Twining characters and orbit Lie algebras

We associate to outer automorphisms of generalized Kac-Moody algebras generalized character-valued indices, the twining characters. A character formula for twining characters is derived which shows that they coincide with the ordinary characters of some other generalized Kac-Moody algebra, the so-called orbit Lie algebra. Some applications to problems in conformal field theory, algebraic geometry and the theory of sporadic simple groups are sketched.Comment: 6 pages, LaTeX, Talk given by C. Schweigert at the XXI international colloquium on group theoretical methods in physics, July 1996, Goslar, German

The proto--neutron--star dynamo -- viability and impediments

We study convective motions taken from hydrodynamic simulations of rotating proto--neutron stars (PNSs) with respect to their ability to excite a dynamo instability which may be responsible for the giant neutron star magnetic fields. Since it is impossible to simulate the magnetic field evolution employing the actual magnetic Reynolds numbers (\Rm) resulting from the hydrodynamic simulations, (smallest) critical \Rms and the corresponding field geometries are derived on the kinematic level by rescaling the velocity amplitudes. It turns out that the actual values of \Rm are by many orders of magnitude larger than the critical values found. A dynamo might therefore start to act vigorously very soon after the onset of convection. But as in general dynamo growth rates are non--monotonous functions of \Rm the later fate of the magnetic field is uncertain. Hence, no reliable statements on the existence and efficiency of PNS dynamos can be drawn without considering the interplay of magnetic field and convection from the beginning. Likewise, in so far as convection inside the PNS is regarded to be essential in re--launching the supernova explosion, a revision of its role in this respect could turn out to be necessary.Comment: 7 pages, 4 figures, accepted by Astronomy & Astrophysic

A Direct Entropic Approach to Uniform and Spatially Continuous Dynamical Models of Thermoelectric Devices

If we accept temperature and entropy as primitive quantities, we can construct a direct approach to a dynamical thermal theory of spatially continuous and uniform processes. The theory of uniform models serves as a simple entry point for learners of modern thermodynamics. Such models can be applied fruitfully to an understanding of (the dynamics of) thermoelectric processes and devices. Entropy, temperature, charge, and voltage allow us to describe the role of energy concisely, and constitutive quantities can be given their natural entropic interpretation. In this paper, aggregate dynamical models of a Peltier device will be created and simulations will be compared to non-steady-state experimental data. Such overall models give us a simple image of the transport of charge and transport, production, and storage of entropy and can be easily extended to the spatially continuous case. Process diagrams for a uniform model can be used to visualize these processes and the role of energy. Device efficiency can be easily read from the model. Apart from external parameters such as load resistances or temperature differences, it depends upon three parameters of the device: internal electric resistance, entropy conductance, and Seebeck coefficient. The Second Law efficiency of a generator suggests how to define the figure of merit (zT) of the thermoelectric material. Distinction between ideal and dissipative processes and the rates at which energy is made available or used allows us to construct a simple argument for the equality of the Seebeck and Peltier coefficient

On fewnomials, integral points and a toric version of Bertini's theorem

An old conjecture of Erdős and Rényi, proved by Schinzel, predicted a bound for the number of terms of a polynomial g(x)∈ℂ[x] when its square g(x)² has a given number of terms. Further conjectures and results arose, but some fundamental questions remained open. In this paper, with methods which appear to be new, we achieve a final result in this direction for completely general algebraic equations f(x,g(x))=0, where f(x,y) is monic of arbitrary degree in y, and has boundedly many terms in x: we prove that the number of terms of such a g(x) is necessarily bounded. This includes the previous results as extremely special cases. We shall interpret polynomials with boundedly many terms as the restrictions to 1-parameter subgroups or cosets of regular functions of bounded degree on a given torus Glm. Such a viewpoint shall lead to some best-possible corollaries in the context of finite covers of Glm, concerning the structure of their integral points over function fields (in the spirit of conjectures of Vojta) and a Bertini-type irreducibility theorem above algebraic multiplicative cosets. A further natural reading occurs in non-standard arithmetic, where our result translates into an algebraic and integral-closedness statement inside the ring of non-standard polynomials

Distinguishing two single-mode Gaussian states by homodyne detection: An information-theoretic approach

It is known that the quantum fidelity, as a measure of the closeness of two quantum states, is operationally equivalent to the minimal overlap of the probability distributions of the two states over all possible POVMs; the POVM realizing the minimum is optimal. We consider the ability of homodyne detection to distinguish two single-mode Gaussian states, and investigate to what extent it is optimal in this information-theoretic sense. We completely identify the conditions under which homodyne detection makes an optimal distinction between two single-mode Gaussian states of the same mean, and show that if the Gaussian states are pure, they are always optimally distinguished.Comment: 6 pages, 4 figures, published version with a detailed discussio

Potential of different composts to improve soil fertility

Composts can influence soil fertility and plant health. These influences can be positive or negative, depending of the quality of the composts. Some practitioners already make use of the positive effects on plant health. For example, they use composts to protect their plants against soil borne diseases in substrate, or to detoxify and reactivate soil after steaming. In order to estimate the potential of Swiss composts to influence soil fertility and plant health positively, we analyzed one hundred composts representative of the different composting systems and qualities available on the market. The organic substance and the nutrient content of the composts varied greatly between the composts; the materials of origin were the major factor influencing these values. The respiration rate and enzyme activities also varied greatly, particularly in the youngest composts. These differences become smaller when the composts become more mature. Maturity, the degradation stage of the organic matter, depended not only on the age of the compost, but also on the management of the process. The N-mineralization potential from compost added to soil showed that a high proportion of young composts immobilized the nitrogen in the soil. This problem was hardly correlated with the materials of origin, but with the management of the first stage of the composting process. Especially composts which had become too dry in this period lost their ammonia-nitrogen, and hence immobilized nitrogen in the soil. Also composts with a low NO3/NH4 ratio, as a rough indicator for an immature compost, immobilized nitrogen in the soil. By contrast, the phytotoxicity of the composts varied very much also in matured composts, showing that the storage of the compost plays a decisive role. While the majority of compost protected cucumber plants against Pythium ultimum, only a few composts suppressed Rhizoctonia solani in basil. With respect to disease suppression, the management of the maturation process seems to play a major role. In conclusion, big differences in compost quality and of their impact on soil fertility and on plant health were observed. The management of the composting process seems to influence the quality of the composts to a higher extent than the materials of origin or the composting system. More attention should be paid to biological quality of composts, in order to produce composts with more beneficial effects on crops