Infinitesimal Amount Research Articles

Grindability Evaluation of Ultrasonic Assisted Grinding of Silicon Nitride Ceramic Using Minimum Quantity Lubrication Based SiO2 Nanofluid

Minimum quantity Lubrication (MQL) is a sustainable lubrication system that is famous in many machining systems. It involve the spray of an infinitesimal amount of mist-like lubricants during machining processes. The MQL system is affirmed to exhibit an excellent machining performance, and it is highly economical. The nanofluids are understood to exhibit excellent lubricity and heat evacuation capability, compared to pure oil-based MQL system. Studies have shown that the surface quality and amount of energy expended in the grinding operations can be reduced considerably due to the positive effect of these nanofluids. This work presents an experimental study on the tribological performance of SiO2 nanofluid during grinding of Si3N4 ceramic. The effect different grinding modes and lubrication systems during the grinding operation was also analyzed. Different concentrations of the SiO2 nanofluid was manufactured using canola, corn and sunflower oils. The quantitative evaluation of the grinding process was done based on the amount of grinding forces, specific grinding energy, frictional coefficient, and surface integrity. It was found that the canola oil exhibits optimal lubrication performance compared to corn oil, sunflower oil, and traditional lubrication systems. Additionally, the introduction of ultrasonic vibrations with the SiO2 nanofluid in MQL system was found to reduce the specific grinding energy, normal grinding forces, tangential grinding forces, and surface roughness by 65%, 57%, 65%, and 18% respectively. Finally, regression analysis was used to obtain an optimum parameter combinations. The observations from this work will aid the smooth transition towards ecofriendly and sustainable machining of engineering ceramics.

Points About Points with A Point: Nature of Smallest Scale Universals

This paper is an investigation of different aspects of the smallest scales possible and their relationships with larger scale phenomena. The relationships between the abstract and the concrete aspects of perspectives about time and space are considered. The phenomenon of continuity of motion is discussed, and the small-scale philosophical implications of continuity of motion could help to explain the reasoning behind why the speed of light is the way that it is, and why the speed of light squared is a constant. Fractions of a point are proven to an extent to be a useful idea, and a thought experiment that demonstrates speeds of fractions of a point per instant is included in this paper. Possible paradoxes related to singularities are discussed briefly within this paper, too. Absolute, relative, and unpredictable definitions of points and instants are discussed and shown to potentially provide some natural reasoning to observed discrepancies between scientific theories, perceived warping of space-time, and the uncertainty principle. Also, a philosophical interpretation of the term extra dimensions which involves the idea of fractions of a point could be useful for attempts at a unified theory of science and is included in this paper Nature of Smallest Scale Universals The nature of the smallest scales theoretically possible can have large-scale ramifications when the large-scale is considered as the philosophical sum of it parts. When considered cumulatively, the nature of the smallest scales can really add up to some larger scale repercussions. Even in the mystery of how something could exist instead of nothing, something existing at all is made more feasible by the realization that it is only asking the smallest possible amount, or an infinitesimal amount, or a mathematically approximately equal amount for the smallest scales to manifest as a phenomenon. This means that in one light, it’s only asking for a whole lot of approximately nothing for a whole lot of stuff to manifest. That sounds approximately like more reasoning behind how something could exist at all than just not knowing. The nature of the smallest scales has other philosophical insights to offer as well. This paper aims to investigate the philosophical nature of the smallest scales, some of the small and large-scale relationships that are implicated by those philosophies, and some of the different repercussions that are results of the philosophies involved.

Psychological Nash equilibria under ambiguity

Psychological games aim to represent situations in which players may have belief-dependent motivations. In this setting, utility functions are directly dependent on the entire hierarchy of beliefs of each player. On the other hand, the literature on strategic ambiguity in classical games highlights that players may have ambiguous (or imprecise) beliefs about opponents’ strategy choices. In this paper, we look at the issue of ambiguity in the framework of simultaneous psychological games by taking into account ambiguous hierarchies of beliefs and study a natural generalization of the psychological Nash equilibrium concept to this framework. We give an existence result for this new concept of equilibrium and provide examples that show that even an infinitesimal amount of ambiguity may alter significantly the equilibria of the game or can work as an equilibrium selection device. Finally, we look at the problem of stability of psychological equilibria with respect to ambiguous trembles on the entire hierarchy of correct beliefs and we provide a limit result that gives conditions so that sequences of psychological equilibria under ambiguous perturbation converge to psychological equilibria of the unperturbed game.

