Characterisation and representation of non-dissipative electromagnetic medium with a double light cone

We study Maxwell's equations on a 4-manifold N with a medium that is non-dissipative and has a linear and pointwise response. In this setting, the medium can be represented by a suitable (2,2)-tensor on the 4-manifold N. Moreover, in each cotangent space on N, the medium defines a Fresnel surface. Essentially, the Fresnel surface is a tensorial analogue of the dispersion equation that describes the response of the medium for signals in the geometric optics limit. For example, in isotropic medium the Fresnel surface is at each point a Lorentz light cone. In a recent paper, I. Lindell, A. Favaro and L. Bergamin introduced a condition that constrains the polarisation for plane waves. In this paper we show (under suitable assumptions) that a slight strengthening of this condition gives a pointwise characterisation of all medium tensors for which the Fresnel surface is the union of two distinct Lorentz null cones. This is for example the behaviour of uniaxial medium like calcite. Moreover, using the representation formulas from Lindell et al. we obtain a closed form representation formula that pointwise parameterises all medium tensors for which the Fresnel surface is the union of two distinct Lorentz null cones. Both the characterisation and the representation formula are tensorial and do not depend on local coordinates

Neural networks in geophysical applications

Neural networks are increasingly popular in geophysics. Because they are universal approximators, these tools can approximate any continuous function with an arbitrary precision. Hence, they may yield important contributions to finding solutions to a variety of geophysical applications. However, knowledge of many methods and techniques recently developed to increase the performance and to facilitate the use of neural networks does not seem to be widespread in the geophysical community. Therefore, the power of these tools has not yet been explored to their full extent. In this paper, techniques are described for faster training, better overall performance, i.e., generalization,and the automatic estimation of network size and architecture

Determination of electromagnetic medium from the Fresnel surface

We study Maxwell's equations on a 4-manifold where the electromagnetic medium is described by an antisymmetric $2\choose 2$-tensor $\kappa$. In this setting, the Tamm-Rubilar tensor density determines a polynomial surface of fourth order in each cotangent space. This surface is called the Fresnel surface and acts as a generalisation of the light-cone determined by a Lorentz metric; the Fresnel surface parameterises electromagnetic wave-speed as a function of direction. Favaro and Bergamin have recently proven that if $\kappa$ has only a principal part and if the Fresnel surface of $\kappa$ coincides with the light cone for a Lorentz metric $g$, then $\kappa$ is proportional to the Hodge star operator of $g$. That is, under additional assumptions, the Fresnel surface of $\kappa$ determines the conformal class of $\kappa$. The purpose of this paper is twofold. First, we provide a new proof of this result using Gr\"obner bases. Second, we describe a number of cases where the Fresnel surface does not determine the conformal class of the original $2\choose 2$-tensor $\kappa$. For example, if $\kappa$ is invertible we show that $\kappa$ and $\kappa^{-1}$ have the same Fresnel surfaces.Comment: 23 pages, 1 figur

USDA Farm Programs: North Dakota Farmer Participation and Opinions

Agricultural and Food Policy,

Wigner Trajectory Characteristics in Phase Space and Field Theory

Exact characteristic trajectories are specified for the time-propagating Wigner phase-space distribution function. They are especially simple---indeed, classical---for the quantized simple harmonic oscillator, which serves as the underpinning of the field theoretic Wigner functional formulation introduced. Scalar field theory is thus reformulated in terms of distributions in field phase space. Applications to duality transformations in field theory are discussed.Comment: 9 pages, LaTex2

A restatement of the normal form theorem for area metrics

An area metric is a (0,4)-tensor with certain symmetries on a 4-manifold that represent a non-dissipative linear electromagnetic medium. A recent result by Schuller, Witte and Wohlfarth provides a pointwise normal form theorem for such area metrics. This result is similar to the Jordan normal form theorem for (1,1)-tensors, and the result shows that any area metric belongs to one of 23 metaclasses with explicit coordinate expressions for each metaclass. In this paper we restate and prove this result for skewon-free (2,2)-tensors and show that in general, each metaclasses has three different coordinate representations, and each of metaclasses I, II, ..., VI, VII need only one coordinate representation.Comment: Updated proof of Proposition A.2 (Claim 5). Fixed typo in Theorem 6 (Metaclass XXIII

Production and Decay of Double \u3ci\u3eL\u3c/i\u3e Vacancies in Argon and Phosphorus

Measurements have been made at two laboratories which indicate that the structure reported at 450-550eV in the electron spectrum from Ar+-Ar collisions by Ogurtsov, Flaks, and Avakyan is spurious. It is argued that the double L vacancies which they invoke to explain the structure are more likely to decay by the two-step Auger process L 2→LM2→M4 than by the one-step process L2→M3 suggested by these authors. Evidence supporting this is found in our electron spectra from P+-Ar collisions, where it is known from energy-loss and charge-state measurements that double L vacancies are produced in phosphorus

Electronic spectroscopy of FUV-irradiated diamondoids: A combined experimental and theoretical study

Irradiation with high energy photons (10.2 - 11.8 eV) was applied to small diamondoids isolated in solid rare gas matrices at low temperature. The photoproducts were traced via UV absorption spectroscopy. We found that upon ionization the smallest of these species lose a peripheral H atom to form a stable closed-shell cation. This process is also likely to occur under astrophysical conditions for gas phase diamondoids and it opens the possibility to detect diamond-like molecules using their rotational spectrum since the dehydrogenated cations possess strong permanent dipole moments. The lowest-energy electronic features of these species in the UV were found to be rather broad, shifting to longer wavelengths with increasing molecular size. Calculations using time-dependent density functional theory support our experimental findings and extend the absorption curves further into the vacuum ultraviolet. The complete sigma - sigma* spectrum displays surprisingly strong similarities to meteoritic nanodiamonds containing 50 times more C atoms.Comment: 11 pages, 9 figures; published in The Astrophysical Journal; corrected minor mistakes compared to the published pape