Arbitrary Mixture Research Articles

EFFICIENT THREE-DIMENSIONAL NLTE DUST RADIATIVE TRANSFER WITH SKIRT

We present an updated version of SKIRT, a 3D Monte Carlo radiative transfer code developed to simulate dusty galaxies. The main novel characteristics of the SKIRT code are the use of a stellar foam to generate random positions, an efficient combination of eternal forced scattering and continuous absorption, and a new library approach that links the radiative transfer code to the DustEM dust emission library. This approach enables a fast, accurate and self-consistent calculation of the dust emission of arbitrary mixtures of transiently heated dust grains and polycyclic aromatic hydrocarbons, even for full 3D models containing millions of dust cells. We have demonstrated the accuracy of the SKIRT code through a set of simulations based on the edge-on spiral galaxy UGC 4754. The models we ran were gradually refined from a smooth, 2D, LTE model to a fully 3D model that includes NLTE dust emission and a clumpy structure of the dusty ISM. We find that clumpy models absorb UV and optical radiation less efficiently than smooth models with the same amount of dust, and that the dust in clumpy models is on average both cooler and less luminous. Our simulations demonstrate that, given the appropriate use of optimization techniques, it is possible to efficiently and accurately run Monte Carlo radiative transfer simulations of arbitrary 3D structures of several million dust cells, including a full calculation of the NLTE emission by arbitrary dust mixtures.

Effects of Radiation Quality and Oxygen on Clustered DNA Lesions and Cell Death

Radiation quality and cellular oxygen concentration have a substantial impact on DNA damage, reproductive cell death and, ultimately, the potential efficacy of radiation therapy for the treatment of cancer. To better understand and quantify the effects of radiation quality and oxygen on the induction of clustered DNA lesions, we have now extended the Monte Carlo Damage Simulation (MCDS) to account for reductions in the initial lesion yield arising from enhanced chemical repair of DNA radicals under hypoxic conditions. The kinetic energy range and types of particles considered in the MCDS have also been expanded to include charged particles up to and including (56)Fe ions. The induction of individual and clustered DNA lesions for arbitrary mixtures of different types of radiation can now be directly simulated. For low-linear energy transfer (LET) radiations, cells irradiated under normoxic conditions sustain about 2.9 times as many double-strand breaks (DSBs) as cells irradiated under anoxic conditions. New experiments performed by us demonstrate similar trends in the yields of non-DSB (Fpg and Endo III) clusters in HeLa cells irradiated by γ rays under aerobic and hypoxic conditions. The good agreement among measured and predicted DSBs, Fpg and Endo III cluster yields suggests that, for the first time, it may be possible to determine nucleotide-level maps of the multitude of different types of clustered DNA lesions formed in cells under reduced oxygen conditions. As particle LET increases, the MCDS predicts that the ratio of DSBs formed under normoxic to hypoxic conditions by the same type of radiation decreases monotonically toward unity. However, the relative biological effectiveness (RBE) of higher-LET radiations compared to (60)Co γ rays (0.24 keV/μm) tends to increase with decreasing oxygen concentration. The predicted RBE of a 1 MeV proton (26.9 keV/μm) relative to (60)Co γ rays for DSB induction increases from 1.9 to 2.3 as oxygen concentration decreases from 100% to 0%. For a 12 MeV (12)C ion (681 keV/μm), the 'predicted RBE for DSB induction increases from 3.4 (100% O(2)) to 9.8 (0% O(2)). Estimates of linear-quadratic (LQ) cell survival model parameters (α and β) are closely correlated to the Monte Carlo-predicted trends in DSB induction for a wide range of particle types, energies and oxygen concentrations. The analysis suggests α is, as a first approximation, proportional to the initial number of DSBs per cell, and β is proportional to the square of the initial number of DSBs per cell. Although the reported studies provide some evidence supporting the hypothesis that DSBs are a biologically critical form of clustered DNA lesion, the induction of Fpg and Endo III clusters in HeLa cells irradiated by γ rays exhibits similar trends with oxygen concentration. Other types of non-DSB cluster may still play an important role in reproductive cell death. The MCDS captures many of the essential trends in the formation of clustered DNA lesions by ionizing radiation and provides useful information to probe the multiscale effects and interactions of ionizing radiation in cells and tissues. Information from Monte Carlo simulations of cluster induction may also prove useful for efforts to better exploit radiation quality and reduce the impact of tumor hypoxia in proton and carbon-ion radiation therapy.

