Theory of resistor networks: The two-point resistance

The resistance between arbitrary two nodes in a resistor network is obtained in terms of the eigenvalues and eigenfunctions of the Laplacian matrix associated with the network. Explicit formulas for two-point resistances are deduced for regular lattices in one, two, and three dimensions under various boundary conditions including that of a Moebius strip and a Klein bottle. The emphasis is on lattices of finite sizes. We also deduce summation and product identities which can be used to analyze large-size expansions of two-and-higher dimensional lattices.Comment: 30 pages, 5 figures now included; typos in Example 1 correcte

Chrysanthemum species used as food and medicine: Understanding quality differences on the global market

Background Chrysanthemum flowers [Ch. x morifolium (Ramat.) Hemsl. and Ch. indicum L.] are a globally used and pharmacologically interesting botanical drug, however, with variable product quality. Objective We aim at understanding the chemical variability of primary material available commercially based on different origins and associated quality problems like contamination with heavy metals. This needs to be assessed in the context of the current regulations for this botanical drug and associated problems. Material and Methods 15 C. indicum L. and 50 C. x morifolium (Ramat.) Hemsl., including a range of geographical cultivars recognized in China, samples from the USA, Europe and China were analyzed using High Performance Thin Layer Chromatography (HPTLC) to compare their general chemical profile. Inductively Coupled Plasma Optical Emission Spectroscopy (ICP-OES) was used to quantify heavy metal contamination. Results The: HPTLC fingerprints of C. indicum samples are clearly distinguishable from C. x morifolium. Fingerprints of samples from the same cultivars collected from markets in different countries (USA and China) show different patterns. Large variance of fingerprints within each cultivar group was observed. The heavy metal analysis showed excessive amounts of some harmful heavy metal in some commercial products with excessive cadmium being the most frequent problem. Conclusions The Chinese medicinal cultivars vary. Differences between samples sourced from the USA and China might be ascribable to geographical factors (e.g. soil composition), degradation during transport/storage or adulteration, but geographical differences should also be taken into account. Importantly, a much more detailed definition of the drug are needed for better quality control. In addition, with continuous contamination problem observed, a more widespread regulation is an essential requirement for better quality

Photoconductivity Parameters In Lithium Niobate

Measurements on a variety of doped (magnesium and/or iron) and undoped lithium niobate crystals in the oxidized state demonstrate an Arrhenius dependence of dark conductivity on reciprocal temperature between 460 and 590 K. All of the crystals had roughly the same conductivity and activation energy (1.21 eV) over the temperature range, implying that all have about the same free-carrier concentration and mobility. The enhanced photoconductivity of magnesium-doped lithium niobate is attributed to a greatly reduced trapping cross section of Fe3+ for electrons, the smaller cross section being due to a changed substitutional site for Fe3+. The Fe3+ trapping cross section is calculated from photoconductivity data to be of order 10-18 m2 in undoped lithium niobate. This implies a photoelectron lifetime of order 6x10-11 s in a relatively pure (2-ppm Fe) oxidized crystal

Theory of impedance networks: The two-point impedance and LC resonances

We present a formulation of the determination of the impedance between any two nodes in an impedance network. An impedance network is described by its Laplacian matrix L which has generally complex matrix elements. We show that by solving the equation L u_a = lambda_a u_a^* with orthonormal vectors u_a, the effective impedance between nodes p and q of the network is Z = Sum_a [u_{a,p} - u_{a,q}]^2/lambda_a where the summation is over all lambda_a not identically equal to zero and u_{a,p} is the p-th component of u_a. For networks consisting of inductances (L) and capacitances (C), the formulation leads to the occurrence of resonances at frequencies associated with the vanishing of lambda_a. This curious result suggests the possibility of practical applications to resonant circuits. Our formulation is illustrated by explicit examples.Comment: 21 pages, 3 figures; v4: typesetting corrected; v5: Eq. (63) correcte

Super-resolution provided by the arbitrarily strong superlinearity of the blackbody radiation

Blackbody radiation is a fundamental phenomenon in nature, and its explanation by Planck marks a cornerstone in the history of Physics. In this theoretical work, we show that the spectral radiance given by Planck's law is strongly superlinear with temperature, with an arbitrarily large local exponent for decreasing wavelengths. From that scaling analysis, we propose a new concept of super-resolved detection and imaging: if a focused beam of energy is scanned over an object that absorbs and linearly converts that energy into heat, a highly nonlinear thermal radiation response is generated, and its point spread function can be made arbitrarily smaller than the excitation beam focus. Based on a few practical scenarios, we propose to extend the notion of super-resolution beyond its current niche in microscopy to various kinds of excitation beams, a wide range of spatial scales, and a broader diversity of target objects