Identification of a nitrogen vacancy in GaN by scanning probe microscopy

Gallium nitride (GaN) is a material with important applications in optoelectronics, wireless communications, and power electronics. Devices for such applications are normally made with GaN single-crystal wafers. Yet an infinitesimal amount of atomic defects in these single crystals considerably hinders the electronic performance of GaN. One kind of atomic defect in GaN crystals that has been theoretically predicted but eludes direct experimental observation is nitrogen (N) vacancies. Here, we unambiguously identify a single N vacancy on a cleaved $m$-plane surface of GaN by direct visualization in real space with scanning tunneling microscopy (STM) and atomic force microscopy (AFM). The presence of a vacancy is established by AFM imaging and force spectroscopy measurements. The identification is accomplished by the analysis of STM images, tunneling current spectroscopy, and comparison with the outcomes from the quantification of band bending near the surface, current calculations, and first-principles simulations. All this information provides insight into the electronic perturbation of a single N vacancy at the surface band structure of GaN. Our results provide further understanding of the effect that point defects have on GaN, and will hopefully contribute to tune the behavior of this technologically relevant material in electronic devices.

Site specific biotinylated antibody functionalized Ag@AuNIs LSPR biosensor for the ultrasensitive detection of exosomal MCT4, a glioblastoma progression biomarker

Glioblastoma (GBM) is an incurable brain tumor in which hypoxic GBM cells (GMs) increase the production and release of exosomes, which are 30–200 nm vesicles crossing the blood–brain-barrier, enabling exosomal biomarkers to be promising targets for the tracking of GBM malignancy. Here, a localized surface plasmon resonance (LSPR) sensor chip was developed to detect an infinitesimal amount of exosomal biomarkers. Self-assembly silver nanoparticles decorated on gold nano-islands (Ag@AuNIs) sensor chip was used to provide site-specific bio-conjunction of biotinylated antibodies for detection of exosomal surface biomarkers. The biotinylated antibody functionalized (BAF) Ag@AuNIs LSPR biosensor sensitively detected cluster of differentiation 63, an exosome marker, and monocarboxylate transporter 4 (MCT4), a GBM progression biomarker, in malignant GMs-derived exosomes in the dynamic range of 3.8 × 10−4 to 50 μg/ml with limit of detection (LOD) of 0.38 ng/ml and 1.4 × 10−3 to 500 μg/ml with LOD of 1.4 ng/ml, respectively. Furthermore, it detected the enhanced level of MCT4 in malignant hypoxic GMs-derived exosomes as well as increased MCT4 in the blood serum-derived exosomes of GBM mice in the dynamic range of 4 × 10−4 to 50 μg/ml with LOD of 0.4 ng/ml. Finally, it could quantify MCT4 in the isolated GMs-derived exosomes from the blood of GBM mice by epidermal growth factor receptor variant III-based immunocapture, suggesting its utility for minimally-invasive monitoring of GBM progression as liquid biopsy. With excellent attributes of high sensitivity and selectivity in label-free sensing for exosomal biomarkers, the BAF Ag@AuNIs LSPR biosensor has great potential for early detection of GBM formation and progression.

Noisy atomic magnetometry in real time

Continuously monitored atomic spin-ensembles allow, in principle, for real-time sensing of external magnetic fields beyond classical limits. Within the linear-Gaussian regime, thanks to the phenomenon of measurement-induced spin-squeezing, they attain a quantum-enhanced scaling of sensitivity both as a function of time, t, and the number of atoms involved, N. In our work, we rigorously study how such conclusions based on Kalman filtering methods change when inevitable imperfections are taken into account: in the form of collective noise, as well as stochastic fluctuations of the field in time. We prove that even an infinitesimal amount of noise disallows the error to be arbitrarily diminished by simply increasing N, and forces it to eventually follow a classical-like behaviour in t. However, we also demonstrate that, ‘thanks’ to the presence of noise, in most regimes the model based on a homodyne-like continuous measurement actually achieves the ultimate sensitivity allowed by the decoherence, yielding then the optimal quantum-enhancement. We are able to do so by constructing a noise-induced lower bound on the error that stems from a general method of classically simulating a noisy quantum evolution, during which the stochastic parameter to be estimated—here, the magnetic field—is encoded. The method naturally extends to schemes beyond the linear-Gaussian regime, in particular, also to ones involving feedback or active control.

