Remarks on the Spectral Properties of Tight Binding and Kronig-Penney Models with Substitution Sequences

We comment on some recent investigations on the electronic properties of models associated to the Thue-Morse chain and point out that their conclusions are in contradiction with rigorously proven theorems and indicate some of the sources of these misinterpretations. We briefly review and explain the current status of mathematical results in this field and discuss some conjectures and open problems.Comment: 15,CPT-94/P.3003,tex,

The Error and Repair Catastrophes: A Two-Dimensional Phase Diagram in the Quasispecies Model

This paper develops a two gene, single fitness peak model for determining the equilibrium distribution of genotypes in a unicellular population which is capable of genetic damage repair. The first gene, denoted by $\sigma_{via}$, yields a viable organism with first order growth rate constant $k > 1$ if it is equal to some target ``master'' sequence $\sigma_{via, 0}$. The second gene, denoted by $\sigma_{rep}$, yields an organism capable of genetic repair if it is equal to some target ``master'' sequence $\sigma_{rep, 0}$. This model is analytically solvable in the limit of infinite sequence length, and gives an equilibrium distribution which depends on \mu \equiv L\eps , the product of sequence length and per base pair replication error probability, and \eps_r , the probability of repair failure per base pair. The equilibrium distribution is shown to exist in one of three possible ``phases.'' In the first phase, the population is localized about the viability and repairing master sequences. As \eps_r exceeds the fraction of deleterious mutations, the population undergoes a ``repair'' catastrophe, in which the equilibrium distribution is still localized about the viability master sequence, but is spread ergodically over the sequence subspace defined by the repair gene. Below the repair catastrophe, the distribution undergoes the error catastrophe when $\mu$ exceeds \ln k/\eps_r , while above the repair catastrophe, the distribution undergoes the error catastrophe when $\mu$ exceeds $\ln k/f_{del}$, where $f_{del}$ denotes the fraction of deleterious mutations.Comment: 14 pages, 3 figures. Submitted to Physical Review

Temperature effects on dislocation core energies in silicon and germanium

Temperature effects on the energetics of the 90-degree partial dislocation in silicon and germanium are investigated, using non-equilibrium methods to estimate free energies, coupled with Monte Carlo simulations. Atomic interactions are described by Tersoff and EDIP interatomic potentials. Our results indicate that the vibrational entropy has the effect of increasing the difference in free energy between the two possible reconstructions of the 90-degree partial, namely, the single-period and the double-period geometries. This effect further increases the energetic stability of the double-period reconstruction at high temperatures. The results also indicate that anharmonic effects may play an important role in determining the structural properties of these defects in the high-temperature regime.Comment: 8 pages in two-column physical-review format with six figure

Transmission and Spectral Aspects of Tight Binding Hamiltonians for the Counting Quantum Turing Machine

It was recently shown that a generalization of quantum Turing machines (QTMs), in which potentials are associated with elementary steps or transitions of the computation, generates potential distributions along computation paths of states in some basis B. The distributions are computable and are thus periodic or have deterministic disorder. These generalized machines (GQTMs) can be used to investigate the effect of potentials in causing reflections and reducing the completion probability of computations. This work is extended here by determination of the spectral and transmission properties of an example GQTM which enumerates the integers as binary strings. A potential is associated with just one type of step. For many computation paths the potential distributions are initial segments of a quasiperiodic distribution that corresponds to a substitution sequence. The energy band spectra and Landauer Resistance (LR) are calculated for energies below the barrier height by use of transfer matrices. The LR fluctuates rapidly with momentum with minima close to or at band-gap edges. For several values of the parameters, there is good transmission over some momentum regions.Comment: 22 pages Latex, 13 postscript figures, Submitted to Phys. Rev.

Atomic structure of dislocation kinks in silicon

We investigate the physics of the core reconstruction and associated structural excitations (reconstruction defects and kinks) of dislocations in silicon, using a linear-scaling density-matrix technique. The two predominant dislocations (the 90-degree and 30-degree partials) are examined, focusing for the 90-degree case on the single-period core reconstruction. In both cases, we observe strongly reconstructed bonds at the dislocation cores, as suggested in previous studies. As a consequence, relatively low formation energies and high migration barriers are generally associated with reconstructed (dangling-bond-free) kinks. Complexes formed of a kink plus a reconstruction defect are found to be strongly bound in the 30-degree partial, while the opposite is true in the case of 90-degree partial, where such complexes are found to be only marginally stable at zero temperature with very low dissociation barriers. For the 30-degree partial, our calculated formation energies and migration barriers of kinks are seen to compare favorably with experiment. Our results for the kink energies on the 90-degree partial are consistent with a recently proposed alternative double-period structure for the core of this dislocation.Comment: 12 pages, two-column style with 8 postscript figures embedded. Uses REVTEX and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/index.html#rn_di

Quantum Interference in Superconducting Wire Networks and Josephson Junction Arrays: Analytical Approach based on Multiple-Loop Aharonov-Bohm Feynman Path-Integrals