TU‐G‐BRA‐02: Monte Carlo Simulation of the Effects of Radiation Quality and Oxygen Concentration on Clustered DNA Lesions Formed by Ionizing Radiation

Many decades of biophysical research provide compelling evidence that the in vitro and in vivo effects of radiation quality on cell death are closely related to the spatial distribution of energy deposits within targets smaller than the cell nucleus. Although cell‐ or tissue‐level repair, tolerance and recovery mechanisms have the potential to amplify or suppress the effects of DNA damage, trends in double strand break (DSB) induction with radiation quality are often quite similar to the trends observed for chromosomal aberrations and reproductive cell death. As such, Monte Carlo simulations of the induction of clustered DNA lesions by ionizing radiation provide useful qualitative and quantitative information about the relative biological effectiveness (RBE) of proton and carbon ions compared to high‐energy photons. We have recently modified the Monte Carlo Damage Simulation (MCDS) to account for reductions in the initial lesion yield arising from enhanced chemical repair of DNA radicals under hypoxic conditions. The kinetic energy range and types of particles considered in the MCDS has been expanded to include ions up to and including 56Fe. Also, the MCDS now has the ability to simulate the induction of individual and clustered DNA lesions for arbitrary mixtures of the same or different types of particles under hypoxic and normoxic conditions.For low linear energy transfer (LET) radiations, cells irradiated under aerobic conditions sustain about 2.9 times as many DSB as cells irradiated under anoxic conditions. Similar trends in the yields of non‐DSB (Fpg and Endo III) clusters occur in HeLa cells irradiated by gamma‐rays under aerobic and anoxic conditions. The differential effects of oxygen concentration on RBE increase with increasing particle LET. The RBE for DSB induction of a 1 MeV proton (26.9 keV/um) relative to 60Co gamma‐rays (0.24 keV/um) increases from 1.9 to 2.3 as oxygen concentration decreases from 100% to 0%. For comparison, the RBE for DSB induction of a 12 MeV 12C ion (681 keV/um) relative to 60Co gamma‐rays increases from 3.4 (100% O2) to 9.8 (0% O2). Although the reported studies provide evidence supporting the hypothesis that DSB are a biologically critical form of clustered DNA lesion, other types of non‐DSB cluster may still play an important role in reproductive cell death. The MCDS captures many of the essential trends in the formation of DSB and non‐DSB clusters with radiation quality and oxygen concentration. The good agreement between measured and predicted cluster yields for DSB, Fpg and Endo III clusters suggests that, for the first time, it may be possible to determine nucleotide‐level maps of the multitude of different types of clustered DNA lesions formed in cells irradiated under reduced oxygen. The MCDS is a useful computational tool to explore the interplay among radiation quality and the effects of tumor hypoxia in proton and carbon ion radiation therapy.Learning Objective:1. To review, understand and quantify the effects of radiation quality and oxygen concentration on the induction of clustered DNA lesions by ionizing radiation

A universally fastest algorithm for Max 2-Sat, Max 2-CSP, and everything in between

