Tensor network methods have become a powerful class of tools to capture strongly correlated matter, but methods to capture the experimentally ubiquitous family of models at finite temperature beyond ...one spatial dimension are largely lacking. We introduce a tensor network algorithm able to simulate thermal states of two-dimensional quantum lattice systems in the thermodynamic limit. The method develops instances of projected entangled pair states and projected entangled pair operators for this purpose. It is the key feature of this algorithm to resemble the cooling down of the system from an infinite temperature state until it reaches the desired finite-temperature regime. As a benchmark, we study the finite-temperature phase transition of the Ising model on an infinite square lattice, for which we obtain remarkable agreement with the exact solution. We then turn to study the finite-temperature Bose-Hubbard model in the limits of two (hard-core) and three bosonic modes per site. Our technique can be used to support the experimental study of actual effectively two-dimensional materials in the laboratory, as well as to benchmark optical lattice quantum simulators with ultracold atoms.
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The Galileo high accuracy service (HAS) is a new capability of the European global navigation satellite system, currently providing satellite orbit and clock corrections and dispersive effects such ...as satellite instrumental biases for code and phase. In its full capability, Galileo HAS will also correct the ionospheric delay on a continental scale (initially over Europe). We analyze a real-time ionospheric correction system based on the fast precise point positioning (F-PPP), and its potential application to the Galileo HAS. The F-PPP ionospheric model is assessed through a 281-day campaign, confirming previously reported results, where the proof of concept was introduced. We introduce a novel real-time test that directly links the instantaneous position error with the error of the ionospheric corrections, a key point for a HAS. The test involved 15 GNSS receivers in Europe acting as user receivers at various latitudes, with distances to the nearest reference receivers ranging from tens to four hundred kilometers. In the position domain, the test results show that the 95th percentile of the instantaneous position error depends on the user-receiver distance, as expected, ranging in the horizontal and vertical components from 10 to 30 cm and from 20 to 50 cm, respectively. These figures not only meet Galileo HAS requirements but outperform them by achieving instantaneous positioning. Additionally, it is shown that formal errors of the ionospheric corrections, which are also transmitted, are typically at the decimeter level (1 sigma), protecting users against erroneous position by weighting its measurements in the navigation filter.
Global Navigation Satellite System signals have been used for years to study high-frequency fluctuations (
f
> 0.1 Hz) in the ionosphere. The customary procedure uses the geometry-free (GF) ...combination of
L
1
and
L
2
carriers, for which it is necessary to acquire the
L
2
GPS signal. Initially,
L
2
had to be acquired from a codeless signal, L2P(Y), using several techniques, some of them requiring the aid of
L
1
. New GPS satellites transmit the new
C
2
civil code, which can be used to acquire directly
L
2
, i.e. L2C. Several publications have reported differences in the GF combination when it is computed from L2P(Y) or L2C. Using two ionospheric scintillation monitoring receivers (ISMRs), these differences were shown to be related to how they acquire
L
2
, i.e. if the receiver acquires
L
2
with the
L
1
aid. However, ISMRs are scarce, so the extension of such a study is not straightforward. The present work uses the geodetic detrending technique to identify whether a conventional geodetic-grade receiver acquires
L
2
with the aid of
L
1
. The study employs six different receiver types with measurements stored in RINEX formats version 2 and 3. In both formats, we are able to identify if
L
2
signal is acquired with
L
1
aid. In this way, we show that some receiver types heavily underestimate high-frequency ionospheric fluctuations when using the GF combination. Our results show that the ionosphere-free combination of these carrier phases is not free from high-frequency ionospheric fluctuations, but in some receivers, almost 90% of the high-frequency effects in
L
1
remain in such combination.
In the context of the European Space Agency/European Space Operations Centre funded Study “GNSS Contribution to Next Generation Global Ionospheric Monitoring,” four ionospheric models based on GNSS ...data (the Electron Density Assimilative Model, EDAM; the Ionosphere Monitoring Facility, IONMON v2; the Tomographic Ionosphere model, TOMION; and the Neustrelitz TEC Models, NTCM) have been run using a controlled set of input data. Each model output has been tested against differential slant TEC (dSTEC) truth data for high (May 2002) and low (December 2006) sunspot periods. Three of the models (EDAM, TOMION, and NTCM) produce dSTEC standard deviation results that are broadly consistent with each other and with standard deviation spreads of ∼1 TECu for December 2006 and ∼1.5 TECu for May 2002. The lowest reported standard deviation across all models and all stations was 0.99 TECu (EDAM, TLSE station for December 2006 night). However, the model with the best overall dSTEC performance was TOMION which has the lowest standard deviation in 28 out of 52 test cases (13 stations, two test periods, day and night). This is probably related to the interpolation techniques used in TOMION exploiting the spatial stationarity of vertical TEC error decorrelation.
