There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Different on-line submicron particle sizing techniques report different “equivalent diameters.” For example, differential mobility analyzers (DMAs) report electrical mobility diameter (dm ), while a number of recently developed instruments (such as the Aerodyne aerosol mass spectrometer, or AMS) measure vacuum aerodynamic diameter (dva ). Particle density and physical morphology (shape) have important effects on diameter measurements. Here a framework is presented for combining the information content of different equivalent diameter measurements into a single coherent mathematical description of the particles. We first present a review of the mathematical formulations used in the literature and their relationships. We then show that combining dm and dva measurements for the same particle population allows the placing of constraints on particle density, dynamic shape factor (x), and fraction of internal void space. The amount of information that can be deduced from the combination of dm and dm measurement...

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Particle Morphology and Density Characterization by Combined Mobility and Aerodynamic Diameter Measurements. Part 1: Theory

A review of atmospheric aerosol measurements

One of the most important parts of formulating a National Ambient Air Quality Standard is specifying the measurement methods for determining and attaining compliance. The samples taken for compliance are often pushed beyond their original purpose to identify sources, to evaluate the effectiveness of controls, and to determine relationships between pollution levels and public health. A full understanding of available sampling and analysis methods is needed, as well as an analysis of their costs, before acceptable monitoring approached can be specified. This review identifies issues related to measurement methods used to determine compliance with standards, describes current and future measurement methods and their limitations, and determines the extent to which existing technology can meet short-term and long-term needs for measuring compliance.

Measurement Methods to Determine Compliance with Ambient Air Quality Standards for Suspended Particles

Let X(t) be the number of tumor cells at time t, and Pr{X(t) = n} = pn(t) is the density of X. A “birth”, i.e., an increase of one of the total population of cancer cells, can occur either by mutation of a normal cell caused by the action of the carcinogen, consisting of randomly (Poisson) distributed hits, or by reproduction of existing cancer cells. A death of a tumor cell occurs as an additive combination of non-immunological and immunological elements. Once a tumor is initiated by carcinogenic action, it undergoes a birth and death process with infinitesimal birth rate linear and infinitesimal death rate composed of a linear and a nonlinear term, the former due to non-immunological deaths, the latter to immunological feedback. The death rate per tumor cell due to immunological response is proportional to the total number of antigen-producing (tumor) cells; thus, the total death rate is quadratic. Although this assumes a very simple mechanism for the action of immunological feedback, it is nevertheless a first step.

The Mathematical Model

Momentum slip correction factor for small particles in nine common gases

In the 50 years since its invention, the acceptance and applicability of the DSMC method have increased significantly. Extensive verification and validation efforts have led to its greater acceptance, whereas the increase in computer speed has been the main factor behind its greater applicability. As the performance of a single processor reaches its limit, massively parallel computing is expected to play an even stronger role in its future development.

Direct simulation Monte Carlo: The quest for speed

The accuracy of a recently proposed direct simulation Monte Carlo (DSMC) algorithm, termed “sophisticated DSMC,” is investigated by comparing simulation results to analytical solutions of the Boltzmann equation for one-dimensional Fourier–Couette flow. An argon-like hard-sphere gas at 273.15 K and 266.644 Pa is confined between two parallel, fully accommodating walls 1 mm apart that have unequal temperatures and unequal tangential velocities. The simulations are performed using a one-dimensional implementation. In harmony with previous work, the accuracy metrics studied are the ratios of the DSMC-calculated transport properties and Sonine polynomial coefficients to their corresponding infinite-approximation Chapman–Enskog theoretical values. The sophisticated DSMC algorithm is shown to reproduce the theoretical results to high precision. The efficiency of the sophisticated DSMC algorithm relative to the original algorithm is demonstrated for a two-dimensional “real-world” application.

Accuracy and efficiency of the sophisticated direct simulation Monte Carlo algorithm for simulating noncontinuum gas flows

Convergence behavior of a new DSMC algorithm

An aerosol lab-on-a-chip (ALOC) integrates one or more of a variety of aerosol collection, classification, concentration (enrichment), and characterization processes onto a single substrate or layered stack of such substrates. By taking advantage of modern micro-machining capabilities, an entire suite of discrete laboratory aerosol handling and characterization techniques can be combined in a single portable device that can provide a wealth of data on the aerosol being sampled. The ALOC offers parallel characterization techniques and close proximity of the various characterization modules helps ensure that the same aerosol is available to all devices (dramatically reducing sampling and transport errors). Micro-machine fabrication of the ALOC significantly reduces unit costs relative to existing technology, and enables the fabrication of small, portable ALOC devices, as well as the potential for rugged design to allow operation in harsh environments. Miniaturization also offers the potential of working with smaller particle sizes and lower pressure drops (leading to reduction of power consumption).

Daniel J. Rader

Papers

Momentum slip correction factor for small particles in nine common gases

Direct simulation Monte Carlo: The quest for speed

Accuracy and efficiency of the sophisticated direct simulation Monte Carlo algorithm for simulating noncontinuum gas flows

Convergence behavior of a new DSMC algorithm

Apparatus to collect, classify, concentrate, and characterize gas-borne particles