Dispersive Estimates Research Articles

The massless Dirac equation in two dimensions: zero-energy obstructions and dispersive estimates

We investigate $L^1\\to L^\\infty$ dispersive estimates for the massless two dimensional Dirac equation with a potential. In particular, we show that the Dirac evolution satisfies the natural $t^{-\\frac{1}{2}}$ decay rate, which may be improved to $t^{-\\frac{1}{2} - \\gamma}$ for any $0\\leq \\gamma<\\frac{3}{2}$ at the cost of spatial weights. We classify the structure of threshold obstructions as being composed of a two dimensional space of p-wave resonances and a finite dimensional space of eigenfunctions at zero energy. We show that, in the presence of a threshold resonance, the Dirac evolution satisfies the natural decay rate except for a finite-rank piece. While in the case of a threshold eigenvalue only, the natural decay rate is preserved. In both cases we show that the decay rate may be improved at the cost of spatial weights.

Dispersion estimates for the discrete Hermite operator

Dispersion estimates for the discrete Hermite operator

Dynamic Optimal Travel Strategies in Intelligent Stochastic Transit Networks

This paper addresses the search for a run-based dynamic optimal travel strategy, to be supplied through mobile devices (apps) to travelers on a stochastic multiservice transit network, which includes a system forecasting of bus travel times and bus arrival times at stops. The run-based optimal strategy is obtained as a heuristic solution to a Markovian decision problem. The hallmarks of this paper are the proposals to use only traveler state spaces and estimates of dispersion of forecast bus arrival times at stops in order to determine transition probabilities. The first part of the paper analyses some existing line-based and run-based optimal strategy search methods. In the second part, some aspects of dynamic transition probability computation in intelligent transit systems are presented, and a new method for dynamic run-based optimal strategy search is proposed and applied.

GS-FrFT Algorithmic Method for Measurement of CD in Fibre Optics

The migration of present data network to the IoT interface, witty utilization of huge liable Single Mode Fiber rather than re-installing the whole network with Dispersion Shifted Fiber for their upgrading to ultra data speed Optical Fiber System based MPLS network for countering the main impediment of Chromatic Dispersion by estimating the real foe and compensating it at the receiver end and hence results the system more efficient with the existing Fiber network. The present scanning method of Fractional Fourier Transform (FrFT) to measure the Chromatic Dispersion (CD) encounters constraints of high latency time along with worst dispersion estimation error 250 picoseconds/nanometre which can be drastically improved with Golden Scan Search (GS) FrFT based algorithm method with 5 to 6 sec latency time and estimation error improved and obtained less than 80 picoseconds/nanometre.

Estimation of Population Size and Dispersal Pattern of Sterile Male Aedes aegypti Using Mark-Release-Recapture (MRR)

Aedes aegypti is currently emerging as a main vector of Dengue, Zika, and Chikungunya transmission. Chemical control was reported to be less effective due to the resistance of this mosquito to some types of insecticides. Therefore, another vector control is needed which is most appropriate to be used, i.e. the sterile insect technique (SIT). Information about optimum range dispersal sterile male Aedes aegypti for optimalization SIT program are needed. This study was designed to determine the dispersal pattern and population estimation of Aedes aegypti sterilized with gamma rays using mark-release-recapture (MRR) method. After the male Aedes aegypti (pupal stage) was irradiated with 70 Gy of gamma rays, the mosquitoes were then marked with Rhodamine-B and released into the study site. MRR experiments were carried out in Batan Indah residential area, and the Aedes aegypti were released in center of the site. Mosquitoes were recaptured at 28 points spread over the Batan Indah Residence for 2, 4, 6, and 8 days after release by using BG-Sentinel Traps. The result showed that the population of Aedes aegypti in the site was estimated to be 5.402 (1.347–14.636; CI 95 %) with the furthest spread distance was 119 meters from the release point. This study also showed that the MRR experiment can be used to estimate the population size and dispersal pattern of Aedes aegypti movement in a given locality. The result of present study provide better understanding for optimalization mosquito-borne disease prevention based on SIT programs.

A dispersive estimate of scalar contributions to hadronic light-by-light scattering

We consider the contribution of scalar resonances to hadronic light-by-light scattering in the anomalous magnetic moment of the muon. While the f0(500) has already been addressed in previous work using dispersion relations, heavier scalar resonances have only been estimated in hadronic models so far. Here, we compare an implementation of the f0(980) resonance in terms of the coupled-channel S-waves for γ⁎γ⁎→ππ/K¯K to a narrow-width approximation, which indicates aμHLbL[f0(980)]=−0.2(2)×10−11. With a similar estimate for the a0(980), the combined effect is thus well below 1×10−11 in absolute value. We also estimate the contribution of heavier scalar resonances. In view of the very uncertain situation concerning their two-photon couplings we suggest to treat them together with other resonances of similar mass when imposing the matching to short-distance constraints. Our final result is a refined estimate of the S-wave rescattering effects in the ππ and K¯K channel up to about 1.3 GeV and including a narrow-width evaluation of the a0(980): aμHLbL[scalars]=−9(1)×10−11.

