scholarly journals Numerical Solution of Parabolic Problems Based on a Weak Space-Time Formulation

2017 ◽  
Vol 17 (1) ◽  
pp. 65-84 ◽  
Author(s):  
Stig Larsson ◽  
Matteo Molteni
Keyword(s):  
Heat Equation ◽  
Numerical Experiments ◽  
Numerical Scheme ◽  
A Priori ◽  
Space Time ◽  
Parabolic Problems ◽  
Weak Space ◽  
Time Formulation ◽  
The Difference

AbstractWe investigate a weak space-time formulation of the heat equation and its use for the construction of a numerical scheme. The formulation is based on a known weak space-time formulation, with the difference that a pointwise component of the solution, which in other works is usually neglected, is now kept. We investigate the role of such a component by first using it to obtain a pointwise bound on the solution and then deploying it to construct a numerical scheme. The scheme obtained, besides being quasi-optimal in the ${L^{2}}$ sense, is also pointwise superconvergent in the temporal nodes. We prove a priori error estimates and we present numerical experiments to empirically support our findings.

scholarly journals Space-Time Finite Element Methods for Parabolic Problems

2015 ◽  
Vol 15 (4) ◽  
pp. 551-566 ◽  
Author(s):  
Olaf Steinbach
Keyword(s):  
Finite Element ◽  
Numerical Experiments ◽  
Numerical Scheme ◽  
Evolution Equations ◽  
A Priori ◽  
Space Time ◽  
Parabolic Problems ◽  
Parabolic Evolution Equations ◽  
Priori Error Estimates ◽  
The Stability

AbstractWe propose and analyze a space-time finite element method for the numerical solution of parabolic evolution equations. This approach allows the use of general and unstructured space-time finite elements which do not require any tensor product structure. The stability of the numerical scheme is based on a stability condition which holds for standard finite element spaces. We also provide related a priori error estimates which are confirmed by numerical experiments.

scholarly journals Validation of Aura-OMI QA4ECV NO<sub>2</sub> Climate Data Records with ground-based DOAS networks: role of measurement and comparison uncertainties

2020 ◽  
Author(s):  
Steven Compernolle ◽  
Tijl Verhoelst ◽  
Gaia Pinardi ◽  
José Granville ◽  
Daan Hubert ◽  
...  
Keyword(s):  
Scattered Light ◽  
A Priori ◽  
Sampling Bias ◽  
Climate Data ◽  
Vertical Column ◽  
Standard Data ◽  
Vertical Column Density ◽  
High Pollution ◽  
The Difference

Abstract. The QA4ECV version 1.1 stratospheric and tropospheric NO2 vertical column density (VCD) climate data records (CDR) from the satellite sensor OMI are validated, using NDACC zenith scattered light DOAS (ZSL-DOAS) and Multi Axis-DOAS (MAX-DOAS) data as a reference. The QA4ECV OMI stratospheric VCD have a small bias of ~ 0.2 Pmolec cm-2 (5–10 %) and a dispersion of 0.2 to 1 Pmolec cm-2 with respect to the ZSL-DOAS measurements. QA4ECV tropospheric VCD observations from OMI are restricted to near-cloud-free scenes, leading to a negative sampling bias (with respect to the unrestricted scene ensemble) of a few Pmolec cm-2 up to −10 Pmolec cm-2 (−40 %) in one extreme high-pollution case. QA4ECV OMI tropospheric VCD has a negative bias with respect to the MAX-DOAS data (−1 to −4 Pmolec cm-2), a feature also found for the OMI OMNO2 standard data product. The tropospheric VCD discrepancies between satellite and ground-based data exceed by far the combined measurement uncertainties. Depending on the site, part of the discrepancy can be attributed to a combination of comparison errors (notably horizontal smoothing difference error), measurement/retrieval errors related to clouds and aerosols, and to the difference in vertical smoothing and a priori profile assumptions.

