Inner magnetospheric plasma interactions and coupling with the ionosphere

The inner magnetosphere occupies a vast volume in space containing a relatively low-density mixture of hot and cold plasmas: the ring current, plasmasphere and radiation belt. Energy is transferred from the ring current to the cold plasmas through Coulomb collisions and wave-particle interactions, producing temperature enhancements in the plasmasphere. The plasma waves generated in the plasmasphere cause pitch-angle and energy diffusion of the energetic particles. The magnetic disturbances generated from the ring current alter the drift paths of radiation belt particles, causing radiation belt flux dropout during magnetic storm main phases. The ionosphere is filled with dense and cold plasmas in a 1000-km-thick shell above the Earth\u27s surface at ～100km altitude. Despite the distinct differences in size, location and physical properties, the ionosphere and the inner magnetosphere are tightly connected to each other. The ionosphere is an important source of magnetospheric ions. Energy transported down from the inner magnetosphere to the ionosphere produces observable temperature enhancements and optical emissions in the ionosphere. The electric coupling between the ionosphere and magnetosphere explains features such as shielding field, non-linear response of the ring current to the plasma-sheet source, and the post-midnight enhancement of the storm-time ring current flux. Even though many signatures are well described from the perspective of magnetosphere-ionosphere coupling, there are still unanswered questions, for example, the precise roles of wave-particle interactions in ring current loss and plasmaspheric heating, the cause of rapid storm initial recovery, the source of O^+ enhancement at substorm expansion, and the causes of outer radiation belt enhancement during storm recovery. The unresolved questions can be answered through careful cross analysis of the observational data from the ongoing and future imaging and multi-point missions with simulation results of large-scale modeling

The Need for Market Segmentation in Buy-Till-You-Defect Models

Buy-till-you-defect [BTYD] models are built for companies operating in a non- contractual setting to predict customers’ transaction frequency, amount and timing as well as customer lifetime. These models tend to perform well, although they often predict unrealistically long lifetimes for a substantial fraction of the customer base. This obvious lack of face validity limits the adoption of these models by practitioners. Moreover, it highlights a flaw in these models. Based on a simulation study and an empirical analysis of different datasets, we argue that such long lifetime predictions can result from the existence of multiple segments in the customer base. In most cases there are at least two segments: one consisting of customers who purchase the service or product only a few times and the other of those who are frequent purchasers. Customer heterogeneity modeling in the current BTYD models is insufficient to account for such segments, thereby producing unrealistic lifetime predictions. We present an extension over the current BTYD models to address the extreme lifetime prediction issue where we allow for segments within the customer base. More specifically, we consider a mixture of log-normals distribution to capture the heterogeneity across customers. Our model can be seen as a variant of the hierarchical Bayes [HB] Pareto/NBD model. In addition, the proposed model allows us to relate segment membership as well as within segment customer heterogeneity to selected customer characteristics. Our model, therefore, also increases the explanatory power of BTYD models to a great extent. We are now able to evaluate the impact of customers’ characteristics on the membership probabilities of different segments. This allows, for example, one to a-priori predict which customers are likely to become frequent purchasers. The proposed model is compared against the benchmark Pareto/NBD model (Schmittlein, Morrison, and Colombo 1987) and its HB extension (Abe 2009) on simulated datasets as well as on a real dataset from a large grocery e-retailer in a Western European country. Our BTYD model indeed provides a useful customer segmentation that allows managers to draw conclusions on how customers’ purchase and defection behavior are associated with their shopping characteristics such as basket size and the delivery fee paid

Dynamic Boundaries in Asymmetric Exclusion Processes

We investigate the dynamics of a one-dimensional asymmetric exclusion process with Langmuir kinetics and a fluctuating wall. At the left boundary, particles are injected onto the lattice; from there, the particles hop to the right. Along the lattice, particles can adsorb or desorb, and the right boundary is defined by a wall particle. The confining wall particle has intrinsic forward and backward hopping, a net leftward drift, and cannot desorb. Performing Monte Carlo simulations and using a moving-frame finite segment approach coupled to mean field theory, we find the parameter regimes in which the wall acquires a steady state position. In other regimes, the wall will either drift to the left and fall off the lattice at the injection site, or drift indefinitely to the right. Our results are discussed in the context of non-equilibrium phases of the system, fluctuating boundary layers, and particle densities in the lab frame versus the frame of the fluctuating wall.Comment: 13 page

"Counting Your Customers": When will they buy next? An empirical validation of probabilistic customer base analysis models based on purchase timing

This research provides a new way to validate and compare buy-till-you-defect [BTYD] models. These models specify a customer’s transaction and defection processes in a non-contractual setting. They are typically used to identify active customers in a com- pany’s customer base and to predict the number of purchases. Surprisingly, the literature shows that models with quite different assumptions tend to have a similar predictive performance. We show that BTYD models can also be used to predict the timing of the next purchase. Such predictions are managerially relevant as they enable managers to choose appropriate promotion strategies to improve revenues. Moreover, the predictive performance on the purchase timing can be more informative on the relative quality of BTYD models. For each of the established models, we discuss the prediction of the purchase timing. Next, we compare these models across three datasets on the predictive performance on the purchase timing as well as purchase frequency. We show that while the Pareto/NBD and its Hierarchical Bayes extension [HB] models perform the best in predicting transaction frequency, the PDO and HB models predict transaction timing more accurately. Furthermore, we find that differences in a model’s predictive performance across datasets can be explained by the correlation between behavioral parameters and the proportion of customers without repeat purchases

