Analytical Flux Research Articles

Applying an accurate spherical model to gamma-ray burst afterglow observations

We present results of model fits to afterglow data sets of GRB970508, GRB980703 and GRB070125, characterized by long and broadband coverage. The model assumes synchrotron radiation (including self-absorption) from a spherical adiabatic blast wave and consists of analytic flux prescriptions based on numerical results. For the first time it combines the accuracy of hydrodynamic simulations through different stages of the outflow dynamics with the flexibility of simple heuristic formulas. The prescriptions are especially geared towards accurate description of the dynamical transition of the outflow from relativistic to Newtonian velocities in an arbitrary power-law density environment. We show that the spherical model can accurately describe the data only in the case of GRB970508, for which we find a circumburst medium density consistent with a stellar wind. We investigate in detail the implied spectra and physical parameters of that burst. For the microphysics we show evidence for equipartition between the fraction of energy density carried by relativistic electrons and magnetic field. We also find that for the blast wave to be adiabatic, the fraction of electrons accelerated at the shock has to be smaller than 1. We present best-fit parameters for the afterglows of all three bursts, including uncertainties in the parameters of GRB970508, and compare the inferred values to those obtained by different authors.

Enhancement of affinity-based biosensors: effect of sensing chamber geometry on sensitivity

Affinity-based biosensing systems have become an important analytical tool for the detection and study of numerous biomolecules. The merging of these sensing technologies with microfluidic flow cells allows for faster detection times, increased sensitivities, and lower required sample volumes. In order to obtain a higher degree of performance from the sensor, it is important to know the effects of the flow cell geometry on the sensor sensitivity. In these sensors, the sensor sensitivity is related to the overall diffusive flux of analyte to the sensing surface; therefore increases in the analyte flux will be manifested as an increase in sensitivity, resulting in a lower limit of detection (LOD). Here we present a study pertaining to the effects of the flow cell height H on the analyte flux J, where for a common biosensor design we predict that the analyte flux will scale as J ≈ H(-2/3). We verify this scaling behavior via both numerical simulations as well as an experimental surface plasmon resonance (SPR) biosensor. We show the reduction of the flow cell height can have drastic effects on the sensor performance, where the LOD of our experimental system concerning the detection of ssDNA decreases by a factor of 4 when H is reduced from 47 μm to 7 μm. We utilize these results to discuss the applicability of this scaling behavior with respect to a generalized affinity-based biosensor.

Practical flux prescriptions for gamma-ray burst afterglows, from early to late times

We present analytic flux prescriptions for broadband spectra of self-absorbed and optically thin synchrotron radiation from gamma-ray burst afterglows, based on one-dimensional relativistic hydrodynamic simulations. By treating the evolution of critical spectrum parameters as a power-law break between the ultrarelativistic and non-relativistic asymptotic solutions, we generalize the prescriptions to any observer time. Our aim is to provide a set of formulas that constitutes a useful tool for accurate fitting of model-parameters to observational data, regardless of the dynamical phase of the outflow. The applicability range is not confined to gamma-ray burst afterglows, but includes all spherical outflows (also jets before the jet-break) that produce synchrotron radiation as they adiabatically decelerate in a cold, power-law medium. We test the accuracy of the prescriptions and show that numerical evidence suggests that typical relative errors in the derivation of physical quantities are about 10 per cent. A software implementation of the presented flux prescriptions combined with a fitting code is freely available on request and on-line. Together they can be used in order to directly fit model parameters to data.