The role of differential phase contrast in electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 176-177
Author(s):  
E.M. Waddell ◽  
J.N. Chapman ◽  
R.P. Ferrier
Keyword(s):  
Phase Contrast ◽  
Practical Method ◽  
Position Vector ◽  
Differential Phase ◽  
Pure Phase ◽  
Differential Phase Contrast ◽  
The Difference ◽  
Image Position ◽  
First Moment

Dekkers and de Lang (1977) have discussed a practical method of realising differential phase contrast in a STEM. The method involves taking the difference signal from two semi-circular detectors placed symmetrically about the optic axis and subtending the same angle (2α) at the specimen as that of the cone of illumination. Such a system, or an obvious generalisation of it, namely a quadrant detector, has the characteristic of responding to the gradient of the phase of the specimen transmittance. In this paper we shall compare the performance of this type of system with that of a first moment detector (Waddell et al.1977).For a first moment detector the response function R(k) is of the form R(k) = ck where c is a constant, k is a position vector in the detector plane and the vector nature of R(k)indicates that two signals are produced. This type of system would produce an image signal given bywhere the specimen transmittance is given by a (r) exp (iϕ (r), r is a position vector in object space, ro the position of the probe, ⊛ represents a convolution integral and it has been assumed that we have a coherent probe, with a complex disturbance of the form b(r-ro) exp (iζ (r-ro)). Thus the image signal for a pure phase object imaged in a STEM using a first moment detector is b2 ⊛ ▽ø. Note that this puts no restrictions on the magnitude of the variation of the phase function, but does assume an infinite detector.

Do Writing Directions Influence How People Map Space onto Time?

2018 ◽  
Vol 77 (4) ◽  
pp. 173-184
Author(s):  
Wenxing Yang ◽  
Ying Sun
Keyword(s):  
Mental Representations ◽  
Space Time ◽  
Horizontal Axis ◽  
Causal Role ◽  
Writing Systems ◽  
Temporal Cognition ◽  
Japanese Speakers ◽  
Psychological Experiments ◽  
Vertical Up

Abstract. The causal role of a unidirectional orthography in shaping speakers’ mental representations of time seems to be well established by many psychological experiments. However, the question of whether bidirectional writing systems in some languages can also produce such an impact on temporal cognition remains unresolved. To address this issue, the present study focused on Japanese and Taiwanese, both of which have a similar mix of texts written horizontally from left to right (HLR) and vertically from top to bottom (VTB). Two experiments were performed which recruited Japanese and Taiwanese speakers as participants. Experiment 1 used an explicit temporal arrangement design, and Experiment 2 measured implicit space-time associations in participants along the horizontal (left/right) and the vertical (up/down) axis. Converging evidence gathered from the two experiments demonstrate that neither Japanese speakers nor Taiwanese speakers aligned their vertical representations of time with the VTB writing orientation. Along the horizontal axis, only Japanese speakers encoded elapsing time into a left-to-right linear layout, which was commensurate with the HLR writing direction. Therefore, two distinct writing orientations of a language could not bring about two coexisting mental time lines. Possible theoretical implications underlying the findings are discussed.

Collection of Ego-Centered Network Data with Computer-Assisted Interviews

Methodology ◽  
2006 ◽  
Vol 2 (1) ◽  
pp. 7-15 ◽  
Author(s):  
Joachim Gerich ◽  
Roland Lehner
Keyword(s):  
Survey Methods ◽  
A Priori ◽  
Dynamic Structure ◽  
Computer Assisted ◽  
Network Data ◽  
Great Effort ◽  
Self Administration ◽  
Face To Face ◽  
Full Network

Although ego-centered network data provide information that is limited in various ways as compared with full network data, an ego-centered design can be used without the need for a priori and researcher-defined network borders. Moreover, ego-centered network data can be obtained with traditional survey methods. However, due to the dynamic structure of the questionnaires involved, a great effort is required on the part of either respondents (with self-administration) or interviewers (with face-to-face interviews). As an alternative, we will show the advantages of using CASI (computer-assisted self-administered interview) methods for the collection of ego-centered network data as applied in a study on the role of social networks in substance use among college students.