Red Drum and Spotted Seatrout Live-Release Tournament Mortality and Dispersal

Abstract Although catch-and-release fishing tournaments undoubtedly reduce mortality of target species, postrelease mortality and fish stockpiling at release sites remain common concerns related to these tournaments. The impacts of live-release tournaments on freshwater species have been widely studied. However, research on estuarine sport fishes is lacking even though catch-and-release tournaments targeting these species are prevalent and popular recreational fisheries exist. Therefore, we estimated the post-weigh-in mortality and dispersal of Red Drum Sciaenops ocellatus and Spotted Seatrout Cynoscion nebulosus released from the 2016–2018 Alabama Deep Sea Fishing Rodeo live-weigh-in categories using acoustic telemetry. To concurrently estimate overall post-weigh-in mortality and dispersal, we used a Bayesian multistate model. Overall Red Drum post-weigh-in mortality (median = 6.12%; posterior credible interval [CrI] = 5.67–9.24%) was lower than overall Spotted Seatrout mortality (median = 30.63%; CrI = 26.74–40.00%). These estimates were within reported catch-and-release mortality ranges; however, they were higher than recent estimates for Spotted Seatrout. Within 1 week postrelease, Spotted Seatrout dispersal estimates (median = 87.03%; CrI = 72.96–95.72%) were higher than Red Drum (median = 55.62%; CrI = 42.75–68.10%) or Micropterus spp. in coastal and inland ecosystems. Long-term stockpiling at the release site was also not present; at the end of our 8-week observation period, median dispersal estimates were 94.41% (CrI = 87.15–98.19%) and 98.54% (CrI = 93.68–99.82%) for Red Drum and Spotted Seatrout, respectively. Red Drum fisheries may benefit most from live-release tournaments given that maximum mortality was <10%, but Spotted Seatrout fisheries may also benefit, especially if considerations are made to further reduce tournament mortality. Although we do not know the ratio of tournament mortality to recreational harvest for these species, live-release tournaments may be able to relieve some harvest pressure on heavily exploited inshore marine fisheries and research validating their usefulness should continue.

Assessment of emission-source contribution to spatial dispersion for coal crusher agglomeration using prognostic model

The emission of inhalable particulates (PM 10 ) from coal comminution processing is detrimental to the air quality. However, limited works have been carried out for the estimation of emission and dispersion of PM 10 from coal crushers and its ancillary operations. In this study, field-based measurements and regulatory dispersion model coupled with Weather Research Forecasting (WRF) were applied to investigate the assimilative capacity (AC) of a region with operational coal crushers. The model run was found ‘acceptable’ when compared with measured values according to set performance criteria. Furthermore, the validated model parameterization was used to forecast the dispersion effects by various emission control alternatives recommended by regulators viz. covering of conveyor belts, paving of the unpaved road, reducing feed rate, etc. Results suggested that the major contribution of PM 10 was from transportation and loading of coal after crushing, while PM 10 levels from crushing dissipated in a smaller area. Paving of transport roads and bunker/silo-based loading were effective control measures as emissions reduced by 30.67%–52.51%. The relationship between distance and emission load revealed that PM 10 concentrations below 100 μg/m 3 were achieved at approximately 750 m away from emission sources in the present study. Crusher's operations with existing emissions of 23.43 g/day/m 2 were detrimental for the region's AC and needed to be stepped down to 11.71 g/day/m 2 . In particular, using modeled meteorological data provided reasonable forecasts for allowable emissions and planning to site crusher operations. Correction to the low-wind conditions resulted in a better simulation of mean annual estimates than daily estimates of PM 10 . Such visualization of spatially explicit frameworks will guide policymakers in strengthening regulations. • Emissions from coal crushers and linked transport roads evaluated for spatial dispersion. • Transport bottlenecks are formed at feed point of crushers resulting in lower dispersion. • Emission reduction vis-à-vis dispersion by adopting controls recommended by regulators forecasted. • Paved roads and bunker/silo based loading enhanced available assimilative capacity. • Wind speed was key variable with low wind correction resulted in better mean annual estimates.