Thermally controlled permeation of ionic molecules through synthetic nanopores functionalized with amine-terminated polymer brushes

We present temperature-dependent ionic transport through an array of nanopores (cylindrical and conical) and a single conical nanopore functionalized with amine-terminated poly(N-isopropylacrylamide) [PNIPAAM-NH2] brushes. For this purpose, nanopores are fabricated in heavy ion irradiated polyethylene terephthlate (PET) membranes by a controlled chemical track-etching technique, which leads to the generation of carboxyl (COOH) groups on the pore surface. End-functionalized polymer chains are immobilized onto the inner pore walls via a ‘grafting-to’ approach through the covalent linkage of surface COOH moieties with the terminal amine groups of the PNIPAAM molecules by using carbodiimide coupling chemistry. The success of the chemical modification reaction is corroborated by measuring the permeation flux of charged analytes across the multipore membranes in an aqueous solution, and for the case of single conical pore by measuring the current–voltage (I–V) characteristics, which are dictated by the electrostatic interaction of the charged pore surface with the mobile ions in an electrolyte solution. The effective nanopore diameter is tuned by manipulating the environmental temperature due to the swelling/shrinking behaviour of polymer brushes attached to the inner nanopore walls, leading to a decrease/increase in the ionic transport across the membrane. This process should permit the thermal gating and controlled release of ionic drug molecules through the nanopores modified with thermoresponsive polymer chains across the membrane.

Simultaneous measurement of the TCA cycle and respiration in isolated mitochondria and intact cells with the XF24‐3 Analyzer

Measuring mitochondrial dysfunction is increasingly important in the study of neurodegenerative and cardiovascular disease, metabolic syndrome, diabetes, cancer, and aging. Mitochondrial function is usually measured by oxygen consumption rates using respirometry methods. However, a critical aspect of mitochondrial function may be overlooked when only O2 consumption is employed: the tricarboxylic acid (TCA) or Krebs cycle, a central metabolic pathway. Measuring the TCA cycle function requires monitoring the flux of an additional analyte, such as carbon dioxide (CO2). The reported method describes simultaneous monitoring of carbon dioxide evolution rates (CDER) and oxygen consumption rates (OCR) using isolated mitochondria and intact cells, in real‐time, using the XF24‐3 Analyzer. This technology employs fluorescent sensors specific for CO2 and O2, which operate reversibly, and reveal details of mitochondrial respiration and TCA cycle activities. Results indicate that O2 consumption and CO2 evolution may be monitored simultaneously, and that data agrees with attributes of TCA cycle and mitochondrial function obtained by other methods. Differential rates of O2 and CO2 flux can be identified relative to substrate utilization and interdependency among the TCA cycle, electron transport, and oxidative phosphorylation systems. Support for this research is provided by Seahorse Bioscience.

Fetch requirements using surface renewal analysis for estimating scalar surface fluxes from measurements in the inertial sublayer

The Surface Renewal, SR, method to estimate scalar surface fluxes is based on the scalar conservation equation and requires the measurement of the scalar (at high frequency) taken at one height as input. The distance downwind from the leading edge needed to deploy instrumentation depends on the measurements required as input in the method used for scalar flux estimation. However, a footprint model for the SR method has not been yet studied. On the basis of the Horst and Weill's (1994) Eulerian analytical flux footprint model, an equation was derived that relates the ramp dimensions required in the SR method as input with the cross-wind integrated scalar concentration distribution. It was tested using measurements of water vapor and carbon dioxide concentrations at a height of 2 m over rangeland grass (0.25 m tall). The agreement was excellent. As a consequence, the footprint model for the SR method operating in the inertial sublayer is identical to the flux-gradient, FG, method. The footprints for the eddy covariance, EC, method and for FG method are close. Consequently, for low vegetation when the eddy covariance, EC, and the SR methods operate at the same level in the inertial sublayer, the footprints may be considered identical. The SR method does not require a three dimensional sonic anemometer. Therefore, for low vegetation the SR method has the potential to be less stringent to fetch requirements than the EC method because the instrumentation required can be deployed closer to the ground.

Analytical substrate flux approximation for the Monod boundary value problem

We present an analytical approximation for the diffusive flux of a substrate into a reactive layer, in which the substrate is degraded according to Monod kinetics. This problem is described by a nonlinear two-point boundary value problem. The approximation is derived based on a Homotopy Analysis Method idea and verified computationally, by comparison against a numerical solution of the problem. The analytical approximation is easy to evaluate and depends only on model parameters.