Side reaction in the hydrogen and carbothermal reductions of BaO and BaCO3: The role of an infinitesimal amount of water

Alkaline earth (AE) metals are irreplaceable ingredients in the synthesis of AE metal-based antiperovskite oxides, and it can be achieved by a chemical reduction of a stable AE metal compound. In this study, hydrogen and carbothermal reduction of BaO and BaCO3 were attempted, and we here report an undesirable side reaction creating barium hydroxide (Ba(OH)2) as the product of the reaction with the small amount of water in ultra-high purity inert gas used in the reduction processes. Such side reaction pathways and products are hardly identifiable in a high-temperature reaction; yet, systematic investigations on phase evolutions using X-ray diffraction, IR spectroscopy, and thermogravimetric analysis enabled the detection of Ba(OH)2·xH2O. Unintentional creation of alkaline earth metal oxides in intermediate and subsequent hydration even under a negligible amount of H2O may lead to an unexpected loss of alkaline earth metal element and, consequently, its deficiency in a desired final product.

Bacterial Extracellular Vesicles in Gastrointestinal Tract Cancer: An Unexplored Territory.

Simple SummaryMicrobial dysbiosis has been credited as one of the contributing factors to the development and progression of gastrointestinal tract cancer. The altered microbiota influences carcinogenesis through the induction of instability and damage to genetic material, modulation of host metabolic and inflammatory pathways, production of carcinogenic metabolites, and suppression of host antitumor response. These microbes secrete extracellular vesicles that are possibly carrying carcinogenic bioactive metabolites within their cargo. Studies have illustrated the ability of bacterial extracellular vesicles to cross the intestinal epithelial barrier and selectively accumulate near intestinal tumor cells. The purpose of this systemic review was to highlight the possible role of gut bacterial vesicles in the development, progression, and pathogenesis of gastrointestinal tract cancer and their possible involvement in the modulation of the tumor microenvironment. An infinitesimal amount of research has been carried out on the impact of bacterial extracellular vesicles on oncogenesis and tumor progression. This review aimed to encourage more investigations on this subject.Bacterial extracellular vesicles are membrane-enclosed, lipid bi-layer nanostructures that carry different classes of biomolecules, such as nucleic acids, lipids, proteins, and diverse types of small molecular metabolites, as their cargo. Almost all of the bacteria in the gut secrete extracellular vesicles to assist them in competition, survival, material exchange, host immune modulation, infection, and invasion. The role of gut microbiota in the development, progression, and pathogenesis of gastrointestinal tract (GIT) cancer has been well documented. However, the possible involvement of bacterial extracellular vesicles (bEVs) in GIT cancer pathophysiology has not been given due attention. Studies have illustrated the ability of bEVs to cross physiological barriers, selectively accumulate near tumor cells, and possibly alter the tumor microenvironment (TME). A systematic search of original published works related to bacterial extracellular vesicles on gastrointestinal cancer was performed for this review. The current systemic review outlines the possible impact of gut microbiota derived bEVs in GIT cancer in light of present-day understanding. The necessity of using advanced sequencing technologies, such as genetic, proteomic, and metabolomic investigation methodologies, to facilitate an understanding of the interrelationship between cancer-associated bacterial vesicles and gastrointestinal cancer is also emphasized. We further discuss the clinical and pharmaceutical potential of bEVs, along with future efforts needed to understand the mechanism of interaction of bEVs in GIT cancer pathogenesis.

Viscous Maxwell-Chern-Simons theory for topological electromagnetic phases of matter

We present the fundamental model of a topological electromagnetic phase of matter: viscous Maxwell-Chern-Simons theory. Our model applies to a quantum Hall fluids with viscosity. We solve both continuum and lattice regularized systems to demonstrate that this is the minimal (exactly solvable) gauge theory with a nontrivial photonic Chern number ($C\neq 0$) for electromagnetic waves coupled to a quantum Hall fluid. The interplay of symmetry and topology is also captured by the spin-1 representations of a photonic skyrmion at high-symmetry points in the Brillouin zone. To rigorously analyze the topological physics, we introduce the viscous Maxwell-Chern-Simons Lagrangian and derive the equations of motion, as well as the boundary conditions, from the principle of least action. We discover topologically-protected chiral (unidirectional) edge states which minimize the surface variation and correspond to massless photonic excitations costing an infinitesimal amount of energy. Physically, our predicted electromagnetic phases are connected to a dynamical photonic mass in the integer quantum Hall fluid. This arises from viscous (nonlocal) Hall conductivity and we identify the nonlocal Chern-Simons coupling with the Hall viscosity. The electromagnetic phase is topologically nontrivial $C\neq 0$ when the Hall viscosity inhibits the total bulk Hall response. Our work bridges the gap between electromagnetic and condensed matter topological physics while also demonstrating the central role of spin-1 quantization in nontrivial photonic phases.