In this paper we introduce “hybrid” Max 2-CSP formulas consisting of “simple clauses”, namely conjunctions and disjunctions of pairs of variables, and general 2-variable clauses, which can be any integer-valued functions of pairs of boolean variables. This allows an algorithm to use both efficient reductions specific to AND and OR clauses, and other powerful reductions that require the general CSP setting. We use new reductions introduced here, and recent reductions such as “clause-learning” and “2-reductions” generalized to our settingʼs mixture of simple and general clauses. We parametrize a hybrid instance by the fraction p of non-simple clauses. We give an exact, exponential-time but polynomial-space algorithm that is the fastest known for p = 0 , which includes the well-studied Max 2-Sat problem but also instances with arbitrary mixtures of AND and OR clauses; for an m-clause instance it runs in time O ⋆ ( 2 m / 6.321 ) . The same algorithm is tied for fastest for general Max 2-CSP ( p = 1 ), with running time O ⋆ ( 2 m / 5.263 ) . The algorithm is the only one to treat mixtures of AND, OR, and general integer-valued clauses more efficiently than the general case, with intermediate running time bounds depending on the value of p. Since even a pure Max 2-Sat input instance may be transformed to a hybrid instance in the course of solving it, the algorithmʼs efficiency and generality go hand in hand. Our algorithm analysis and optimization use the familiar measure-and-conquer approach, but in a variation resulting in mathematical programs that are convex rather than quasi-convex, and can be solved efficiently and with a certificate of optimality. We produce a family of running-time upper-bound formulas, each optimized for instances with a particular value of p but valid for all instances.

Exact Crossover Green Function in the Two-Channel and Two-Impurity Kondo Models

Symmetry-breaking perturbations destabilize the critical points of the two-channel and two-impurity Kondo models, thereby leading to a crossover from non-Fermi liquid behavior to standard Fermi liquid physics. Here we use an analogy between this crossover and one occurring in the boundary Ising model to calculate the full crossover Green function analytically. In remarkable agreement with our numerical renormalization group calculations, the single exact function applies for an arbitrary mixture of the relevant perturbations in each model. This rich behavior resulting from finite channel asymmetry, interlead charge transfer, and/or magnetic field should be observable in quantum dot or tunneling experiments.

The nature of single-ion activity coefficients calculated from potentiometric measurements on cells with liquid junctions

Potentiometric measurements on cells with liquid junctions are sometimes used for calculations of single-ion activity coefficients in electrolyte solutions, the incidence of this being increased recently. As surmised by Guggenheim in the 1930s, such coefficients (of ions i), γ i , are actually complicated functions of mean ionic activity coefficients, γ ±, and transport numbers of ions, t i . In the present paper specific functions γ i ( γ ±, t i ) are derived for a number of cell types with an arbitrary mixture of strong electrolytes in a one-component solvent in the liquid-junction system. The cell types include cells with (i) identical electrodes, (ii) dissimilar electrodes reversible to the same ions, (iii) dissimilar electrodes reversible to ions of opposite charge signs, (iv) dissimilar electrodes reversible to different ions of the same charge sign, and (v) identical reference electrodes and an ion-selective membrane permeable to ions of only one type. Pairs of functions for oppositely charged ions are found to be consistent with the mean ionic activity coefficients as would be expected for pairs of the proper γ i quantities by definition of γ ±. The functions are tested numerically on some of the reported γ i datasets that are the more tractable. A generally good agreement is found with data reported for cells with single electrolytes HCl and KCl in solutions, and with binary mixtures in the liquid-junction systems of KCl from the reference solutions and NaCl and HCl from the test solutions. It is found that values of γ i ( γ ±, t i ) functions, in general, do depend on the reference solution composition, which is at variance with the recent claim by Lladosa et al. [E. Lladosa, A. Arce, G. Wilczek-Vera, J.H. Vera, J. Chem. Thermodyn. 42 (2010) 244–250] that “the ionic activity coefficients are independent of the nature and concentration of the reference solution”. The results of the present study validate Guggenheim’s interpretation and afford to amplify it by stating that such coefficients are misnomers in the sense that they do not represent thermodynamic properties of ions, and ought not to be called activity coefficients.

Acoustical scattering by multilayer spherical elastic scatterer containing electrorheological layer

A computational procedure for analyzing acoustical scattering by multilayer concentric spherical scatterers having an arbitrary mixture of acoustic and elastic materials is proposed. The procedure is then used to analyze the scattering by a spherical scatterer consisting of a solid shell and a solid core encasing an electrorheological (ER) fluid layer, and the tunability in the scattering characteristics afforded by the ER layer is explored numerically. Tunable scatterers with two different ER fluids are analyzed. One, corn starch in peanut oil, shows that a significant increase in scattering cross-section is possible in moderate frequencies. Another, fine poly-methyl methacrylate (PMMA) beads in dodecane, shows only slight change in scattering cross-sections overall. But, when the shell is thin, a noticeable local resonance peak can appear near ka=1, and this resonance can be turned on or off by the external electric field.