Low Mach number limit of the full compressible Hall-magnetohydrodynamic equation with general initial data

In this paper, we are concerned with the low Mach number limit for the full compressible Hall-magnetohydrodynamic equations within the frame work of local smooth solution in R3. Under the assumption of large temperature variations, we first obtain the uniform estimates of the solutions in a ε-weighted Sobolev space, which establishes the local existence theorem of the full compressible Hall-magnetohydrodynamic equations on a finite time interval independent of the Mach number. Then, the low Mach limit is proved by combining the uniform estimates and the dispersive estimates on the wave equation due to Métivier and Schochet (2001).

Dispersive estimates for periodic discrete one-dimensional Schrödinger operators

Dispersive estimates for periodic discrete one-dimensional Schrödinger operators

On Rates of Isopycnal Dispersion at the Submesoscale

AbstractPast studies of dispersion with float‐pairs have indicated that they may remain close together for much longer when they equilibrate on the same isopycnal, presumably due to the reduced influence of vertical shear. To examine this question more closely, we use a set of 13 and 15 float pair combinations that equilibrated within 0.1 °C (∼σθ = 0.01 kg m−3) of each other on two density surfaces in the main thermocline in a Lagrangian dispersion study. Their average rate of separation after launch was 0.0021 ± 0.0014 ms−1 (∼5.5 km after 30 days). Relative dispersion is accurately expressed by <D2> = 4•106 exp (t/10.8) m2 from start to about 30 days. Relative diffusivity (K) versus separation dropped well below the classical 4/3rds power law settling out at about 2–3 m2s−1 for separations less than ∼6 km, far lower than results from other float studies, but in accord with dye dispersion estimates.

Transverse Mixing in Rivers With Longitudinally Varied Morphology

AbstractImproving the quantification of the transverse mixing coefficient in rivers is essential for a better estimation of pollutant dispersion. This coefficient is evaluated from tracing experiments or from semi‐empirical equations assuming uniform flow conditions. This assumption, verified for laboratory experiments, is questionable for river studies. For example, piedmont rivers exhibit nonuniform flows due to their longitudinal morphological variations. This work aims at studying the longitudinal variability of the transverse mixing coefficient in a river with longitudinally varied morphology and the overlooked impact of the flow nonuniformity on the coefficient’s values. Tracing experiments were conducted in the Durance River in France using slug injections and concentration measurements made at the cross‐sections delineating homogeneous sub‐reaches. Using the well‐known 1D transverse diffusion model, values of the transverse mixing coefficient are determined for all consecutive sub‐reaches. These values substantially vary along the studied river, with stronger mixing efficiency at pools and complex riffles and weaker mixing efficiency in straight sub‐reaches with emerging obstacles. The dimensionless transverse mixing coefficient is strongly related to a parameter quantifying the deviation from flow‐uniformity, i.e., indicating flow acceleration, deceleration or a succession of both within the sub‐reaches. While usual formulas from the literature fail to predict our empirical results, a new equation including the flow nonuniformity parameter fits our experimental data with high accuracy. After further validation, such equation may be used for predicting the transverse mixing coefficient in rivers with longitudinally varied morphology.

Exceptions and exemptions under the ballast water management convention – Sustainable alternatives for ballast water management?

The International Convention for the Control and Management of Ships' Ballast Water and Sediments (BWM Convention) aims to mitigate the introduction risk of harmful aquatic organisms and pathogens (HAOP) via ships’ ballast water and sediments. The BWM Convention has set regulations for ships to utilise exceptions and exemptions from ballast water management under specific circumstances. This study evaluated local and regional case studies to provide clarity for situations, where ships could be excepted or exempted from ballast water management without risking recipient locations to new introductions of HAOP.Ships may be excepted from ballast water management if all ballasting operations are conducted in the same location (Regulation A-3.5 of the BWM Convention). The same location case study determined whether the entire Vuosaari harbour (Helsinki, Finland) should be considered as the same location based on salinity and composition of HAOP between the two harbour terminals. The Vuosaari harbour case study revealed mismatching occurrences of HAOP between the harbour terminals, supporting the recommendation that exceptions based on the same location concept should be limited to the smallest feasible areas within a harbour.The other case studies evaluated whether ballast water exemptions could be granted for ships using two existing risk assessment (RA) methods (Joint Harmonised Procedure [JHP] and Same Risk Area [SRA]), consistent with Regulation A-4 of the BWM Convention. The JHP method compares salinity and presence of target species (TS) between donor and recipient ports to indicate the introduction risk (high or low) attributed to transferring unmanaged ballast water. The SRA method uses a biophysical model to determine whether HAOP could naturally disperse between ports, regardless of their transportation in ballast water. The results of the JHP case study for the Baltic Sea and North-East Atlantic Ocean determined that over 97% of shipping routes within these regions resulted in a high-risk indication. The one route assessed in the Gulf of Maine, North America also resulted in a high-risk outcome. The SRA assessment resulted in an overall weak connectivity between all ports assessed within the Gulf of the St. Lawrence, indicating that a SRA-based exemption would not be appropriate for the entire study area.In summary, exceptions and exemptions should not be considered as common alternatives for ballast water management. The availability of recent and detailed species occurrence data was considered the most important factor to conduct a successful and reliable RA. SRA models should include biological factors that influence larval dispersal and recruitment potential (e.g., pelagic larval duration, settlement period) to provide a more realistic estimation of natural dispersal.