Fast and slow dynamics for classical and quantum walks on mean-field small world networks

This work investigates the dynamical properties of classical and quantum random walks on mean-field small-world (MFSW) networks in the continuous time version. The adopted formalism profits from the large number of exact mathematical properties of their adjacency and Laplacian matrices. Exact expressions for both transition probabilities in terms of Bessel functions are derived. Results are compared to numerical results obtained by working directly the Hamiltonian of the model. For the classical evolution, any infinitesimal amount of disorder causes an exponential decay to the asymptotic equilibrium state, in contrast to the polynomial behavior for the homogeneous case. The typical quantum oscillatory evolution has been characterized by local maxima. It indicates polynomial decay to equilibrium for any degree of disorder. The main finding of the work is the identification of a faster classical spreading as compared to the quantum counterpart. It stays in opposition to the well known diffusive and ballistic for, respectively, the classical and quantum spreading in the linear chain.

Team COUNCIL OF RICKS submission for EUPA YPIC 2017

Using primarily LC-MS/MS de novo sequencing techniques, we concluded that the peptides form the following sentence from Sir JJ Thomson’s preface to Rays of Positive Electricity and Their Application to Chemical Analyses:“I feel sure that there are many problems in chemistry which could be solved with far greater ease by this than by any other method. The method is surprisingly sensitive, more so even than that of spectrum analysis, requires an infinitesimal amount of material, and does not require this to be specially purified.”Here, we detail our process for deciphering the peptide mixture composition and finding the sentence they form and from what book the sentence comes from.

The Yield Curve’s Search for the Natural Rate of Interest

Two novel models specify interest rates from factors other than time to demonstrate bond market expectations of riskless rates converge to the natural rate of interest. The first yield curve model is based upon risk rather than time. The riskless rate is the incremental yield for an infinitesimal amount of risk and is computed directly from bond yields. Resulting expected riskless rates are comparable to survey measures of expected short-term rates. Conversely, expected riskless rates for specific periods produce expected bond yields for those periods that also are comparable to survey expectations measures. The model produces a typical concave yield curve shape. The second model aligns with Wicksell’s original conception of a natural rate of interest as determined by productivity of real capital rather than time. The natural rate is the capital factor share of incremental growth from capital investment. The savings/consumption function is determined by equivalence between incremental capital product and forgone consumption, replacing the problematic IS equation. This proxy provides a real rate of interest consistent with short-term yields in the U.S. and other advanced economies, especially when adjusted for central bank intervention. The measure is more stable and easier to estimate than other natural rate measures. This natural rate of interest proxy provides better forecasts of riskless rates over multi-year horizons than do expectations measures. Future yield curves are expected to be flatter and future real rates lower than historical averages.

Recrystallization and Water Absorption Properties of Vitrified Trehalose Near Room Temperature.

To provide the physicochemical properties of vitrified trehalose for predicting its recrystallization. Thin films of vitrified trehalose solutions were prepared at room temperature and exposed to various humid and temperature atmospheres. The in-situ amount of retained water in the vacuum-dried trehalose thin film during exposure was determined using its FTIR spectrum by quantifying the extremely infinitesimal amount of retained water in the trehalose solution. Recrystallization of the sample was also assessed by the FTIR spectrum of trehalose dihydrate. The effective water absorption coefficient, h meff , exponentially increased to the water activity of the trehalose sample, A w , at 25°C and 40°C at which the increasing rates are comparable. The surface energy of trehalose dihydrate, γ, was found to be lower than the value calculated from the reported equation, neglecting the effects of the activity of the solute and solvent water. The retained water in trehalose considerably increases its affinity for water vapor, and the change in this affinity with regard to the water activity is nearly independent of temperature. The dihydrate nucleation rate of trehalose-water system is maximal when trehalose weight ratio is ~0.8 at 25°C and is slightly higher (~0.85) at 40°C.

