Continuous Mass Distributions. Gravitational Potential and Field

2020 ◽  
pp. 157-183
Author(s):  
Victor Ilisie
Keyword(s):  
Gravitational Potential ◽  
Mass Distributions ◽  
Continuous Mass

Label-free, mass-sensitive single-molecule imaging using interferometric scattering microscopy

2020 ◽  
Author(s):  
Nikolas Hundt
Keyword(s):  
Single Molecule ◽  
Cellular Systems ◽  
Single Molecule Imaging ◽  
Label Free ◽  
Measurement Sensitivity ◽  
Mass Distributions ◽  
Quantitative Measurements ◽  
Contrast Mechanism ◽  
Cellular Components ◽  
Scattering Signal

Abstract Single-molecule imaging has mostly been restricted to the use of fluorescence labelling as a contrast mechanism due to its superior ability to visualise molecules of interest on top of an overwhelming background of other molecules. Recently, interferometric scattering (iSCAT) microscopy has demonstrated the detection and imaging of single biomolecules based on light scattering without the need for fluorescent labels. Significant improvements in measurement sensitivity combined with a dependence of scattering signal on object size have led to the development of mass photometry, a technique that measures the mass of individual molecules and thereby determines mass distributions of biomolecule samples in solution. The experimental simplicity of mass photometry makes it a powerful tool to analyse biomolecular equilibria quantitatively with low sample consumption within minutes. When used for label-free imaging of reconstituted or cellular systems, the strict size-dependence of the iSCAT signal enables quantitative measurements of processes at size scales reaching from single-molecule observations during complex assembly up to mesoscopic dynamics of cellular components and extracellular protrusions. In this review, I would like to introduce the principles of this emerging imaging technology and discuss examples that show how mass-sensitive iSCAT can be used as a strong complement to other routine techniques in biochemistry.

Improvement of monitoring of tertiary filtration with particle counting

2006 ◽  
Vol 6 (1) ◽  
pp. 1-9
Author(s):  
V. Miska ◽  
J.H.J.M. van der Graaf ◽  
J. de Koning
Keyword(s):  
Particle Surface ◽  
Minor Effect ◽  
Particle Size Distributions ◽  
Particle Volume ◽  
Mass Distributions ◽  
Particle Counting ◽  
Total Particle ◽  
Particle Counts ◽  
A Minor ◽  
Sample Dilution

Nowadays filtration processes are still monitored with conventional analyses like turbidity measurements and, in case of flocculation–filtration, with phosphorus analyses. Turbidity measurements have the disadvantage that breakthrough of small flocs cannot be displayed, because of the blindness regarding changes in the mass distributions. Additional particle volume distributions calculated from particle size distributions (PSDs) would provide a better assessment of filtration performance. Lab-scale experiments have been executed on a flocculation–filtration column fed with effluent from WWTP Beverwijk in The Netherlands. Besides particle counting at various sampling points, the effect of sample dilution on the accuracy of PSD measurements has been reflected. It was found that the dilution has a minor effect on PSD of low turbidity samples such as process filtrate. The correlation between total particle counts, total particle volume (TPV) and total particle surface is not high but is at least better for diluted measurements of particles in the range 2–10 μm. Furthermore, possible relations between floc-bound phosphorus and TPV removal had been investigated. A good correlation coefficient is found for TPV removal versus floc-bound phosphorus removal for the experiments with polyaluminiumchloride and the experiments with single denitrifying and blank filtration.

Earth's gravity field parameters determination by the space geodesy dynamical approach

2017 ◽  
Vol 919 (1) ◽  
pp. 7-12
Author(s):  
N.A Sorokin
Keyword(s):  
Coordinate System ◽  
Gravitational Potential ◽  
Coefficient Matrix ◽  
Measured Quantity ◽  
Second Derivative ◽  
Measured Variable ◽  
Second Derivatives ◽  
Rectangular Coordinates ◽  
Cartesian Coordinate ◽  
Derivatives Of

The method of the geopotential parameters determination with the use of the gradiometry data is considered. The second derivative of the gravitational potential in the correction equation on the rectangular coordinates x, y, z is used as a measured variable. For the calculated value of the measured quantity required for the formation of a free member of the correction equation, the the Cunningham polynomials were used. We give algorithms for computing the second derivatives of the Cunningham polynomials on rectangular coordinates x, y, z, which allow to calculate the second derivatives of the geopotential at the rectangular coordinates x, y, z.Then we convert derivatives obtained from the Cartesian coordinate system in the coordinate system of the gradiometer, which allow to calculate the free term of the correction equation. Afterwards the correction equation coefficients are calculated by differentiating the formula for calculating the second derivative of the gravitational potential on the rectangular coordinates x, y, z. The result is a coefficient matrix of the correction equations and corrections vector of the free members of equations for each component of the tensor of the geopotential. As the number of conditional equations is much more than the number of the specified parameters, we go to the drawing up of the system of normal equations, from which solutions we determine the required corrections to the harmonic coefficients.

