scholarly journals Axisymmetry of critical points for the Onsager functional

2021 ◽  
Vol 379 (2201) ◽  
pp. 20200110
Author(s):  
J. M. Ball
Keyword(s):  
Critical Points ◽  
Three Dimensional ◽  
Dipole Interaction ◽  
Stationary Solutions ◽  
Polar Coordinates ◽  
Complex Materials ◽  
Link Type ◽  
Rational Mechanics

A simple proof is given of the classical result (Fatkullin I, Slastikov V. 2005 Critical points of the Onsager functional on a sphere. Nonlinearity 18 , 2565–2580 ( doi:10.1088/0951-7715/18/6/008 ); Liu H et al. 2005 Axial symmetry and classification of stationary solutions of Doi-Onsager equation on the sphere with Maier-Saupe potential. Commun. Math. Sci. 3 , 201–218 ( doi:10.4310/CMS.2005.v3.n2.a7 )) that critical points for the Onsager functional with the Maier-Saupe molecular interaction are axisymmetric, including the case of stable critical points with an additional dipole-dipole interaction (Zhou H et al. 2007 Characterization of stable kinetic equilibria of rigid, dipolar rod ensembles for coupled dipole-dipole and Maier-Saupe potentials. Nonlinearity 20 , 277–297 ( doi:10.1088/0951-7715/20/2/003 )). The proof avoids spherical polar coordinates, instead using an integral identity on the sphere S 2 . For general interactions with absolutely continuous kernels the smoothness of all critical points is established, generalizing a result in (Vollmer MAC. 2017 Critical points and bifurcations of the three-dimensional Onsager model for liquid crystals. Archive for Rational Mechanics and Analysis 226 , 851–922 ( doi:10.1007/s00205-017-1146-8 )) for the Onsager interaction. It is also shown that non-axisymmetric critical points exist for a wide variety of interactions including that of Onsager. This article is part of the theme issue ‘Topics in mathematical design of complex materials’.

scholarly journals Accurate and Efficient Numerical Methods for Computing Ground States and Dynamics of Dipolar Bose-Einstein Condensates via the Nonuniform FFT

2016 ◽  
Vol 19 (5) ◽  
pp. 1141-1166 ◽  
Author(s):  
Weizhu Bao ◽  
Qinglin Tang ◽  
Yong Zhang
Keyword(s):  
Numerical Methods ◽  
Ground State ◽  
High Efficiency ◽  
Three Dimensional ◽  
Ground States ◽  
Dipole Interaction ◽  
Polar Coordinates ◽  
Pitaevskii Equation ◽  
Nonuniform Fft ◽  
Bose Einstein

AbstractWe propose efficient and accurate numerical methods for computing the ground state and dynamics of the dipolar Bose-Einstein condensates utilising a newly developed dipole-dipole interaction (DDI) solver that is implemented with the non-uniform fast Fourier transform (NUFFT) algorithm. We begin with the three-dimensional (3D) Gross-Pitaevskii equation (GPE) with a DDI term and present the corresponding two-dimensional (2D) model under a strongly anisotropic confining potential. Different from existing methods, the NUFFT based DDI solver removes the singularity by adopting the spherical/polar coordinates in the Fourier space in 3D/2D, respectively, thus it can achieve spectral accuracy in space and simultaneously maintain high efficiency by making full use of FFT and NUFFT whenever it is necessary and/or needed. Then, we incorporate this solver into existing successful methods for computing the ground state and dynamics of GPE with a DDI for dipolar BEC. Extensive numerical comparisons with existing methods are carried out for computing the DDI, ground states and dynamics of the dipolar BEC. Numerical results show that our new methods outperform existing methods in terms of both accuracy and efficiency.

