift space (Σ, σ) to be intrinsically ergodic, along with sufficient conditions for every subshift factor of Σ to be intrinsically ergodic. As an application, we show that every subshift factor of a β-shift is intrinsically ergodic, which answers an open question included in Mike Boyle’s article “Open problems in symbolic dynamics”. We obtain the same result for S-gap shifts, and describe an application of our conditions to more general coded systems. One novelty of our approach is the introduction of a new version of the specification property that is well adapted to the study of symbolic spaces with a non-uniform structure.     

Laser desorption in transmission geometry inside a Fourier-transform ion cyclotron resonance mass spectrometer

We report here the first application of laser desorption (LD) in transmission geometry (backside irradiation of the sample through a transparent support) inside a Fourier-transform ion cyclotron resonance mass spectrometer (FT-ICR). A probe-mounted fiber optic assembly was used to simplify the implementation of this LD technique. This setup requires little or no instrument modifications, has minimum maintenance requirements, and is relatively inexpensive to build. The performance of the probe was tested by determining the molecular weight of a commercial polystyrene standard from its matrix-assisted laser desorption/ionization (MALDI) spectrum. The measured average molecular weight is comparable to that obtained for the same sample by MALDI in the conventional top-illumination arrangement (reflection geometry) and by the manufacturer of the sample by gel permeation chromatography. The average velocities measured for ions evaporated by transmission mode LD of several neat samples are about half the velocity of those obtained by using the reflection geometry. Therefore, transmission mode irradiation of the sample holds promise to desorb ions that are easier to trap in an ICR cell. An oscillating capillary nebulizer was adapted for the deposition of analytes to improve sampling reproducibility.     

Impact of gradient timing error on the tissue sodium concentration bioscale measured using flexible twisted projection imaging

The rapid biexponential transverse relaxation of the sodium MR signal from brain tissue requires efficient k-space sampling for quantitative imaging in a time that is acceptable for human subjects. The flexible twisted projection imaging (flexTPI) sequence has been shown to be suitable for quantitative sodium imaging with an ultra-short echo time to minimize signal loss. The fidelity of the k-space center location is affected by the readout gradient timing errors on the three physical axes, which is known to cause image distortion for projection-based acquisitions. This study investigated the impact of these timing errors on the voxel-wise accuracy of the tissue sodium concentration (TSC) bioscale measured with the flexTPI sequence. Our simulations show greater than 20% spatially varying quantification errors when the gradient timing errors are larger than 10 μs on all three axes. The quantification is more tolerant of gradient timing errors on the Z-axis. An existing method was used to measure the gradient timing errors with <1 μs error. The gradient timing error measurement is shown to be RF coil dependent, and timing error differences of up to ～16 μs have been observed between different RF coils used on the same scanner. The measured timing errors can be corrected prospectively or retrospectively to obtain accurate TSC values.     

A review of the studies on environmental transport and speciation analysis of radionuclides in India

Department of Atomic Energy, India, has a systematic environmental monitoring program to ensure that the impact of radionuclides on human and environment is well within the limits, stipulated by the regulatory body. Concentrations of radionuclides are estimated in air, water, soil, sediment and biota in the environment around the power plant site on a regular basis. The environmental migration pattern and impact of radionuclides in the environment depends upon not only on the total concentration but the physico-chemical nature of radionuclide also. This paper presents a brief review of the studies of environmental transportation of radionuclides and influence of speciation with special reference to Indian conditions. A fairly good amount of results are available on the influence of speciation of radionuclides on the wet and dry deposition and preliminary results are available on the speciation analysis in dietary items, in soil and in ground water. Initial studies are concentrated on tritium, ¹³⁷Cs, Uranium, ⁹⁰Sr and their chemical analogues.     

Molecular dynamics simulation of nanoparticle self-assembly at a liquid-liquid interface

We have used molecular dynamics simulations to investigate the in situ self-assembly of modified hydrocarbon nanoparticles (mean diameter of 1.2 nm) at a water-trichloroethylene (TCE) interface. The nanoparticles were first distributed randomly in the water phase. The MD simulation shows the in situ formation of nanoparticle clusters and the migration of both single particles and clusters from the water phase to the trichloroethylene phase, possibly due to the hydrophobic nature of the nanoparticles. Eventually, the single nanoparticles or clusters equilibrate at the water-TCE interface, and the surrounding liquid molecules pack randomly when in contact with the nanoparticle surfaces. In addition, the simulations show that the water-TCE interfacial thickness analyzed from density profiles is influenced by the presence of nanoparticles either near or in contact with the interface but is independent of the number of nanoparticles present. The nanoparticles, water molecules, and TCE molecules all exhibit diffusion anisotropy.     

Tensor methods for the exceptional group E6

We present a tensor formalism to describe irreducible representations of the exceptional group E₆. Irreducible tensors are characterized by covariant and contravariant indices associated with the irreducible representation 27, and a third (orthogonal-type) index associated with the 78; contractions of these indices with a set of invariant tensors are required to vanish for irreducibility. The formalism is applied to the reduction of Kronecker products of E₆ irreducible representations. As a further illustration of the method, we construct explicitly the Higgs potential for scalar fields in the E₆ representations 27, 78, 351, 351′.     

Deterministic inhomogeneous inertia ratchets

We study the deterministic dynamics of a periodically driven particle in the underdamped case in a spatially symmetric periodic potential. The system is subjected to a space-dependent friction coefficient, which is similarly periodic as the potential but with a phase difference. We observe that frictional inhomogeneity in a symmetric periodic potential mimics most of the qualitative features of deterministic dynamics in a homogeneous system with an asymmetric periodic potential. We point out the need of averaging over the initial phase of the external drive at small frictional inhomogeneity parameter values or analogously low potential asymmetry regimes in obtaining ratchet current. We also show that at low amplitudes of the drive, where ratchet current is not possible in the deterministic case, noise plays a significant role in realizing ratchet current.     

Asymptotic freedom constraints on grand unified gauge theories

Constraints on the fermion and Higgs scalar content of grand unified gauge theories, imposed by the requirement of asymptotic freedom for the gauge couplings, are derived for models which have fermion representations with only color singlets and color triplets. The constraintn _f ≦16 on the numbern _f of flavors of color triplet quarks in pure QCD is removed. Definitive limits are placed on the representation content of theories based on the exceptional groups.