Plasmasphere Modeling with Ring Current Heating

Coulomb collisions between ring current ions and the thermal plasma in the plasmasphere will heat the plasmaspheric electrons and ions. During a storm such heating would lead to significant changes in the temperature and density of the thermal plasma. This was modeled using a time- dependent, one-stream hydrodynamic model for plasmaspheric flows, in which the model flux tube is connected to the ionosphere. The model simultaneously solves the coupled continuity, momentum, and energy equations of a two-ion (H(+) and O(+) quasineutral, currentless plasma. Heating rates due to collisions with ring current ions were calculated along the field line using a kinetic ring current model. First, diurnally reproducible results were found assuming only photoelectron heating of the thermal electrons. Then results were found with heating of the H(+) ions by the ring current during the recovery phase of a magnetic storm

Ring Current Development During Storm Main Phase

The development of the ring current ions in the inner magnetosphere during the main phase of a magnetic storm is studied. The temporal and spatial evolution of the ion phase space densities in a dipole field are calculated using a three dimensional ring current model, considering charge exchange and Coulomb losses along drift paths. The simulation starts with a quiet time distribution. The model is tested by comparing calculated ion fluxes with Active Magnetospheric Particle Tracer Explorers/CCE measurement during the storm main phase on May 2, 1986. Most of the calculated omnidirectional fluxes are in good agreement with the data except on the dayside inner edge (L less than 2.5) of the ring current, where the ion fluxes are underestimated. The model also reproduces the measured pitch angle distributions of ions with energies below 10 keV. At higher energy, an additional diffusion in pitch angle is necessary in order to fit the data. The role of the induced electric field on the ring current dynamics is also examined by simulating a series of substorm activities represented by stretching and collapsing the magnetic field lines. In response to the impulsively changing fields, the calculated ion energy content fluctuates about a mean value that grows steadily with the enhanced quiescent field

Digital PCR on a SlipChip

This paper describes a SlipChip to perform digital PCR in a very simple and inexpensive format. The fluidic path for introducing the sample combined with the PCR mixture was formed using elongated wells in the two plates of the SlipChip designed to overlap during sample loading. This fluidic path was broken up by simple slipping of the two plates that removed the overlap among wells and brought each well in contact with a reservoir preloaded with oil to generate 1280 reaction compartments (2.6 nL each) simultaneously. After thermal cycling, end-point fluorescence intensity was used to detect the presence of nucleic acid. Digital PCR on the SlipChip was tested quantitatively by using Staphylococcus aureus genomic DNA. As the concentration of the template DNA in the reaction mixture was diluted, the fraction of positive wells decreased as expected from the statistical analysis. No cross-contamination was observed during the experiments. At the extremes of the dynamic range of digital PCR the standard confidence interval determined using a normal approximation of the binomial distribution is not satisfactory. Therefore, statistical analysis based on the score method was used to establish these confidence intervals. The SlipChip provides a simple strategy to count nucleic acids by using PCR. It may find applications in research applications such as single cell analysis, prenatal diagnostics, and point-of-care diagnostics. SlipChip would become valuable for diagnostics, including applications in resource-limited areas after integration with isothermal nucleic acid amplification technologies and visual readout

Effects of Different Geomagnetic Storm Drivers on the Ring Current: CRCM Results

The storm-time magnetic disturbance at the Earth\u27s equator, as commonly measured by the Dst index, is induced by currents in the near-Earth magnetosphere. The ring current is generally considered the most important contributor, but other magnetospheric currents have also been found to have significant effects. Of the two main types of solar geomagnetic storm drivers, Coronal Mass Ejections (CMEs) tend to have a much greater impact on Dst than Corotating Interaction Regions (CIRs). Ring current models have been found to underestimate Dst, particularly during storms driven by CIRs. One possible explanation is that the models neglect to handle some aspect of ring current physics that is particularly important for CIRs. This study uses the Comprehensive Ring Current Model (CRCM) to estimate the ring current contribution to Dst for a selection of storms of various strengths and different drivers (CMEs and CIRs) that have solar wind parameters that fit a typical profile. The model boundary is set to 10 RE at the equator, encompassing the entire ring current region. The magnetic field is held fixed, based on average storm parameters, which limits our model results to the effects of convection and plasma sheet density at the model boundary. Our model results generally show good agreement with the size and timing of fluctuations in Dst, which indicates that convection and boundary conditions play an important role in shaping Dst. We also find excellent agreement with the magnitude of Dst for CME-driven storms. For CIR-drivenstorms, however, the magnitude at the peak of the storm frequently deviates from actual Dst. In general, we agree with the results of previous research that CIR-driven storms are more underpredicted. However, this study includes some weaker CIR-driven stormsfor which Dst is actually overpredicted. Overall, when examining the dependence of modeled Dst* on actual Dst* at storm peak, we find that there is a statistically significant difference between CME- and CIR-driven storms. We also find that approximately half of the total ring current energy lies beyond an L-value of 6.6. However, this figure could be overestimated due to the use of a static magnetic field, which limits radial transport. Key Points Modeled vs actual Dst at storm peak is significantly different for CMEs and CIRs Convection and plasma sheet density are important for ring current energization Model shows half of total ring current energy lies beyond an L-value of 6.6