VERSAL DEFORMATIONS OF THREE-DIMENSIONAL LIE ALGEBRAS AS L∞ ALGEBRAS

2005 ◽  
Vol 07 (02) ◽  
pp. 145-165 ◽  
Author(s):  
ALICE FIALOWSKI ◽  
MICHAEL PENKAVA
Keyword(s):  
Vector Space ◽  
Lie Algebras ◽  
Moduli Space ◽  
Deformation Theory ◽  
Three Dimensional ◽  
3 Dimensional ◽  
Exterior Degree ◽  
Versal Deformations

We consider versal deformations of 0|3-dimensional L∞ algebras, also called strongly homotopy Lie algebras, which correspond precisely to ordinary (non-graded) three-dimensional Lie algebras. The classification of such algebras is well-known, although we shall give a derivation of this classification using an approach of treating them as L∞ algebras. Because the symmetric algebra of a three-dimensional odd vector space contains terms only of exterior degree less than or equal to three, the construction of versal deformations can be carried out completely. We give a characterization of the moduli space of Lie algebras using deformation theory as a guide to understanding the picture.

scholarly journals Classification of human physical activity based on the raw accelerometry data via spherical coordinate transformation

2019 ◽  
Author(s):  
Michał Kos ◽  
Małgorzata Bogdan ◽  
Nancy W. Glynn ◽  
Jaroslaw Harezlak
Keyword(s):  
Physical Activity ◽  
Classification Accuracy ◽  
Three Dimensional ◽  
Upper Body ◽  
Spherical Coordinate ◽  
Group Data ◽  
Activity Types ◽  
Wearable Accelerometers

AbstractHuman health is strongly associated with person’s lifestyle and levels of physical activity. Therefore, characterization of daily human activity is an important task. Accelerometers have been used to obtain precise measurements of body acceleration. Wearable accelerometers collect data as a three-dimensional time series with frequencies up to 100Hz. Using such accelerometry signal, we are able to classify different types of physical activity.In our work, we present a novel procedure for physical activity classification based on the raw accelerometry signal. Our proposal is based on the spherical representation of the data. We classify four activity types: resting, upper body activities (sitting), upper body activities (standing) and lower body activities. The classifier is constructed using decision trees with extracted features consisting of spherical coordinates summary statistics, moving averages of the radius and the angles, radius variance and spherical variance.The classification accuracy of our method has been tested on data collected on a sample of 47 elderly individuals who performed a series of activities in laboratory settings. The achieved classification accuracy is over 90% when the subject-specific data are used and 84% when the group data are used. Main contributor to the classification accuracy is the angular part of the collected signal, especially spherical variance. To the best of our knowledge, spherical variance has never been previously used in the analysis of the raw accelerometry data. Its major advantage over other angular measures is its invariance to the accelerometer location shifts.

Classification of three corynebacterial strains isolated from a small paddock in North Rhine-Westphalia: proposal of Corynebacterium kalinowskii sp. nov., Corynebacterium comes sp. nov. and Corynebacterium occultum sp. nov.

2021 ◽  
Vol 71 (8) ◽  
Author(s):  
Lena Schaffert ◽  
Matthias Ruwe ◽  
Johanna Milse ◽  
Katharina Hanuschka ◽  
Vera Ortseifen ◽  
...  
Keyword(s):  
Genome Structure ◽  
16S Rrna Genes ◽  
Rrna Genes ◽  
Phenotypic Characterization ◽  
Whole Genome ◽  
Content Type ◽  
Link Type ◽  
Yellow Orange

Three novel corynebacterial species were isolated from soil sampled at a paddock in Vilsendorf, North Rhine-Westphalia, Germany. The strains were coccoid or irregular rod-shaped, catalase-positive and pale white to yellow-orange in colour. By whole genome sequencing and comparison of the 16S rRNA genes as well as the whole genome structure, it was shown that all three strains represent novel species of the family Corynebacteriaceae , order Corynebacteriales , class Actinobacteria . This project describes the isolation, identification, sequencing, and phenotypic characterization of the three novel Corynebacterium species. We propose the names Corynebacterium kalinowskii sp. nov. (DSM 110639T=LMG 31801T), Corynebacterium comes sp. nov. (DSM 110640T=LMG 31802T), and Corynebacterium occultum sp. nov. (DSM 110642T=LMG 31803T).