Arbitrary mixture of two charged interacting particles in a magnetic Aharonov–Bohm ring: persistent currents and Berry's phases

Aharonov–Bohm physics at the two-particle level is investigated for distinguishable interacting charged particles through the exact solution of a toy model with confined states. The effect of the inaccessible magnetic flux is distributed between the center-of-mass and the internal pair level, and the nontrivial manner in which the two levels mutually affect each other demonstrates the interplay between interactions, the nontrivial topology, the Aharonov–Bohm flux and the characteristics of a charged quantal mixture. Analytical expressions for energy spectra, wavefunctions, (flux-dependent) critical interactions for binding and current densities are derived, and these offer the rare possibility of studying persistent currents from the point of view of an interacting nanoscopic system. Two cyclic adiabatic processes are identified, one coupled to the center-of-mass behavior and the other defined on the two-body interaction potential, with the associated Berry's phases also analytically determined; these are found to be directly linked to the electric and probability (persistent) currents in nontrivial ways that are shown to be universal (independent of the actual form of the interaction). The direct connection of the two-body Berry's phase to the electric current for a neutral system is found to disappear in the case of identical particles—hence revealing the character of a charged mixture as being crucial for exhibiting this universal behavior.

Simplification and hierarchical representations of mixtures of exponential families

A mixture model in statistics is a powerful framework commonly used to estimate the probability measure function of a random variable. Most algorithms handling mixture models were originally specifically designed for processing mixtures of Gaussians. However, other distributions such as Poisson, multinomial, Gamma/Beta have gained interest in signal processing in the past decades. These common distributions are unified in the framework of exponential families in statistics. In this paper, we present three generic clustering algorithms working on arbitrary mixtures of exponential families: the Bregman soft clustering, the Bregman hard clustering, and the Bregman hierarchical clustering. These algorithms allow one to estimate a mixture model from observations, to simplify such a mixture model, and to automatically learn the “optimal” number of components in a simplified mixture model according to a resolution parameter. In addition, we present jMEF, an open source Java TM library allowing users to create, process and manage mixtures of exponential families. In particular, jMEF includes the three aforementioned Bregman clustering algorithms.

Mapping surrogate gasoline compositions into RON/MON space

Abstract In this paper, new experimentally determined octane numbers (RON and MON) of blends of a tri-component surrogate consisting of toluene, n-heptane, i-octane (called toluene reference fuel TRF) arranged in an augmented simplex design are used to derive a simple response surface model for the octane number of any arbitrary TRF mixture. The model is second-order in its complexity and is shown to be more accurate to the standard “linear-by-volume” (LbV) model which is often used when no other information is available. Such observations are due to the existence of both synergistic and antagonistic blending of the octane numbers between the three components. In particular, antagonistic blending of toluene and iso-octane leads to a maximum in sensitivity that lies on the toluene/iso-octane line. The model equations are inverted so as to map from RON/MON space back into composition space. Enabling one to use two simple formulae to determine, for a given fuel with known RON and MON, the volume fractions of toluene, n-heptane and iso-octane to be blended in order to emulate that fuel. HCCI engine simulations using gasoline with a RON of 98.5 and a MON of 88 were simulated using a TRF fuel, blended according to the derived equations to match the RON and MON. The simulations matched the experimentally obtained pressure profiles well, especially when compared to simulations using only PRF fuels which matched the RON or MON. This suggested that the mapping is accurate and that to emulate a refinery gasoline, it is necessary to match not only the RON but also the MON of the fuel.