Natal and intergenerational dispersal of riverine smallmouth bass (Micropterus dolomieu)

Quantifying the scale of offspring dispersal is essential for understanding demographic connectivity across landscapes and rates of population spread. However, characterizing natal dispersal in fishes is complicated by the difficulties of tracking origins and movement during early life-history stages. We combined direct observation of natal dispersal based on otolith chemistry with indirect estimates of dispersal from population genetics to quantify intergenerational dispersal of smallmouth bass (Micropterus dolomieu) inhabiting a river network. Average parent–offspring dispersal was estimated as 7.7 km from genetic isolation-by-distance and demographic population data. Otolith chemistry indicated that adults were captured an average of 8.3 km from their natal tributary, supporting the genetics-based estimate. Our estimate of intergenerational dispersal is higher than previous estimates for lotic fishes and considerably higher than estimates for smallmouth bass in lake systems. Differences in availability of seasonal habitats for smallmouth bass may account for the contrasting scales of dispersal between lake and river populations. The large intergenerational dispersal distance of riverine smallmouth bass should be considered in conservation of fisheries or efforts to control invasive populations in river networks.

Estimation of PQ distance dispersion for atrial fibrillation detection

Background and objective: Atrial fibrillation (AF) is the most common cardiac arrhythmia in the world. It is associated with significantly increased morbidity and mortality. Diagnosis of the disease can be based on the analysis of the electrical atrial activity, on quantification of the heart rate irregularity or on a mixture of the both approaches. Since the amplitude of the atrial waves is small, their analysis can lead to false results. On the other hand, the heart rate based analysis usually leads to many unnecessary warnings. Therefore, our goal is to develop a new method for effective AF detection based on the analysis of the electrical atrial waves.Methods: The proposed method employs the fact that there is a lack of repeatable P waves preceding QRS complexes during AF. We apply the operation of spatio-temporal filtering (STF) to magnify and detect the prominent spatio-temporal patterns (STP) within the P waves in multi-channel ECG recordings. Later we measure their distances (PQ) to the succeeding QRS complexes, and we estimate dispersion of the obtained PQ series. For signals with normal sinus rhythm, this dispersion is usually very low, and contrary, for AF it is much raised. This allows for effective discrimination of this cardiologic disorder.Results: Tested on an ECG database consisting of AF cases, normal rhythm cases and cases with normal rhythm restored by the use of cardioversion, the method proposed allowed for AF detection with the accuracy of 98.75% on the basis of both 8–channel and 2–channel signals of 12 s length. When the signals length was decreased to 6 s, the accuracy varied in the range of 95%−97.5% depending on the number of channels and the dispersion measure applied.Conclusions: Our approach allows for high accuracy of atrial fibrillation detection using the analysis of electrical atrial activity. The method can be applied to an early detection of the desease and can advantageously be used to decrease the number of false warnings in systems based on the analysis of the heart rate.

The effect of data aggregation on dispersion estimates in count data models.

For the modelling of count data, aggregation of the raw data over certain subgroups or predictor configurations is common practice. This is, for instance, the case for count data biomarkers of radiation exposure. Under the Poisson law, count data can be aggregated without loss of information on the Poisson parameter, which remains true if the Poisson assumption is relaxed towards quasi-Poisson. However, in biodosimetry in particular, but also beyond, the question of how the dispersion estimates for quasi-Poisson models behave under data aggregation have received little attention. Indeed, for real data sets featuring unexplained heterogeneities, dispersion estimates can increase strongly after aggregation, an effect which we will demonstrate and quantify explicitly for some scenarios. The increase in dispersion estimates implies an inflation of the parameter standard errors, which, however, by comparison with random effect models, can be shown to serve a corrective purpose. The phenomena are illustrated by γ-H2AX foci data as used for instance in radiation biodosimetry for the calibration of dose-response curves.

