Frequency-dependent (ac) Conduction in Disordered Composites: a Percolative Study

In a recent paper [Phys. Rev. B{\bf57}, 3375 (1998)], we examined in detail the nonlinear (electrical) dc response of a random resistor cum tunneling bond network ($RRTN$, introduced by us elsewhere to explain nonlinear response of metal-insulator type mixtures). In this work which is a sequel to that paper, we consider the ac response of the $RRTN$-based correlated $RC$ ($CRC$) model. Numerical solutions of the Kirchoff's laws for the $CRC$ model give a power-law exponent (= 0.7 near $p = p_c$) of the modulus of the complex ac conductance at moderately low frequencies, in conformity with experiments on various types of disordered systems. But, at very low frequencies, it gives a simple quadratic or linear dependence on the frequency depending upon whether the system is percolating or not. We do also discuss the effective medium approximation ($EMA$) of our $CRC$ and the traditional random $RC$ network model, and discuss their comparative successes and shortcomings.Comment: Revised and reduced version with 17 LaTeX pages plus 8 JPEG figure

Multimode solutions of first-order elliptic quasilinear systems obtained from Riemann invariants

Two new approaches to solving first-order quasilinear elliptic systems of PDEs in many dimensions are proposed. The first method is based on an analysis of multimode solutions expressible in terms of Riemann invariants, based on links between two techniques, that of the symmetry reduction method and of the generalized method of characteristics. A variant of the conditional symmetry method for constructing this type of solution is proposed. A specific feature of that approach is an algebraic-geometric point of view, which allows the introduction of specific first-order side conditions consistent with the original system of PDEs, leading to a generalization of the Riemann invariant method for solving elliptic homogeneous systems of PDEs. A further generalization of the Riemann invariants method to the case of inhomogeneous systems, based on the introduction of specific rotation matrices, enables us to weaken the integrability condition. It allows us to establish a connection between the structure of the set of integral elements and the possibility of constructing specific classes of simple mode solutions. These theoretical considerations are illustrated by the examples of an ideal plastic flow in its elliptic region and a system describing a nonlinear interaction of waves and particles. Several new classes of solutions are obtained in explicit form, including the general integral for the latter system of equations

A small satellite version of a soft x-ray polarimeter

We describe a new implementation of a broad-band soft X-ray polarimeter, substantially based on a previous design. This implementation, the Pioneer Soft X-ray Polarimeter (PiSoX) is a SmallSat, designed for NASA’s call for Astrophysics Pioneers, small missions that could be CubeSats, balloon experiments, or SmallSats. As in REDSoX, the grating arrangement is designed optimally for the purpose of polarimetry with broad-band focussing optics by matching the dispersion of the spectrometer channels to laterally graded multilayers (LGMLs). The system can achieve polarization modulation factors over 90%. For PiSoX, the optics are lightweight Si mirrors in a one-bounce parabolic configuration. High efficiency, blazed gratings from opposite sectors are oriented to disperse to a LGML forming a channel covering the wavelength range from 35 Å to 75 Å (165 - 350 eV). Upon satellite rotation, the intensities of the dispersed spectra, after reflection and polarizing by the LGMLs, give the three Stokes parameters needed to determine a source’s linear polarization fraction and orientation. The design can be extended to higher energies as LGMLs are developed further. We describe examples of the potential scientific return from instruments based on this design.Accepted manuscrip

Measuring aerosol black carbon age with aethalometers

Aerosol mixing state is a parameter influencing optical properties of absorbing particles that is hard to measure. It was proposed that the lensing effect where transparent shell covers the absorbing particle can significantly enhance optical absorption (Bond et al., 2006). Aerosol mixing state can be assessed using advanced mass spectrometers ATOFMS (Healy et al., 2012), and with SP2 for particles with diameters above about 100 nm (Subramanian et al., 2010). Filter-based measurements of aerosol optical absorption are widely used to determine Black Carbon (BC) concentrations in real time. Measurements at multiple wavelengths permit the separation of contributions of BC from different combustion sources (Sandradewi 2008). However, filter-based methods are influenced by the non-linear response due to the »loading« effect, caused by the increasing sample deposit on the filter (Gundel 1984, Weingartner 2003, Arnott 2005, Virkkula 2007).The filterloading effect is the reduction of the filter based photometer sensitivity due to filter loading. It was shown that filter-loading effect differs between locations and seasons with indication that the filter loading effect in Aethalometer relates to the particle coating (Virkkula et al., 2007; Drinovec et al., 2015). Using Aethalometer model AE33 (Magee Scientific) it is possible to measure filter loading parameter k with high time resolution (Drinovec et al., 2015).Influence of coating on the parameter k was investigated both during the ambient and laboratory campaigns

Interpretation of the loading effect in absorption filter photometers - dual spot aethalometer measurements

Filter-based measurements of aerosol optical absorption are widely used to determine Black Carbon (BC) concentrations in real time. Measurements at multiple wavelengths permit the separation of contributions of BC from different combustion sources. Filterbased methods can suffer from non-linearity due increasing sample deposit on the filter. The dual-spot Aethalometer model AE33 provides a real-time determination of this loading effect, by determining the compensation parameter k in real time for each of the wavelengths. We present an interpretation of k in terms of aerosol composition. Optical properties of combustion aerosols were investigated under laboratory conditions. Optical properties of emitted aerosols varied greatly with the combustion regime. The type of combustion also influenced the parameter k, which is attributed to different particle coating thickness. Optical and chemical properties of aerosols were measured with high time resolution during summer and winter at different sites. The ratio of the sum of inorganic secondary and organic aerosol mass to BC (expected to be high for air parcels containing aged aerosols) correlates well with the parameter k measured by the AE33 at 880 nm. To investigate the influence of coating on parameter k, a drier and a thermodenuder were used to remove the coating. These results indicate that the compensation parameter k can be used for discrimination between fresh and aged aerosols