Low-temperature gas opacity

We introduce a new tool - AESOPUS: Accurate Equation of State and OPacity Utility Software - for computing the equation of state and the Rosseland mean (RM) opacities of matter in the ideal gas phase. Results are given as a function of one pair of state variables, (i.e. temperature T in the range 3.2 <= log(T) <= 4.5, and parameter R= rho/(T/10^6 K)^3 in the range -8 <= log(R) <= 1), and arbitrary chemical mixture. The chemistry is presently solved for about 800 species, consisting of almost 300 atomic and 500 molecular species. The gas opacities account for many continuum and discrete sources, including atomic opacities, molecular absorption bands, and collision-induced absorption. Several tests made on AESOPUS have proved that the new opacity tool is accurate in the results,flexible in the management of the input prescriptions, and agile in terms of computational time requirement. We set up a web-interface (http://stev.oapd.inaf.it/aesopus) which enables the user to compute and shortly retrieve RM opacity tables according to his/her specific needs, allowing a full degree of freedom in specifying the chemical composition of the gas. Useful applications may regard RM opacities of gas mixtures with i) scaled-solar abundances of metals, choosing among various solar mixture compilations available in the literature; ii) varying CNO abundances, suitable for evolutionary models of red and asymptotic giant branch stars and massive stars in the Wolf-Rayet stages; iii) various degrees of enhancement in alpha-elements, and C-N, Na-O and Mg-Al abundance anti-correlations, necessary to properly describe the properties of stars in early-type galaxies and Galactic globular clusters; iv) zero-metal abundances appropriate for studies of gas opacity in primordial conditions.

Chapman–Enskog solutions to arbitrary order in Sonine polynomials V: Summational expressions for the viscosity-related bracket integrals

The Chapman–Enskog solutions of the Boltzmann equations provide a basis for the computation of important transport coefficients for both simple gases and gas mixtures. These coefficients include the viscosity, the thermal conductivity, and the diffusion coefficient. In a preceding paper on simple gases (I), we have shown that the use of higher-order Sonine polynomial expansions enables one to obtain results of arbitrary precision that are free of numerical error. In two subsequent papers (II–III), we extended our original simple gas work to encompass binary gas mixture computations of the viscosity, thermal conductivity, diffusion, and thermal diffusion coefficients to high-order. In a fourth paper (IV) we derived general summational representations for the diffusion- and thermal conductivity-related bracket integrals and provided compact, explicit expressions for all of these bracket integrals needed to compute the diffusion- and thermal conductivity-related transport coefficients up to order 5 in the Sonine polynomial expansions used. In all of this previous work we retained the full dependence of our solutions on the molecular masses, the molecular sizes, the mole fractions, and the intermolecular potential model via the omega integrals up to the final point of solution via matrix inversion. The elements of the matrices to be inverted are, in each case, determined by appropriate combinations of bracket integrals which contain, in general form, all of the various dependencies. Since accurate expressions for the needed bracket integrals have not previously been available in the literature beyond orders 2 or 3, and since such expressions are necessary for any extensive program of computations of the transport coefficients involving Sonine polynomial expansions to higher orders, we have investigated alternative methods of constructing appropriately general bracket integral expressions that do not rely on the term-by-term, expansion and pattern matching techniques that we developed for our previous work. It is our purpose in this paper to report the results of our efforts to obtain useful, alternative, general expressions for the bracket integrals associated with the viscosity-related Chapman–Enskog solutions for gas mixtures. Specifically, we have obtained such expressions in summational form that are conducive to use in high-order viscosity coefficient computations for arbitrary gas mixtures and have computed and reported explicit expressions for all of the orders up to 5.

Rateless Coding for Arbitrary Channel Mixtures With Decoder Channel State Information

Rateless coding has recently been the focus of much practical as well as theoretical research. In this paper, rateless codes are shown to find a natural application in channels where the channel law varies unpredictably. Such unpredictability means that to ensure reliable communication block codes are limited by worst case channel variations. However, the dynamic decoding nature of rateless codes allows them to adapt opportunistically to channel variations. If the channel state selector is not malicious, but also not predictable, decoding can occur earlier, producing a rate of communication that can be much higher than the worst case. The application of rateless or ldquofountainrdquo codes to the binary erasure channel (BEC) can be understood as an application of these ideas. Further, this sort of decoding can be usefully understood as an incremental form of erasure decoding. The use of ideas of erasure decoding result in a significant increase in reliability.