Electrochemical behaviour and voltammetric sensitivity at arrays of nanoscale interfaces between immiscible liquids

Arrays of nanoscale interfaces between immiscible electrolyte solutions were formed using silicon nitride nanopore array membranes. Nanopores in the range from 75 nm radius down to 17 nm radius were used to form the nano-interfaces. It was found that the liquid organic phase electrolyte solution filled the pores so that inlaid nano-interfaces were formed with the aqueous phase. Cyclic voltammetry at these nano-interface arrays demonstrated steady-state behaviour at the larger interfaces but the voltammetric wave-shape became progressively worse as the interface size decreased. It was found that the ion transfer currents were ca. 50% of those expected based on theoretical calculations, which is attributed to overlap of diffusion zones at adjacent nano-interfaces. Here, the separation between adjacent nano-interfaces was 20-times the interface radius. The analytical sensitivity for ion transfer from the aqueous to the 1,6-dichlorohexane organic phase was estimated from calibration plots of current density versus concentration of aqueous tetraethylammonium cation. The sensitivity was in the range of 65 μA cm(-2) μM(-1) (at 75 nm radius interfaces) to 265 μA cm(-2) μM(-1) (at 17 nm radius interfaces). The sensitivity depended directly on the inverse of the nano-interface radius, implying that smaller interfaces will provide better sensitivity, due to the enhanced flux of analyte arising from convergent diffusion to smaller electrochemical interfaces.

Flow-Through vs Flow-Over: Analysis of Transport and Binding in Nanohole Array Plasmonic Biosensors

We quantify the efficacy of flow-through nanohole sensing, as compared to the established flow-over format, through scaling analysis and numerical simulation. Nanohole arrays represent a growing niche within surface plasmon resonance-based sensing methods, and employing the nanoholes as nanochannels can enhance transport and analytical response. The additional benefit offered by flow-through operation is, however, a complex function of operating parameters and application-specific binding chemistry. Compared here are flow-over sensors and flow-through nanohole array sensors with equivalent sensing area, where the nanohole array sensing area is taken as the inner-walls of the nanoholes. The footprints of the sensors are similar (e.g., a square 20 μm wide flow-over sensor has an equivalent sensing area as a square 30 μm wide array of 300 nm diameter nanoholes with 450 nm periodicity in a 100 nm thick gold film). Considering transport alone, an analysis here shows that given equivalent sensing area and flow rate the flow-through nanohole format enables greatly increased flux of analytes to the sensing surface (e.g., 40-fold for the case of Q = 10 nL/min). Including both transport and binding kinetics, a computational model, validated by experimental data, provides guidelines for performance as a function of binding time constant, analyte diffusivity, and running parameters. For common binding kinetics and analytes, flow-through nanohole arrays offer ∼10-fold improvement in response time, with a maximum of 20-fold improvement for small biomolecules with rapid kinetics.

A self referencing platinum nanoparticle decorated enzyme-based microbiosensor for real time measurement of physiological glucose transport

Glucose is the central molecule in many biochemical pathways, and numerous approaches have been developed for fabricating micro biosensors designed to measure glucose concentration in/near cells and/or tissues. An inherent problem for microsensors used in physiological studies is a low signal-to-noise ratio, which is further complicated by concentration drift due to the metabolic activity of cells. A microsensor technique designed to filter extraneous electrical noise and provide direct quantification of active membrane transport is known as self-referencing. Self-referencing involves oscillation of a single microsensor via computer-controlled stepper motors within a stable gradient formed near cells/tissues (i.e., within the concentration boundary layer). The non-invasive technique provides direct measurement of trans-membrane (or trans-tissue) analyte flux. A glucose micro biosensor was fabricated using deposition of nanomaterials (platinum black, multiwalled carbon nanotubes, Nafion) and glucose oxidase on a platinum/iridium microelectrode. The highly sensitive/selective biosensor was used in the self-referencing modality for cell/tissue physiological transport studies. Detailed analysis of signal drift/noise filtering via phase sensitive detection (including a post-measurement analytical technique) are provided. Using this highly sensitive technique, physiological glucose uptake is demonstrated in a wide range of metabolic and pharmacological studies. Use of this technique is demonstrated for cancer cell physiology, bioenergetics, diabetes, and microbial biofilm physiology. This robust and versatile biosensor technique will provide much insight into biological transport in biomedical, environmental, and agricultural research applications.