On the Role of Transferrin in 67Ga Uptake by Tumor Cells

1988 ◽  
Vol 27 (04) ◽  
pp. 151-153
Author(s):  
P. Thouvenot ◽  
F. Brunotte ◽  
J. Robert ◽  
L. J. Anghileri
Keyword(s):  
Specific Binding ◽  
Subcellular Fractionation ◽  
Animal Blood ◽  
Tumor Bearing ◽  
Cell Structures ◽  
The Difference ◽  
Sarcoma Cells ◽  
In Vitro Uptake

In vitro uptake of 67Ga-citrate and 59Fe-citrate by DS sarcoma cells in the presence of tumor-bearing animal blood plasma showed a dramatic inhibition of both 67Ga and 59Fe uptakes: about ii/io of 67Ga and 1/5o of the 59Fe are taken up by the cells. Subcellular fractionation appears to indicate no specific binding to cell structures, and the difference of binding seems to be related to the transferrin chelation and transmembrane transport differences

REFLECTION COEFFICIENT OF AN ELECTROMAGNETIC WAVE IN CONDUCTIVE MEDIA

2018 ◽  
pp. 100-106
Author(s):  
M. S. Sudakova ◽  
M. L. Vladov ◽  
M. R. Sadurtdinov
Keyword(s):  
Reflection Coefficient ◽  
Ground Penetrating Radar ◽  
Electromagnetic Waves ◽  
Water Contamination ◽  
Survey Design ◽  
Direct And Inverse Problems ◽  
The Difference ◽  
Ground Penetrating ◽  
Ideal Dielectric

Within the ground penetrating radar bandwidth the medium is considered to be an ideal dielectric, which is not always true. Electromagnetic waves reflection coefficient conductivity dependence showed a significant role of the difference in conductivity in reflection strength. It was confirmed by physical modeling. Conductivity of geological media should be taken into account when solving direct and inverse problems, survey design planning, etc. Ground penetrating radar can be used to solve the problem of mapping of halocline or determine water contamination.

Speculative Realism and Science Fiction

2017 ◽  
Author(s):  
Brian Willems
Keyword(s):  
Science Fiction ◽  
Identity Formation ◽  
Cormac Mccarthy ◽  
Doris Lessing ◽  
Speculative Realism ◽  
Neil Gaiman ◽  
The World ◽  
The Difference ◽  
Quentin Meillassoux

A human-centred approach to the environment is leading to ecological collapse. One of the ways that speculative realism challenges anthropomorphism is by taking non-human things to be as valid objects of investivation as humans, allowing a more responsible and truthful view of the world to take place. Brian Willems uses a range of science fiction literature that questions anthropomorphism both to develop and challenge this philosophical position. He looks at how nonsense and sense exist together in science fiction, the way in which language is not a guarantee of personhood, the role of vision in relation to identity formation, the difference between metamorphosis and modulation, representations of non-human deaths and the function of plasticity within the Anthropocene. Willems considers the works of Cormac McCarthy, Paolo Bacigalupi, Neil Gaiman, China Miéville, Doris Lessing and Kim Stanley Robinson are considered alongside some of the main figures of speculative materialism including Graham Harman, Quentin Meillassoux and Jane Bennett.

On the Use of Quantum Thermal Bath in Unimolecular Fragmentation Simulations

2019 ◽  
Author(s):  
Riccardo Spezia ◽  
Hichem Dammak
Keyword(s):  
Degrees Of Freedom ◽  
Molecular Simulations ◽  
Zero Point ◽  
Thermal Bath ◽  
Unimolecular Dissociation ◽  
Point Energy ◽  
Rotational Degrees Of Freedom ◽  
The Difference ◽  
Nuclear Effects

<div> <div> <div> <p>In the present work we have investigated the possibility of using the Quantum Thermal Bath (QTB) method in molecular simulations of unimolecular dissociation processes. Notably, QTB is aimed in introducing quantum nuclear effects with a com- putational time which is basically the same as in newtonian simulations. At this end we have considered the model fragmentation of CH4 for which an analytical function is present in the literature. Moreover, based on the same model a microcanonical algorithm which monitor zero-point energy of products, and eventually modifies tra- jectories, was recently proposed. We have thus compared classical and quantum rate constant with these different models. QTB seems to correctly reproduce some quantum features, in particular the difference between classical and quantum activation energies, making it a promising method to study unimolecular fragmentation of much complex systems with molecular simulations. The role of QTB thermostat on rotational degrees of freedom is also analyzed and discussed. </p> </div> </div> </div>

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