The Structure, Dynamics and Electronic Structure of Liquid Ag-Se Alloys Investigated by Ab Initio Simulation

Ab initio molecular-dynamics simulations have been used to investigate the structure, dynamics and electronic properties of the liquid alloy Ag(1-x)Se(x) at 1350 K and at the three compositions x=0.33, 0.42 and 0.65. The calculations are based on density-functional theory in the local density approximation and on the pseudopotential plane-wave method. The reliability of the simulations is confirmed by detailed comparisons with very recent neutron diffraction results for the partial structure factors and radial distribution functions (RDF) of the stoichiometric liquid Ag2Se. The simulations show a dramatic change of the Se-Se RDF with increasing Se content. This change is due to the formation of Se clusters bound by covalent bonds, the Se-Se bond length being almost the same as in pure c-Se and l-Se. The clusters are predominantly chain-like, but for higher x a large fraction of 3-fold coordinated Se atoms is also found. It is shown that the equilibrium fractions of Se present as isolated atoms and in clusters can be understood on a simple charge-balance model based on an ionic interpretation. The Ag and Se diffusion coefficients both increase with Se content, in spite of the Se clustering. An analysis of the Se-Se bond dynamics reveals surprisingly short bond lifetimes of less than 1 ps. The changes in the density of states with composition arise directly from the formation of Se-Se covalent bonds. Results for the electronic conductivity obtained using the Kubo-Greenwood approximation are in adequate agreement with experiment for l-Ag2Se, but not for the high Se contents. Possible reasons for this are discussed.Comment: 14 pages, Revtex, 14 Postscript figures embedded in the tex

Spanning Trees on Lattices and Integration Identities

For a lattice $\Lambda$ with $n$ vertices and dimension $d$ equal or higher than two, the number of spanning trees $N_{ST}(\Lambda)$ grows asymptotically as $\exp(n z_\Lambda)$ in the thermodynamic limit. We present exact integral expressions for the asymptotic growth constant $z_\Lambda$ for spanning trees on several lattices. By taking different unit cells in the calculation, many integration identities can be obtained. We also give $z_{\Lambda (p)}$ on the homeomorphic expansion of $k$-regular lattices with $p$ vertices inserted on each edge.Comment: 15 pages, 3 figures, 1 tabl

First principles simulations of liquid Fe-S under Earth's core conditions

First principles electronic structure calculations, based upon density functional theory within the generalized gradient approximation and ultra-soft Vanderbilt pseudopotentials, have been used to simulate a liquid alloy of iron and sulfur at Earth's core conditions. We have used a sulfur concentration of $\approx 12$wt, in line with the maximum recent estimates of the sulfur abundance in the Earth's outer core. The analysis of the structural, dynamical and electronic structure properties has been used to report on the effect of the sulfur impurities on the behavior of the liquid. Although pure sulfur is known to form chains in the liquid phase, we have not found any tendency towards polymerization in our liquid simulation. Rather, a net S-S repulsion is evident, and we propose an explanation for this effect in terms of the electronic structure. The inspection of the dynamical properties of the system suggests that the sulfur impurities have a negligible effect on the viscosity of Earth's liquid core.Comment: 24 pages (including 8 figures

Initial Ionization of Compressible Turbulence

We study the effects of the initial conditions of turbulent molecular clouds on the ionization structure in newly formed H_{ii} regions, using three-dimensional, photon-conserving radiative transfer in a pre-computed density field from three-dimensional compressible turbulence. Our results show that the initial density structure of the gas cloud can play an important role in the resulting structure of the H_{ii} region. The propagation of the ionization fronts, the shape of the resulting H_{ii} region, and the total mass ionized depend on the properties of the turbulent density field. Cuts through the ionized regions generally show ``butterfly'' shapes rather than spherical ones, while emission measure maps are more spherical if the turbulence is driven on scales small compared to the size of the H_{ii} region. The ionization structure can be described by an effective clumping factor $\zeta=< n > \cdot /^2$, where $n$ is number density of the gas. The larger the value of $\zeta$, the less mass is ionized, and the more irregular the H_{ii} region shapes. Because we do not follow dynamics, our results apply only to the early stage of ionization when the speed of the ionization fronts remains much larger than the sound speed of the ionized gas, or Alfv\'en speed in magnetized clouds if it is larger, so that the dynamical effects can be negligible.Comment: 9 pages, 10 figures, version with high quality color images can be found in http://research.amnh.org/~yuexing/astro-ph/0407249.pd