scholarly journals CLASSIFICATION OF SEISMIC PHASES BASED ON MACHINE LEARNING

2020 ◽  
Vol 5 (333) ◽  
pp. 33-42
Author(s):  
Nurtas Marat ◽  
◽  
Baishemirov Zharasbek ◽  
Tastanov Madi ◽  
Zhanabekov Zhandos ◽  
...  
Keyword(s):  
Machine Learning ◽  
Seismic Wave ◽  
Seismic Waves ◽  
Time Window ◽  
Time Windows ◽  
Three Dimensional ◽  
Multi Scale ◽  
Unit Circles

In the course of recent years, progresses in sensor innovation has lead to increments in the interest for automated strategies for investigating seismological signals. Fundamental to the comprehension of the components creating seismic signals is the information on the phases of seismic waves. Having the option to indicate the kind of wave prompts better performing seismic forecasting frameworks. In this article, we propose another strategy for the characterization of seismic waves quantification from a three-channel seismograms. The seismograms are isolated into covering time windows, where each time-window is mapped to a lot of multi-scale three-dimensional unitary vectors that portray the direction of the seismic wave present in the window at a few physical scales. The issue of arranging seismic waves gets one of ordering focuses on a few two-dimensional unit circles. We take care of this issue by utilizing kernel based machine learning that are remarkably adjusted to the geometry of the circle. The grouping of the seismic wave depends on our capacity to gain proficiency with the limits between sets of focuses on the circles related with the various kinds of seismic waves. At each signal scale, we characterize a thought of vulnerability connected to the order that considers the geometry of the dissemination of tests on the circle. At long last, we join the grouping results acquired at each scale into a unique label.

scholarly journals Characterization of a Novel Thermostable Carboxylesterase from Geobacillus kaustophilus HTA426 Shows the Existence of a New Carboxylesterase Family

2009 ◽  
Vol 191 (9) ◽  
pp. 3076-3085 ◽  
Author(s):  
Silvia Montoro-García ◽  
Irene Martínez-Martínez ◽  
José Navarro-Fernández ◽  
Hideto Takami ◽  
Francisco García-Carmona ◽  
...  
Keyword(s):  
Acyl Chain ◽  
Three Dimensional ◽  
Catalytic Triad ◽  
Dimensional Structure ◽  
E Coli ◽  
Optimum Growth Temperature ◽  
Geobacillus Kaustophilus ◽  
Chain Lengths

ABSTRACT The gene GK3045 (741 bp) from Geobacillus kaustophilus HTA426 was cloned, sequenced, and overexpressed into Escherichia coli Rosetta (DE3). The deduced protein was a 30-kDa monomeric esterase with high homology to carboxylesterases from Geobacillus thermoleovorans NY (99% identity) and Geobacillus stearothermophilus (97% identity). This protein suffered a proteolytic cut in E. coli, and the problem was overcome by introducing a mutation in the gene (K212R) without affecting the activity. The resulting Est30 showed remarkable thermostability at 65°C, above the optimum growth temperature of G. kaustophilus HTA426. The optimum pH of the enzyme was 8.0. In addition, the purified enzyme exhibited stability against denaturing agents, like organic solvents, detergents, and urea. The protein catalyzed the hydrolysis of p-nitrophenyl esters of different acyl chain lengths, confirming the esterase activity. The sequence analysis showed that the protein contains a catalytic triad formed by Ser93, Asp192, and His222, and the Ser of the active site is located in the conserved motif Gly91-X-Ser93-X-Gly95 included in most esterases and lipases. However, this carboxylesterase showed no more than 17% sequence identity with the closest members in the eight families of microbial carboxylesterases. The three-dimensional structure was modeled by sequence alignment and compared with others carboxylesterases. The topological differences suggested the classification of this enzyme and other Geobacillus-related carboxylesterases in a new α/β hydrolase family different from IV and VI.