Particle distribution tail and related energy formula

We present a simple derivation of the energy formula found by Tan, relative to the single channel hamiltonian relevant for ultracold Fermi gases. This derivation is generalized to particles with different masses, to arbitrary mixtures, and to two-dimensional space. We show how, in a field theoretical approach, the $1/k^4$ tail in the momentum distribution and the energy formula arise in a natural way. As a specific example, we consider quantitative calculations of the energy, from different formulas within the ladder diagrams approximation in the normal state. The comparison of the results provides an indication on the quality of the approximation.

Chapman–Enskog solutions to arbitrary order in Sonine polynomials IV: Summational expressions for the diffusion- and thermal conductivity-related bracket integrals

The Chapman–Enskog solutions of the Boltzmann equations provide a basis for the computation of important transport coefficients for both simple gases and gas mixtures. These coefficients include the viscosity, the thermal conductivity, and the diffusion coefficient. In a preceding paper on simple gases, we have shown that the use of higher-order Sonine polynomial expansions enables one to obtain results of arbitrary precision that are free of numerical error. In two subsequent papers, we have extended our original simple gas work to encompass binary gas mixture computations of the viscosity, thermal conductivity, diffusion, and thermal diffusion coefficients to high-order. In all of this previous work we retained the full dependence of our solutions on the molecular masses, the molecular sizes, the mole fractions, and the intermolecular potential model via the omega integrals up to the final point of solution via matrix inversion. The elements of the matrices to be inverted are, in each case, determined by appropriate combinations of bracket integrals which contain, in general form, all of the various dependencies. Since accurate, explicit, general expressions for bracket integrals are not available in the literature beyond order 3, and since such general expressions are necessary for any extensive program of computations of the transport coefficients involving Sonine polynomial expansions to higher orders, we have investigated alternative methods of constructing appropriately general bracket integral expressions that do not rely on the term-by-term, expansion and pattern matching techniques that we developed for our previous work. It is our purpose in this paper to report the results of our efforts to obtain useful, alternative, general expressions for the bracket integrals associated with the diffusion- and thermal conductivity-related Chapman–Enskog solutions for gas mixtures. Specifically, we have obtained such expressions in summational form that are conducive to use in high-order transport coefficient computations for arbitrary gas mixtures and have computed and reported explicit expressions for all of the orders up to 5.

Mediating Role of Multivalent Cations in DNA Electrostatics: An Epsilon-Modified Poisson−Boltzmann Study of B-DNA−B-DNA Interactions in Mixture of NaCl and MgCl2 Solutions

Potentials of mean force acting between two ions in SPC/E water have been determined via molecular dynamics simulations using the spherical cavity approach ( J. Phys. Chem. B 2006 , 110 , 10878 ). The potentials were obtained for Me(2+)-Me(+) pairs, where Me(2+) means cations Mg(2+) and Ca(2+) and Me(+) denotes monovalent ions Li(+), Na(+), and K(+). The hard-core interaction distance for effective Me(2+)-Me(+) potentials appears to be of about 5 A that looks like a sum of the effective radii of a Me(2+) ion (3 A) and of an alkali metal ion Me(+) (about 2 A). These ion-ion interaction parameters were used in the epsilon-Modified Poisson-Boltzmann (epsilon-MPB) calculations ( J. Phys. Chem. B 2007 , 111 , 5264 ) of ionic distributions around DNA generalized for the arbitrary mixture of different ion species. Ionic distributions around an all-atom geometry model of B-DNA in solution of a mixture of NaCl and MgCl(2) were obtained. It was found that even a small fraction of ions Mg(2+) led to sharp condensation of Mg(2+) near the phosphate groups of DNA due to polarization deficiency of cluster [Mg(H(2)O)(6)](2+) in an external field. The epsilon-MPB calculations of the B-DNA-B-DNA interaction energies suggest that adding 1 mM of Mg(2+) to 50 mM solution of NaCl notably affects the force acting between the two macromolecules. Being compared to Poisson-Boltzmann results and to MPB calculations for the primitive model of ions, the epsilon-MPB results also indicate an important contribution of dielectric saturation effects to the mediating role of divalent cations in the DNA-DNA interaction energies.

