scholarly journals Discrete gradient fields on infinite complexes

2011 ◽  
Vol 30 (3) ◽  
pp. 623-639 ◽  
Author(s):  
Rafael Ayala ◽  
◽  
Jose Antonio Vilches ◽  
Gregor Jerše ◽  
Neža Mramor Kosta ◽  
...  
Keyword(s):  
Discrete Gradient ◽  
Gradient Fields

scholarly journals Merging Discrete Morse Vector Fields: A Case of Stubborn Geometric Parallelization

Algorithms ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 360
Author(s):  
Douglas Lenseth ◽  
Boris Goldfarb
Keyword(s):  
Vector Fields ◽  
Persistent Homology ◽  
Gradient Field ◽  
Basic Question ◽  
Wrong Answer ◽  
Discrete Gradient ◽  
Gradient Fields ◽  
The Given ◽  
Well Posed ◽  
Local Nature

We address the basic question in discrete Morse theory of combining discrete gradient fields that are partially defined on subsets of the given complex. This is a well-posed question when the discrete gradient field V is generated using a fixed algorithm which has a local nature. One example is ProcessLowerStars, a widely used algorithm for computing persistent homology associated to a grey-scale image in 2D or 3D. While the algorithm for V may be inherently local, being computed within stars of vertices and so embarrassingly parallelizable, in practical use, it is natural to want to distribute the computation over patches Pi, apply the chosen algorithm to compute the fields Vi associated to each patch, and then assemble the ambient field V from these. Simply merging the fields from the patches, even when that makes sense, gives a wrong answer. We develop both very general merging procedures and leaner versions designed for specific, easy-to-arrange covering patterns.

Generation and Detection of Dynamic Gravitational‐Gradient Fields

1967 ◽  
Vol 38 (2) ◽  
pp. 512-518 ◽  
Author(s):  
Robert L. Forward ◽  
Larry R. Miller
Keyword(s):  
Gravitational Gradient ◽  
Gradient Fields

Temperature anomalies of a cold period on the territory of Ukraine in 2010-2019

2020 ◽  
Vol 101-102 (3-4) ◽  
pp. 19-25
Author(s):  
Olena Nashmudinova
Keyword(s):  
Air Temperature ◽  
Heat Waves ◽  
Regional Climate ◽  
Regional Climate Change ◽  
Negative Temperature ◽  
Cold Period ◽  
Positive Anomaly ◽  
Temperature Anomalies ◽  
Gradient Fields ◽  
Air Temperature Anomalies

Regional climate change in Ukraine in recent decades is accompanied by an increase in the repetitiveness of intense waves, both heat and cold; there is a tendency to increase the frequency of warm winters, but sometimes there are periods with significant decreases in temperature. The aim of the study is to determine the specifics of the formation of air temperature anomalies in the cold period 2010–2019. According to the distribution of the average monthly air temperature at the stations Odessa, Kiev, Kharkiv, Lviv investigated positive and negative deviations from the climate norm. In January, the average monthly air temperature in most cases was above normal, except for 1–3 years. The maximum positive anomaly was 4–5°C in Kyiv and Lviv (2015), the largest negative deviations were 3.8°C. In February, the trend continues – only 2–3 years with negative anomalies, the largest deviations to 3–6°C in 2011 and 2012, and positive deviations maximum in 2016. In March, negative temperature anomalies were observed 3–4 years, with a maximum of 2–3°C in 2018, positive anomalies in 4–6°C were observed in 2014, 2017. Temperatures in November were variable, with the prevailing positive anomaly, a high of 6–8°C in 2010. The distribution of air temperature in December was characterized by positive deviations of a maximum of 5–6°C in 2011, 2015, 2017 and 2019. Months of the greatest positive and negative air temperature anomalies over Europe have been highlighted. Among the colder months, the biggest anomaly stood out in January 2010 and February 2012 to 5–6°C. Among the warm months, the temperature anomaly was observed in February 2016, positive deviations from the norm to 8°C. Heat waves formed in winter with a zonal type of circulation, when warm moist air from the Atlantic shifted across the periphery of the Icelandic low. In March, waves of heat formed in low–gradient fields. Powerful waves of cold over the European sector were mainly formed under the influence of “eastern processes” in the spread of the Siberian anticyclone to Europe. In some years, significant cooling over Ukraine is formed in cyclonic systems with a high–altitude thermobaric field characterized by polar or ultrapolar hollow.