Self-referencing optrodes for measuring spatially resolved, real-time metabolic oxygen flux in plant systems

The ability to non-invasively measure metabolic oxygen flux is a very important tool for physiologists interested in a variety of questions ranging from basic metabolism, growth/development, and stress adaptation. Technologies for measuring oxygen concentration near the surface of cells/tissues include electrochemical and optical techniques. A wealth of knowledge was gained using these tools for quantifying real-time physiology. Fiber-optic microprobes (optrodes) have recently been developed for measuring oxygen in a variety of biomedical and environmental applications. We have adopted the use of these optical microsensors for plant physiology applications, and used the microsensors in an advanced sensing modality known as self-referencing. Self-referencing is a non-invasive microsensor technique used for measuring real-time flux of analytes. This paper demonstrates the use of optical microsensors for non-invasively measuring rhizosphere oxygen flux associated with respiration in plant roots, as well as boundary layer oxygen flux in phytoplankton mats. Highly sensitive/selective optrodes had little to no hysteresis/calibration drift during experimentation, and an extremely high signal-to-noise ratio. We have used this new tool to compare various aspects of rhizosphere oxygen flux for roots of Glycine max, Zea mays, and Phaseolus vulgaris, and also mapped developmentally relevant profiles and distinct temporal patterns. We also characterized real-time respiratory patterns during inhibition of cytochrome and alternative oxidase pathways via pharmacology. Boundary layer oxygen flux was also measured for a phytoplankton mat during dark:light cycling and exposure to pharamacological inhibitors. This highly sensitive technology enables non-invasive study of oxygen transport in plant systems under physiologically relevant conditions.

Upscaling of CO 2 vertical migration through a periodic layered porous medium: The capillary-free and capillary-dominant cases

We present an upscaled model for the vertical migration of a CO 2 plume through a vertical column filled with a periodic layered porous medium. This model may describe the vertical migration of a CO 2 plume in a perfectly layered horizontal aquifer. Capillarity and buoyancy are taken into account and semi-explicit upscaled flux functions are proposed in the two following cases: (i) capillarity is the main driving force and (ii) buoyancy is the only driving force. In both cases, we show that the upscaled buoyant flux is a bell-shaped function of the saturation, as in the case of a homogeneous porous medium. In the capillary-dominant case, we show that the upscaled buoyant flux is the harmonic mean of the buoyant fluxes in each layer. The upscaled saturation is governed by the continuity of the capillary pressure at the interface between layers. In the capillary-free case, the upscaled buoyant flux and upscaled saturation are determined by the flux continuity condition at the interface. As the flux is not continuous over the entire range of saturation, the upscaled saturation is only defined where continuity is verified, i.e. in two saturation domains. As a consequence, the upscaled buoyant flux is described by a piecewise continuous function. Two analytical approximations of this flux are proposed and this capillary-free upscaled model is validated for two cases of heterogeneity. Upscaled and cell averaged saturations are in good agreement. Furthermore, the proposed analytical upscaled fluxes provide satisfactory approximations as long as the saturation set at the inlet of the column is in a range where analytical and numerical upscaled fluxes are close.

OBSERVATIONAL EVIDENCE OF A CORONAL MASS EJECTION DISTORTION DIRECTLY ATTRIBUTABLE TO A STRUCTURED SOLAR WIND

We present the first observational evidence of the near-Sun distortion of the leading edge of a coronal mass ejection (CME) by the ambient solar wind into a concave structure. On 2007 November 14, a CME was observed by coronagraphs onboard the STEREO-B spacecraft, possessing a circular cross section. Subsequently the CME passed through the field of view of the STEREO-B Heliospheric Imagers where the leading edge was observed to distort into an increasingly concave structure. The CME observations are compared to an analytical flux rope model constrained by a magnetohydrodynamic solar wind solution. The resultant bimodal speed profile is used to kinematically distort a circular structure that replicates the initial shape of the CME. The CME morphology is found to change rapidly over a relatively short distance. This indicates an approximate radial distance in the heliosphere where the solar wind forces begin to dominate over the magnetic forces of the CME influencing the shape of the CME.