We investigate analytically and numerically the mean-field superconducting-normal phase boundaries of two-dimensional superconducting wire networks and Josephson junction arrays immersed in a transverse magnetic field. The geometries we consider include square, honeycomb, triangular, and kagome' lattices. Our approach is based on an analytical study of multiple-loop Aharonov-Bohm effects: the quantum interference between different electron closed paths where each one of them encloses a net magnetic flux. Specifically, we compute exactly the sums of magnetic phase factors, i.e., the lattice path integrals, on all closed lattice paths of different lengths. A very large number, e.g., up to $10^{81}$ for the square lattice, exact lattice path integrals are obtained. Analytic results of these lattice path integrals then enable us to obtain the resistive transition temperature as a continuous function of the field. In particular, we can analyze measurable effects on the superconducting transition temperature, $T_c(B)$, as a function of the magnetic filed $B$, originating from electron trajectories over loops of various lengths. In addition to systematically deriving previously observed features, and understanding the physical origin of the dips in $T_c(B)$ as a result of multiple-loop quantum interference effects, we also find novel results. In particular, we explicitly derive the self-similarity in the phase diagram of square networks. Our approach allows us to analyze the complex structure present in the phase boundaries from the viewpoint of quantum interference effects due to the electron motion on the underlying lattices.Comment: 18 PRB-type pages, plus 8 large figure

Safety and efficacy of an essential oil from Elettaria cardamomum (L.) Maton when used as a sensory additive in feed for all animal species

Following a request from the European Commission, the EFSA Panel on Additives and Products or Substances used in Animal Feed (FEEDAP) was asked to deliver a scientific opinion on the safety and efficacy of an essential oil from the seeds of Elettaria cardamomum (L.) Maton when used as a sensory additive for all animal species. Characterisation of the essential oil identified 37 components accounting for > 99% of its composition, with terpineol acetate (> 35%) and 1,8-cineole (> 20%) being the most prevalent compounds. In the absence of toxicological data of the feed additive itself, a component-based approach was applied to assess the safety of the essential oil as a mixture. Based on structural and metabolic similarity, the components of cardamom oil were allocated to seven assessment groups. Assuming the absence of toxicologically relevant interactions among components, dose addition was applied within each assessment group by calculating the combined margin of exposure as a basis for risk characterisation. The FEEDAP Panel concluded that the additive under assessment is safe at the proposed use level of 5 mg/kg in feed for all animal species. A concentration of 5 mg/L water for drinking is considered safe for all animal species. The use of cardamom essential oil in animal feed is considered safe for the consumer. In the absence of studies, the Panel cannot conclude on the safety for the users when handling the additive. The use of the essential oil under assessment in animal production is not expected to pose a risk for the environment. Since the seeds of E. cardamomum and their preparations are recognised to flavour food and their function in feed would be essentially the same, no further demonstration of efficacy is considered necessary. The Panel made a recommendation to limit the content of methyleugenol in the oil

Safety and efficacy of a natural mixture of dolomite plus magnesite and magnesium-phyllosilicates (Fluidol) as feed additive for all animal species

The additive, a natural mixture of dolomite plus magnesite and magnesium-phyllosilicates, is intended to be used as a technological additive (functional groups: anticaking agents) in feedingstuffs for all animal species. The additive is safe in complete feed for dairy cows, piglets and pigs for fattening at a maximum concentration of 20,000 mg/kg. No conclusions can be drawn for all the other animal species/categories. The additive is not genotoxic. As the additive is essentially not absorbed from the gut lumen, the Panel on Additives and Products or Substances used in Animal Feed considers that use of the additive in animal nutrition is safe for consumers of food products from animals fed diets containing the additive. The additive is not an irritant to the eyes and the skin, it is not a skin sensitiser and it is of low toxicity by the inhalation route. The components of the additive (dolomite, magnesite, talc and chlorite) are natural constituents of soil. Consequently, the use of the additive in animal nutrition will not pose a risk to the environment. The additive is effective as an anticaking agent at a minimum inclusion level of 5,000 mg/kg feed

Safety and efficacy of methylester of conjugated linoleic acid (t10,c12 isomer) for pigs for fattening, sows and cows

A mixture of methylated conjugated linoleic acid (CLA) isomers (t10,c12 and c9,t11) in equal proportions was not genotoxic and caused no reproductive toxicity. In a sub-acute study in dogs, a sub-chronic toxicity study in rats and a chronic study in dogs, no adverse effects were seen up to the highest levels tested. The maximum recommended feed concentration (5 g CLA (t10,c12)-ME from Lutalin (R)/kg feed for piglets, pigs for fattening and sows) or dose (30 g CLA (t10,c12)-ME from Lutrell (R) Pure/cow per day) is considered safe for target species. The CLA content of milk from cows treated with the highest recommended dose did not exceed background values (in milk of untreated cows) for both CLA isomers. An estimate of consumer exposure to both CLA isomers from food from pigs receiving 3 g of both CLA isomers/kg feed is <= 320 mg CLA isomers/person and day. This quantity corresponds to about 9% of the quantity considered safe for 6 months and is considered unlikely to raise concerns for consumer safety. Exposure of users by inhalation of the additive is likely to be minimal. Neither of the products under application, the liquid or the solid product, was tested as such for skin and eye irritation and skin sensitisation. The use of the additive in animal nutrition would not pose a risk to the environment. In pigs for fattening, CLA (t10,c12)-ME has a potential for improving feed to gain ratio. More consistent effects are a reduction in subcutaneous fat, an increase in intramuscular fat and fat firmness. No essential effects were found in sows. Administration of CLA to dairy cows reduces in a dose-dependent manner the fat content of milk, and milk fat yield. Energy balance in early lactation is improved by CLA (t10,c12)-ME; however, reproductive parameters were not influenced