Characterization of photosystem II with the atomic-force microscope

1992 ◽  
Vol 50 (2) ◽  
pp. 1146-1147
Author(s):  
Kathleen M. Marr ◽  
Mary K. Lyon
Keyword(s):  
Photosystem Ii ◽  
Atomic Force Microscope ◽  
Three Dimensional ◽  
Biologically Active ◽  
Atomic Force ◽  
Freeze Etching ◽  
Image Averaging ◽  
Oxygen Evolving ◽  
Averaging Techniques

Photosystem II (PSII) is different from all other reaction centers in that it splits water to evolve oxygen and hydrogen ions. This unique ability to evolve oxygen is partly due to three oxygen evolving polypeptides (OEPs) associated with the PSII complex. Freeze etching on grana derived insideout membranes revealed that the OEPs contribute to the observed tetrameric nature of the PSIl particle; when the OEPs are removed, a distinct dimer emerges. Thus, the surface of the PSII complex changes dramatically upon removal of these polypeptides. The atomic force microscope (AFM) is ideal for examining surface topography. The instrument provides a topographical view of individual PSII complexes, giving relatively high resolution three-dimensional information without image averaging techniques. In addition, the use of a fluid cell allows a biologically active sample to be maintained under fully hydrated and physiologically buffered conditions. The OEPs associated with PSII may be sequentially removed, thereby changing the surface of the complex by one polypeptide at a time.

convergent-beam diffraction from surfaces

1987 ◽  
Vol 45 ◽  
pp. 30-33
Author(s):  
J. A. Eades ◽  
A. E. Smith ◽  
D. F. Lynch
Keyword(s):  
Reciprocal Lattice ◽  
Three Dimensional ◽  
Grazing Incidence ◽  
Three Dimensions ◽  
Plane Figure ◽  
Transmission Electron ◽  
Convergent Beam ◽  
Beam Patterns ◽  
Beam Diffraction

It is quite simple (in the transmission electron microscope) to obtain convergent-beam patterns from the surface of a bulk crystal. The beam is focussed onto the surface at near grazing incidence (figure 1) and if the surface is flat the appropriate pattern is obtained in the diffraction plane (figure 2). Such patterns are potentially valuable for the characterization of surfaces just as normal convergent-beam patterns are valuable for the characterization of crystals.There are, however, several important ways in which reflection diffraction from surfaces differs from the more familiar electron diffraction in transmission.GeometryIn reflection diffraction, because of the surface, it is not possible to describe the specimen as periodic in three dimensions, nor is it possible to associate diffraction with a conventional three-dimensional reciprocal lattice.

Construction of plastic contact deformation maps on ceramics: a case study on aluminum nitride

1996 ◽  
Vol 54 ◽  
pp. 636-637
Author(s):  
D. L. Callahan
Keyword(s):  
Plastic Deformation ◽  
Aluminum Nitride ◽  
Mechanical Response ◽  
Three Dimensional ◽  
Bright Field Image ◽  
Perfectly Plastic ◽  
Contrast Analysis ◽  
Deformation Patterns

Modern polishing, precision machining and microindentation techniques allow the processing and mechanical characterization of ceramics at nanometric scales and within entirely plastic deformation regimes. The mechanical response of most ceramics to such highly constrained contact is not predictable from macroscopic properties and the microstructural deformation patterns have proven difficult to characterize by the application of any individual technique. In this study, TEM techniques of contrast analysis and CBED are combined with stereographic analysis to construct a three-dimensional microstructure deformation map of the surface of a perfectly plastic microindentation on macroscopically brittle aluminum nitride.The bright field image in Figure 1 shows a lg Vickers microindentation contained within a single AlN grain far from any boundaries. High densities of dislocations are evident, particularly near facet edges but are not individually resolvable. The prominent bend contours also indicate the severity of plastic deformation. Figure 2 is a selected area diffraction pattern covering the entire indentation area.

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