The expected imprint of flux rope geometry on suprathermal electrons in magnetic clouds

Abstract. Magnetic clouds are a subset of interplanetary coronal mass ejections characterized by a smooth rotation in the magnetic field direction, which is interpreted as a signature of a magnetic flux rope. Suprathermal electron observations indicate that one or both ends of a magnetic cloud typically remain connected to the Sun as it moves out through the heliosphere. With distance from the axis of the flux rope, out toward its edge, the magnetic field winds more tightly about the axis and electrons must traverse longer magnetic field lines to reach the same heliocentric distance. This increased time of flight allows greater pitch-angle scattering to occur, meaning suprathermal electron pitch-angle distributions should be systematically broader at the edges of the flux rope than at the axis. We model this effect with an analytical magnetic flux rope model and a numerical scheme for suprathermal electron pitch-angle scattering and find that the signature of a magnetic flux rope should be observable with the typical pitch-angle resolution of suprathermal electron data provided ACE's SWEPAM instrument. Evidence of this signature in the observations, however, is weak, possibly because reconnection of magnetic fields within the flux rope acts to intermix flux tubes.

The Formation of Large-Scale Current Sheets within Magnetic Clouds

Magnetic clouds are a class of interplanetary coronal mass ejections (CME) predominantly characterised by a smooth rotation in the magnetic field direction, indicative of a magnetic flux rope structure. Many magnetic clouds, however, also contain sharp discontinuities within the smoothly varying magnetic field, suggestive of narrow current sheets. In this study we present observations and modelling of magnetic clouds with strong current sheet signatures close to the centre of the apparent flux rope structure. Using an analytical magnetic flux rope model, we demonstrate how such current sheets can form as a result of a cloud’s kinematic propagation from the Sun to the Earth, without any external forces or influences. This model is shown to match observations of four particular magnetic clouds remarkably well. The model predicts that current sheet intensity increases for increasing CME angular extent and decreasing CME radial expansion speed. Assuming such current sheets facilitate magnetic reconnection, the process of current sheet formation could ultimately lead a single flux rope becoming fragmented into multiple flux ropes. This change in topology has consequences for magnetic clouds as barriers to energetic particle propagation.

Representation of the plasma fluid equations in “Miller equilibrium” analytical flux surface geometry

The plasma fluid equations are represented explicitly in the magnetic flux surface coordinate system resulting from the analytical “Miller equilibrium” solution of the Grad–Shafranov equation. The magnetic geometry is characterized by the elongation, triangularity, and location of the displaced major radius of the flux surface. The resulting fluid equations can be solved directly without the necessity of first solving the Grad–Shafranov equation numerically to define the flux surface coordinates.

Non‐invasive self‐referencing electrochemical sensors for quantifying real‐time biofilm analyte flux

Current techniques for characterizing biofilm physiology lack the signal filtering capability required for quantifying signals associated with real time biologically active transport. Though a great deal was learned from previous investigations, no results have been reported on the characterization of in vivo, real time biofilm flux using non-invasive (non-destructive) techniques. This article introduces the self-referencing technique for applications in biofilm physiology. Self-referencing is a non-invasive sensing modality which is capable of sensing changes in biologically active analyte flux as small as 10 fmol cm(-2) s(-1). Studies directly characterizing flux, as opposed to concentration, have the advantage of quantifying real time changes in biologically active transport which are otherwise lost to background noise. The use of this modality for characterizing biofilm physiology is validated with a reversible enzyme inhibition study. The experiment used self-referencing potentiometric sensors for quantifying real time ammonium and nitrite flux. Amperometric and optical sensing methods, though not presented herein, are also powerful sensing tools which benefit from operation in self-referencing mode. Reversible ammonia monooxygenase inhibition by a copper chelator (thiourea), and subsequent relief by excess copper addition was successfully demonstrated using self-referencing ion-selective microelectrodes for a mature Nitrosomonas europaea biofilm.