Hydrodynamic Modeling of Cerebrospinal Fluid Motion Within the Spinal Cavity

2000 ◽  
Author(s):  
M. Atif Yardimci ◽  
Francis Loth ◽  
Noam Alperin
Keyword(s):  
Pressure Gradient ◽  
Spinal Canal ◽  
Fluid Motion ◽  
Velocity Shear ◽  
Sectional Area ◽  
Flow Waveform ◽  
Cross Sectional ◽  
Gradient Fields ◽  
Gradient Waveform

Abstract In the present work, a geometric and hydrodynamic characterization of an anatomically relevant spinal canal model is presented. A numerical model was employed to investigate effects of cross-sectional geometry and spinal cord motion on unsteady velocity, shear stress, and pressure gradient fields. The velocity field was shown to be blunt, due to the inertial character of the flow, with velocity peaks located near the boundaries of the spinal canal rather than at the midpoint between boundaries. The pressure gradient waveform was found to be almost exclusively dependent on the flow waveform and cross-sectional area.

scholarly journals Automated dynamic motion correction using normalized gradient fields for 82rubidium PET myocardial blood flow quantification

2018 ◽  
Vol 27 (6) ◽  
pp. 1982-1998 ◽  
Author(s):  
Benjamin C. Lee ◽  
Jonathan B. Moody ◽  
Alexis Poitrasson-Rivière ◽  
Amanda C. Melvin ◽  
Richard L. Weinberg ◽  
...  
Keyword(s):  
Blood Flow ◽  
Myocardial Blood Flow ◽  
Motion Correction ◽  
Flow Quantification ◽  
Blood Flow Quantification ◽  
Dynamic Motion ◽  
Myocardial Blood Flow Quantification ◽  
Gradient Fields ◽  
Normalized Gradient

scholarly journals Using adjoint sensitivity as a local structure function in variational data assimilation

2001 ◽  
Vol 8 (6) ◽  
pp. 347-355 ◽  
Author(s):  
G. Hello ◽  
F. Bouttier
Keyword(s):  
Data Assimilation ◽  
Structure Function ◽  
Local Structure ◽  
Initial Conditions ◽  
Storm Track ◽  
Variational Data Assimilation ◽  
Sensitive Area ◽  
Adjoint Sensitivity ◽  
Weather Events ◽  
Gradient Fields

Abstract. One approach recently proposed in order to improve the forecast of weather events, such as cyclogenesis, is to increase the number of observations in areas depending on the flow configuration. These areas are obtained using, for example, the sensitivity to initial conditions of a selected predicted cyclone. An alternative or complementary way is proposed here. The idea is to employ such an adjoint sensitivity field as a local structure function within variational data assimilation, 3D-Var in this instance. Away from the sensitive area, observation increments project on the initial fields with the usual climatological (or weakly flow-dependent, in the case of 4D-Var) structure functions. Within the sensitive area, the gradient fields are projected using all the available data in the zone, conventional or extra, if any. The formulation of the technique is given and the approach is further explained by using a simple 1D scheme. The technique is implemented in the ARPEGE/IFS code and applied to 11 FASTEX (Fronts and Atlantic Storm-Track Experiment) cyclone cases, together with the targeted observations performed at the time of the campaign. The new approach is shown to allow for the desired stronger impact of the available observations and to systematically improve the forecasts of the FASTEX cyclones, unlike the standard 3D-Var.

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