Orthogonality catastrophe and fractional exclusion statistics.

We show that the N-particle Sutherland model with inverse-square and harmonic interactions exhibits orthogonality catastrophe. For a fixed value of the harmonic coupling, the overlap of the N-body ground state wave functions with two different values of the inverse-square interaction term goes to zero in the thermodynamic limit. When the two values of the inverse-square coupling differ by an infinitesimal amount, the wave function overlap shows an exponential suppression. This is qualitatively different from the usual power law suppression observed in the Anderson's orthogonality catastrophe. We also obtain an analytic expression for the wave function overlaps for an arbitrary set of couplings, whose properties are analyzed numerically. The quasiparticles constituting the ground state wave functions of the Sutherland model are known to obey fractional exclusion statistics. Our analysis indicates that the orthogonality catastrophe may be valid in systems with more general kinds of statistics than just the fermionic type.

Selective reduction of NO over Cu/Al2O3: Enhanced catalytic activity by infinitesimal loading of Rh on Cu/Al2O3

This study demonstrates that an isolated Cu2+ species formed by interacting with tetrahedral Al species on γ-Al2O3 shows a high catalytic activity for NO reduction with C3H6 and CO under high oxygen concentrations (lean conditions), and that an infinitesimal amount of Rh (0.01wt%, 100ppm) loaded on 0.5wt% Cu/Al2O3 is a more effective catalyst for the reactions, under a wide range of oxygen concentrations, than 0.5wt% Pd/Al2O3 or 1.0wt% Rh/Al2O3. Although 0.5wt% Cu/Al2O3 itself is effective for the reaction at lean conditions, it shows low catalytic activity under stoichiometric and low oxygen concentrations (rich conditions). On the other hand, the loading of 0.01wt% Rh on Cu/Al2O3 dramatically improves catalytic activities under stoichiometric and rich conditions, with maintaining the high NO reduction activity of Cu/Al2O3 itself under lean conditions. Therefore, a Rh species in the Rh/Cu/Al2O3 system must play a role as an active site under stoichiometric and rich conditions. Under lean conditions using Rh/Cu/Al2O3, an isolated Cu2+ species on γ-Al2O3 mainly contributes to the NO reduction properties of the catalyst. No such advantage was observed for Pd/Cu/Al2O3; that is, the catalytic activity of Cu/Al2O3 under lean conditions is diminished by Pd loading. Hence, we reveal that the roles of the Rh and Cu species in the Rh-loaded Cu/Al2O3 catalyst are effectively shared according to oxygen concentration in selective reduction of NO, when loaded with an infinitesimal amount of Rh. These observations provide novel guidelines for the development of catalysts that more beneficially use precious metal resources.

A New Solution Concept for the Ultimatum Game leading to the Golden Ratio

The Ultimatum Game is a paradigmatic two-player game. A proposer can offer a certain fraction of some valuable good. A responder can accept the offer or reject it, implying that the two players receive nothing. The only subgame-perfect Nash equilibrium is to only offer an infinitesimal amount and to accept this. However, this equilibrium is not in agreement with experimental observations, which show varying accepted offers around 40%. While some authors suggest that the fairest split of 50% vs. 50% would be explainable on theoretical grounds or by computer simulation, a few authors (including myself) have recently suggested that the Golden Ratio, about 0.618 vs. about 0.382, would be the solution, in striking agreement with observations. Here we propose a solution concept, based on an optimality approach and epistemic arguments, leading to that suggested solution. The optimality principle is explained both in an axiomatic way and by bargaining arguments, and the relation to Fibonacci numbers is outlined. Our presentation complements the Economic Harmony theory proposed by R. Suleiman and is based on infinite continued fractions. The results are likely to be important for the theory of fair salaries, justice theory and the predictive value of game theory.