On The New Better Than Used Renewal Failure Rate at Specified Time

In this paper we introduce a new class of life distribution called the new better (worse) than used renewal failure rate at specified time t 0 NBURFR-t 0 (NWURFR-t 0). Some closure properties, such as closure under convolution, arbitrary and general mixture, and Shock model are discussed. Furthermore, a nonparametric test is proposed to test exponentiality against the NBURFR-t 0 class. The critical values, the powers and Pitman efficiencies are calculated for t 0 = 0:25.

Basic principles of electrolyte chemistry for microfluidic electrokinetics. Part I: Acid–base equilibria and pH buffers

We review fundamental and applied acid-base equilibrium chemistry useful to microfluidic electrokinetics. We present elements of acid-base equilibrium reactions and derive rules for pH calculation for simple buffers. We also present a general formulation to calculate pH of more complex, arbitrary mixtures of electrolytes, and discuss the effects of ionic strength and temperature on pH calculation. More practically, we offer advice on buffer preparation and on buffer reporting. We also discuss "real world" buffers and likely contamination sources. In particular, we discuss the effects of atmospheric carbon dioxide on buffer systems, namely, the increase in ionic strength and acidification of typical electrokinetic device buffers. In Part II of this two-paper series, we discuss the coupling of acid-base equilibria with electrolyte dynamics and electrochemistry in typical microfluidic electrokinetic systems.

On the Minimum Entropy of a Mixture of Unimodal and Symmetric Distributions

Progressive encoding of a signal generally involves an estimation step, designed to reduce the entropy of the residual of an observation over the entropy of the observation itself. Oftentimes the conditional distributions of an observation, given already-encoded observations, are well fit within a class of symmetric and unimodal distributions (e.g., the two-sided geometric distributions in images of natural scenes, or symmetric Paretian distributions in models of financial data). It is common practice to choose an estimator that centers, or aligns, the modes of the conditional distributions, since it is common sense that this will minimize the entropy, and hence the coding cost of the residuals. But with the exception of a special case, there has been no rigorous proof. Here we prove that the entropy of an arbitrary mixture of symmetric and unimodal distributions is minimized by aligning the modes. The result generalizes to unimodal and rotation-invariant distributions in R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> . We illustrate the result through some experiments with natural images.

Generation of nanoparticles by spark discharge

The production of nanoparticles by microsecond spark discharge evaporation in inert gas is studied systematically applying transmission electron microscopy, mobility analysis and BET surface area measurement. The method of spark discharge is of special interest, because it is continuous, clean, extremely flexible with respect to material, and scale-up is possible. The particle size distributions are narrow and the mean primary particle size can be controlled via the energy per spark. Separated, unagglomerated particles, 3–12 nm in size, or agglomerates can be obtained depending on the flow rate. The nanoparticulate mass produced is typically 5 g/kWh. A formula is given, which estimates the mass production rate via thermal conductivity, evaporation enthalpy and the boiling point of the material used. We showed that with gas purified at the spot, the method produced gold particles that were so clean that sintering of agglomerated particles occurred at room temperature. The influence of a number of parameters on the primary particle size and mass production rate was studied and qualitatively understood with a model of Lehtinen and Zachariah (J Aerosol Sci 33:357–368, 2002). Surprisingly high charging probabilities for one polarity were obtained. Spark generation is therefore of special interest for producing monodisperse aerosols or particles of uniform size via electrical mobility analysis. Qualitative observations in the present study include the phenomenon of material exchange between the electrodes by the spark, which opens the possibility of producing arbitrary mixtures of materials on a nanoscale. If spark generation of nanoparticles is performed in a standing or almost standing gas, an aerogel of a web-like structure forms between surfaces of different electrical potential.