Strategies for detecting and identifying biological signals amidst the variation commonly found in RNA sequencing data

BackgroundRNA sequencing analysis focus on the detection of differential gene expression changes that meet a two-fold minimum change between groups. The variability present in RNA sequencing data may obscure the detection of valuable information when specific genes within certain samples display large expression variability. This paper develops methods that apply variance and dispersion estimates to intra-group data to identify genes with expression values that diverge from the group envelope. STRING database analysis of the identified genes characterize gene affiliations involved in physiological regulatory networks that contribute to biological variability. Individuals with divergent gene groupings within network pathways can thereby be identified and judiciously evaluated prior to standard differential analysis.ResultsA three-step process is presented for evaluating biological variability within a group in RNA sequencing data in which gene counts were: (1) scaled to minimize heteroscedasticity; (2) rank-ordered to detect potentially divergent “trendlines” for every gene in the data set; and (3) tested with the STRING database to identify statistically significant pathway associations among the genes displaying marked trendline variability and dispersion. This approach was used to identify the “trendline” profile of every gene in three test data sets. Control data from an in-house data set and two archived samples revealed that 65–70% of the sequenced genes displayed trendlines with minimal variation and dispersion across the sample group after rank-ordering the samples; this is referred to as a linear trendline. Smaller subsets of genes within the three data sets displayed markedly skewed trendlines, wide dispersion and variability. STRING database analysis of these genes identified interferon-mediated response networks in 11–20% of the individuals sampled at the time of blood collection. For example, in the three control data sets, 14 to 26 genes in the defense response to virus pathway were identified in 7 individuals at false discovery rates ≤1.92 E-15.ConclusionsThis analysis provides a rationale for identifying and characterizing notable gene expression variability within a study group. The identification of highly variable genes and their network associations within specific individuals empowers more judicious inspection of the sample group prior to differential gene expression analysis.

Global estimates for the Hartree–Fock–Bogoliubov equations

We prove that certain Sobolev-type norms, slightly stronger than those given by energy conservation, stay bounded uniformly in time and N. This allows one to extend the local existence results of the second and third author globally in time. The proof is based on interaction Morawetz-type estimates and Strichartz estimates (including some new end-point results) for the equation in mixed coordinates such as The main new technical ingredient is a dispersive estimate in mixed coordinates, which may be of interest in its own right.

On the one dimensional Dirac equation with potential

We investigate L1→L∞ dispersive estimates for the one dimensional Dirac equation with a potential. In particular, we show that the Dirac evolution satisfies the natural t−12 decay rate, which may be improved to t−32 at the cost of spatial weights when the thresholds are regular. We classify the structure of threshold obstructions, showing that there is at most a one dimensional space at each threshold. We show that, in the presence of a threshold resonance, the Dirac evolution satisfies the natural decay rate, and satisfies the faster weighted bound except for a piece of rank at most two, one per threshold. Further, we prove high energy dispersive bounds that are near optimal with respect to the required smoothness of the initial data. To do so we use a variant of a high energy argument that was originally developed to study Kato smoothing estimates for magnetic Schrödinger operators. This method has never been used before to obtain L1→L∞ estimates. As a consequence of our analysis we prove a uniform limiting absorption principle, Strichartz estimates, and prove the existence of an eigenvalue free region for the one dimensional Dirac operator with a non-self-adjoint potential.

CFD and EnKF coupling estimation of LNG leakage and dispersion

As a kind of clean fuel, increasing quantities of natural gas have been transported as liquefied natural gas (LNG) worldwide. The safety of LNG storage has gained the concerns from the public due to the potential severe consequences that may arise from LNG leakage. In this paper, a three-dimensional model with the combination of computational fluid dynamics (CFD) and the ensemble Kalman filter (EnKF) is proposed to predict LNG vapor dispersion and estimate the strength of the LNG leakage source. The LNG vapor dispersion CFD model is validated by the experimental data with good feasibility, and is further demonstrated with the reasonable modeling of the characteristics of the LNG vapor dispersion in a typical receiving terminal. The effectiveness of the proposed CFD and EnKF coupling model is evaluated and validated by a twin experiment. The results of the twin experiment indicate that the proposed CFD and EnKF coupling model allows the integration of observation data into the CFD simulations to enhance the prediction accuracy of the LNG vapor spatial-temporal distribution and thereby realizing a reasonable estimation of the LNG leakage velocity under complex environments. This study can provide technical supports for safety control, loss prevention and emergency response in case of LNG leakage accidents.