ON-DEMAND CONTINUOUS MASS-BALANCE SEDIMENT BUDGETS FOR RIVER SCIENCE AND MANAGEMENT

2017 ◽  
Author(s):  
David J. Topping ◽  
◽  
Ronald E. Griffiths ◽  
David J. Dean ◽  
Paul E. Grams ◽  
...  
Keyword(s):  
Mass Balance ◽  
Sediment Budgets ◽  
On Demand ◽  
Continuous Mass

QELSS diffusion data for moderately broad molar mass distribution polymer samples compared with data from classical gradient techniques

1989 ◽  
Vol 54 (7) ◽  
pp. 1821-1829
Author(s):  
Bedřich Porsch ◽  
Simon King ◽  
Lars-Olof Sundelöf
Keyword(s):  
Diffusion Coefficient ◽  
Mass Distribution ◽  
Molar Mass ◽  
Molar Mass Distribution ◽  
Diffusion Data ◽  
Mass Distributions ◽  
Classical Diffusion ◽  
Polydisperse Polymer

The differences between the QELSS and classical diffusion coefficient of a polydisperse polymer resulting from distinct definitions of experimentally accessible average values are calculated for two assumed specific forms of molar mass distributions. Predicted deviations are compared with the experiment using NBS 706 standard polystyrene. QELSS Dz of this sample relates within 2-4% to the classical diffusion coefficient, if the Schulz-Zimm molar mass distribution is assumed to be valid. In general, differences between the height-area and QELSS diffusion coefficient of about 20% may be found for Mw/Mn ~ 2, and this value may increase above 35%, if strongly tailing molar mass distribution pertains to the sample.

scholarly journals Mixed NNLO QCD×electroweak corrections of $$ \mathcal{O} $$(Nfαsα) to single-W/Z production at the LHC

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Stefan Dittmaier ◽  
Timo Schmidt ◽  
Jan Schwarz
Keyword(s):  
Z Bosons ◽  
Leading Order ◽  
Current Standard ◽  
Gauge Invariant ◽  
Mass Distributions ◽  
Self Energy ◽  
Electroweak Gauge Boson ◽  
First Results ◽  
Invariant Part ◽  
The Impact

Abstract First results on the radiative corrections of order $$ \mathcal{O} $$ O (Nfαsα) are presented for the off-shell production of W or Z bosons at the LHC, where Nf is the number of fermion flavours. These corrections comprise all diagrams at $$ \mathcal{O} $$ O (αsα) with closed fermion loops, form a gauge-invariant part of the next-to-next-to-leading-order corrections of mixed QCD×electroweak type, and are the ones that concern the issue of mass renormalization of the W and Z resonances. The occurring irreducible two-loop diagrams, which involve only self-energy insertions, are calculated with current standard techniques, and explicit analytical results on the electroweak gauge-boson self-energies at $$ \mathcal{O} $$ O (αsα) are given. Moreover, the generalization of the complex-mass scheme for a gauge-invariant treatment of the W/Z resonances is described for the order $$ \mathcal{O} $$ O (αsα). While the corrections, which are implemented in the Monte Carlo program Rady, are negligible for observables that are dominated by resonant W/Z bosons, they affect invariant-mass distributions at the level of up to 2% for invariant masses of ≳ 500 GeV and are, thus, phenomenologically relevant. The impact on transverse-momentum distributions is similar, taking into account that leading-order predictions to those distributions underestimate the spectrum.

scholarly journals Gravitational Interaction in the Chimney Lattice Universe

Universe ◽  
2021 ◽  
Vol 7 (4) ◽  
pp. 101
Author(s):  
Maxim Eingorn ◽  
Andrew McLaughlin ◽  
Ezgi Canay ◽  
Maksym Brilenkov ◽  
Alexander Zhuk
Keyword(s):  
Helmholtz Equation ◽  
Gravitational Potential ◽  
Fourier Expansion ◽  
Gravitational Interaction ◽  
Alternative Solution ◽  
The Third ◽  
Present Universe ◽  
Delta Functions ◽  
Yukawa Potentials ◽  
The Universe

We investigate the influence of the chimney topology T×T×R of the Universe on the gravitational potential and force that are generated by point-like massive bodies. We obtain three distinct expressions for the solutions. One follows from Fourier expansion of delta functions into series using periodicity in two toroidal dimensions. The second one is the summation of solutions of the Helmholtz equation, for a source mass and its infinitely many images, which are in the form of Yukawa potentials. The third alternative solution for the potential is formulated via the Ewald sums method applied to Yukawa-type potentials. We show that, for the present Universe, the formulas involving plain summation of Yukawa potentials are preferable for computational purposes, as they require a smaller number of terms in the series to reach adequate precision.

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