Optimal stomatal behavior with competition for water and risk of hydraulic impairment

For over 40 y the dominant theory of stomatal behavior has been that plants should open stomates until the carbon gained by an infinitesimal additional opening balances the additional water lost times a water price that is constant at least over short periods. This theory has persisted because of its remarkable success in explaining strongly supported simple empirical models of stomatal conductance, even though we have also known for over 40 y that the theory is not consistent with competition among plants for water. We develop an alternative theory in which plants maximize carbon gain without pricing water loss and also add two features to both this and the classical theory, which are strongly supported by empirical evidence: (i) water flow through xylem that is progressively impaired as xylem water potential drops and (ii) fitness or carbon costs associated with low water potentials caused by a variety of mechanisms, including xylem damage repair. We show that our alternative carbon-maximization optimization is consistent with plant competition because it yields an evolutionary stable strategy (ESS)-species with the ESS stomatal behavior that will outcompete all others. We further show that, like the classical theory, the alternative theory also explains the functional forms of empirical stomatal models. We derive ways to test between the alternative optimization criteria by introducing a metric-the marginal xylem tension efficiency, which quantifies the amount of photosynthesis a plant will forego from opening stomatal an infinitesimal amount more to avoid a drop in water potential.

A novel visualization method of bubble cavitation caused by infinitesimal amount of microbubbles

Microbubbles modified with targeting ligands have a potential in early diagnosis by ultrasound because the targeted-bubble has both a selective property for accumulation in diseased area and a high degree of echogenicity. However, conventional ultrasonic imaging methods, such as B-mode and ultrasound color Doppler method, do not have enough sensitivity for microbubbles when only very small amount of microbubbles exists in ROI. In order to detect infinitesimal amount of microbubbles, we proposed a novel visualization of bubble cavitation signal (BCS) induced by high intensity US irradiation. In this method, high intensity US (h-US) is irradiated to microbubble with a fixed time delay after introducing an imaging US (i-US) and BCS is detected by power Doppler imaging unit. Due to the time delay of two waves, BCS appears on power Doppler image as a vertical line image (T-image) whose intensity is modulated by the amplitude of BCS. By this method, BCS measurement which is free both for direct propagated h-US and Doppler signal caused by bubble motion can be achieved. We detected the infinitesimal amount of bubbles (Sonazoid) with the concentration of 8×10-8 μL/ml, which is 100 times lower than minimum detectable sensitivity of B-mode observation.

Infinite efficiency of the collisional Penrose process: Can a overspinning Kerr geometry be the source of ultrahigh-energy cosmic rays and neutrinos?

The origin of the ultra-high-energy particles we receive on the Earth from the outer space such as EeV cosmic rays and PeV neutrinos remains an enigma. All mechanisms known to us currently make use of electromagnetic interaction to accelerate charged particles. In this paper we propose a mechanism exclusively based on gravity rather than electromagnetic interaction. We show that it is possible to generate ultra-high-energy particles starting from particles with moderate energies using the collisional Penrose process in an overspinning Kerr spacetime transcending the Kerr bound only by an infinitesimal amount, i.e., with the Kerr parameter $a=M(1+\epsilon)$, where we take the limit $\epsilon \rightarrow 0^+$. We consider two massive particles starting from rest at infinity that collide at $r=M$ with divergent center-of-mass energy and produce two massless particles. We show that massless particles produced in the collision can escape to infinity with the ultra-high energies exploiting the collisional Penrose process with the divergent efficiency $\eta \sim {1}/{\sqrt{\epsilon}} \rightarrow \infty$. Assuming the isotropic emission of massless particles in the center-of-mass frame of the colliding particles, we show that half of the particles created in the collisions escape to infinity with the divergent energies. To a distant observer, ultra-high-energy particles appear to originate from a bright spot which is at the angular location $\xi \sim {2M}/{r_{obs}}$ with respect to the singularity on the side which is rotating towards the observer. We show that the anisotropy in emission in the center-of-mass frame, which is dictated by the differential cross-section of underlying particle physics process, leaves a district signature on the spectrum of ultra-high-energy massless particles. Thus, it provides a unique probe into fundamental particle physics.

Mapping of steady-state electric fields and convective drifts in geomagnetic fields – Part 2: The IGRF

Abstract. A method of mapping electric fields along geomagnetic field lines is applied to the IGRF (International Geomagnetic Reference Field) model. The method involves integrating additional sets of first order differential equations simultaneously with those for tracing a magnetic field line. These provide a measure of the rate of change of the separation of two magnetic field lines separated by an infinitesimal amount. From the results of the integration Faraday's law is used to compute the electric field as a function of position along the field line. Examples of computations from a software package developed to implement the method are presented. This is expected to be of use in conjugate studies of magnetospheric phenomena such as SuperDARN (Super Dual Auroral Radar) observations of convection in conjugate hemispheres, or comparison of satellite electric field observations with fields measured in the ionosphere.