Key Points
ESA study on GNSS contributions to future ionosphere modelling
As part of this study, four assimilative modelling techniques were compared
Based on the intercomparison results, recommendations for future developments
In this work, a geostatistic interpolation algorithm, called kriging, has been applied to improve the Technical University of Catalonia (UPC) global ionospheric maps (GIMs) computed with GPS data. ...This new UPC GIM, from now on UPC kriging GIM, has lower RMS in the observed slant total electron content (STEC) than the current UPC GIM and IGS GIM. Improvements are about 16% and 2%, respectively, using the data of several worldwide distributed GPS stations (self-consistency test). The UPC kriging GIM also presents a better performance than UPC GIM regarding the vertical total electron content (VTEC) measurements from TOPEX/Poseidon and JASON dual-frequency altimetric data. For both standard deviation and RMS, this improvement is about 0.3 TECU (6%) and 0.1 TECU (3%) for TOPEX and JASON, respectively. Moreover, it has also been shown a certain accuracy improvement of the resultant IGS GIM when the UPC kriging GIM replaces the present UPC GIM in the corresponding combination.
Severe infectious diseases that require surgery after acupuncture therapy are quite rare. There are only a few cases of pyomyositis following acupuncture reported in the literature. This paper ...presents a case of cervical pyomyositis developed after such treatment.
A 36-year-old man presented with swelling and pain in the posterior cervical region as well as high fever and torticollis, after having received three sessions of acupuncture therapy during the preceding weeks aimed to treat his neck stiffness. Ultrasound guided fine needle aspiration (FNA) and contrast-enhanced Computed Tomography (CT) were performed, which showed a large abscess along the paraspinal muscles. The symptoms were resolved after surgical treatment and antibiotherapy.
Although highly infrequent, pyomyositis is a probable complication of acupuncture. In order to minimise the risk of complications, strict hygenic precautions and knowledge of the human anatomy are mandatory to decrease the rate of complications of acupuncture.
In this paper, different aspects of the application of the second‐order ionospheric term (abbreviated as I2) and its impact on geodetic estimates are studied. A method to correct the GPS observations ...from this effect is proposed. This method provides a more accurate correction to the GPS measurements (in some cases, it can even be 50% better) with respect to other ways of computing such effect. Moreover, this method can be applied routinely to estimate geodetic parameters. Applying the I2 correction to subdaily differential positioning, several relationships between the deviation of the parameter estimates and the I2 term are derived in the context of a new global approach to the problem. In particular, it is shown that the effect in receiver position mainly depends on the differential value of this term between GPS receivers, while the satellite clocks are directly affected by the undifferenced values. Data from the International GNSS Service (IGS) global network of receivers have been gathered over a period of 21 months. These data have been used to study the I2 effect on the geodetic estimates, such as receiver positions, satellite clocks, and orbits. The most important effect appears for the satellite clocks, and it can be greater than 1 cm depending on the geographical location, comparable to the IGS nominal accuracies. The effect on orbits consists of a global contribution of several millimeters (which confirms the geocenter displacement detected by other authors) plus a subdaily contribution, also of several millimeters, that is geographically dependent, also comparable to the IGS nominal accuracies. As for the position of receivers, the obtained shifts are, in general, at submillimeter level and are directed southward for low‐latitude receivers and northward for high‐latitude receivers. These results will be explained in detail since they are not completely in agreement with the ones presented in previous works.
This work reviews an ionospheric activity indicator useful for identifying disturbed periods affecting the performance of Global Navigation Satellite System (GNSS). This index is based in the Along ...Arc TEC Rate (AATR) and can be easily computed from dual-frequency GNSS measurements. The AATR indicator has been assessed over more than one Solar Cycle (2002–2017) involving about 140 receivers distributed world-wide. Results show that it is well correlated with the ionospheric activity and, unlike other global indicators linked to the geomagnetic activity (i.e.
D
ST
or
Ap
), it is sensitive to the regional behaviour of the ionosphere and identifies specific effects on GNSS users. Moreover, from a devoted analysis of different Satellite Based Augmentation System (SBAS) performances in different ionospheric conditions, it follows that the AATR indicator is a very suitable mean to reveal whether SBAS service availability anomalies are linked to the ionosphere. On this account, the AATR indicator has been selected as the metric to characterise the ionosphere operational conditions in the frame of the European Space Agency activities on the European Geostationary Navigation Overlay System (EGNOS). The AATR index has been adopted as a standard tool by the International Civil Aviation Organization (ICAO) for joint ionospheric studies in SBAS. In this work we explain how the AATR is computed, paying special attention to the cycle-slip detection, which is one of the key issues in the AATR computation, not fully addressed in other indicators such as the Rate Of change of the TEC Index (ROTI). After this explanation we present some of the main conclusions about the ionospheric activity that can extracted from the AATR values during the above mentioned long-term study. These conclusions are: (a) the different spatial correlation related with the MOdified DIP (MODIP) which allows to clearly separate high, mid and low latitude regions, (b) the large spatial correlation in mid latitude regions which allows to define a planetary index, similar to the geomagnetic ones, (c) the seasonal dependency which is related with the longitude and (d) the variation of the AATR value at different time scales (hourly, daily, seasonal, among others) which confirms most of the well-known time dependences of the ionospheric events, and finally, (e) the relationship with the space weather events.
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