Preliminary design of surrounding heliostat fields

Recently, the author has shown elsewhere a simplified model that allows quick evaluations of the annual overall energy collected by a surrounding heliostat field. This model is the combination of an analytical flux density function produced by a heliostat, developed by the own author, and an optimized mirror density distribution developed by University of Houston for the Solar One Project. As main conclusion of this previous work, it was recognized that such pseudo-continuous simplified model should not substitute much more accurate discrete evaluations, which manage thousands of individual heliostat coordinates. Here in this work, the difficulty of generating a preliminary discrete layout of a large number of heliostats is addressed. The main novelty is the direct definition of thousands of heliostat coordinates through basically two parameters i.e. a simplified blocking factor and an additional security distance. Such procedure, which was formerly theoretically suggested by the author, is put into practice here, showing examples and commenting their problems and advantages. Getting a previous set of thousands of heliostat coordinates would be a major first step in the complex process of designing solar power tower (SPT).

Modeling of stochastic broadening in a poloidally diverted discharge with piecewise analytic symplectic mapping flux functions

A highly accurate calculation of the magnetic field line Hamiltonian in DIII-D [J. L. Luxon and L. E. Davis, Fusion Technol. 8, 441 (1985)] is made from piecewise analytic equilibrium fit data for shot 115467 3000ms. The safety factor calculated from this Hamiltonian has a logarithmic singularity at an ideal separatrix. The logarithmic region inside the ideal separatrix contains 2.5% of toroidal flux inside the separatrix. The logarithmic region is symmetric about the separatrix. An area-preserving map for the field line trajectories is obtained in magnetic coordinates from the Hamiltonian equations of motion for the lines and a canonical transformation. This map is used to calculate trajectories of magnetic field lines in DIII-D. The field line Hamiltonian in DIII-D is used as the generating function for the map and to calculate stochastic broadening from field-errors and spatial noise near the separatrix. A very negligible amount (0.03%) of magnetic flux is lost from inside the separatrix due to these nonaxisymmetric fields. It is quite easy to add magnetic perturbations to generating functions and calculate trajectories for maps in magnetic coordinates. However, it is not possible to integrate across the separatrix. It is also difficult to find the physical position corresponding to magnetic coordinates. For open field lines, periodicity in the poloidal angle is assumed, which is not satisfactory. The goal of this paper is to demonstrate the efficacy of the symplectic mapping approach rather than using realistic DIII-D parameters or modeling specific experimental results.

Optical Nanoscale Pool‐on‐Surface Design for Control Sensing Recognition of Multiple Cations

AbstractGeneral design of optical chemical nanosensors is needed to develop efficient sensing systems with high flexibility, and low capital cost for control recognition of toxic analytes. Here, we designed optical chemical nanosensors for simple, high‐speed detection of multiple toxic metal ions. The systematic design of the nanosensors was based on densely patterned chromophores with intrinsic mobility, namely, “building‐blocks” onto three‐dimensional (3D) nanoscale structures. The ability to precisely modify the nanoscale pore surfaces by using a broad range of chromophores that have different molecular sizes and characteristics enables detection of multiple toxic ions. A key feature of this building‐blocks design strategy is that the surface functionality and good adsorption characteristics of the fabricated nanosensor arrays enabled the development of “pool‐on‐surface” sensing systems in which high flux of the metal analytes across the probe molecules was achieved without significant kinetic hindrance. Such a sensing design enabled sensitive recognition of metal ions up to sub‐picomolar detection limits (∼10−11 mol dm−3), for first time, with rapid response time within few seconds. Moreover, because these sensing pools exhibited long‐term stability, reversibility and selectivity in detecting most pollutant cations, for example, Cr(VI), Pb(II), Co(II), and Pd(II) ions, they are practical and inexpensive. The key result in our study is that the pool‐on‐surface design for optical nanosensors exhibited significant ion‐selective ability of these target ions from environmental samples and waste disposals.