Expanding theQ–Rspace to three dimensions

2009 ◽  
Vol 641 ◽  
pp. 497-507 ◽  
Author(s):  
BEAT LÜTHI ◽  
MARKUS HOLZNER ◽  
ARKADY TSINOBER
Keyword(s):  
Velocity Gradient ◽  
Isotropic Turbulence ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Numerical Data ◽  
Three Dimensions ◽  
Data Set ◽  
Viscous Term ◽  
Johns Hopkins University ◽  
Three Dimensional Representation

The two-dimensional space spanned by the velocity gradient invariantsQandRis expanded to three dimensions by the decomposition ofRinto its strain production −1/3sijsjkskiand enstrophy production 1/4ωiωjsijterms. The {Q;R} space is a planar projection of the new three-dimensional representation. In the {Q; −sss; ωωs} space the Lagrangian evolution of the velocity gradient tensorAijis studied via conditional mean trajectories (CMTs) as introduced by Martínet al. (Phys. Fluids, vol. 10, 1998, p. 2012). From an analysis of a numerical data set for isotropic turbulence ofReλ~ 434, taken from the Johns Hopkins University (JHU) turbulence database, we observe a pronounced cyclic evolution that is almost perpendicular to theQ–Rplane. The relatively weak cyclic evolution in theQ–Rspace is thus only a projection of a much stronger cycle in the {Q; −sss; ωωs} space. Further, we find that the restricted Euler (RE) dynamics are primarily counteracted by the deviatoric non-local part of the pressure Hessian and not by the viscous term. The contribution of the Laplacian ofAij, on the other hand, seems the main responsible for intermittently alternating between low and high intensityAijstates.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

Energy and Momentum Eigenspectrum of the Hulthén-screened Cosine Kratzer Potential Using Proper Quantization Rule and SUSYQM Method

2021 ◽  
Author(s):  
Kaushal R Purohit ◽  
Rajendrasinh H PARMAR ◽  
Ajay Kumar Rai
Keyword(s):  
Quantum Mechanics ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Numerical Data ◽  
Time Dependent ◽  
Quantization Rule ◽  
Approximation Approach ◽  
Momentum Spectra ◽  
Energy And Momentum ◽  
Three Dimensional Space

Abstract Using the Qiang-Dong proper quantization rule (PQR) and the supersymmetric quantum mechanics approach, we obtained the eigenspectrum of the energy and momentum for time independent and time dependent Hulthen-screened cosine Kratzer potentials. For the suggested time independent Hulthen-screened cosine Kratzer potential, we solved the Schrodinger equation in D dimensions (HSCKP). The Feinberg-Horodecki equation for time-dependent Hulthen-screened cosine Kratzer potential was also solved (tHSCKP). To address the inverse square term in the time independent and time dependent equations, we employed the Greene-Aldrich approximation approach. We were able to extract time independent and time dependent potentials, as well as their accompanying energy and momentum spectra. In three-dimensional space, we estimated the rotational vibrational (RV) energy spectrum for many homodimers ($H_2, I_2, O_2$) and heterodimers ($MnH, ScN, LiH, HCl$). We also used the recently introduced formula approach to obtain the relevant eigen function. We also calculated momentum spectra for the dimers $MnH$ and $ScN$. The method is compared to prior methodologies for accuracy and validity using numerical data for heterodimer $LiH, HCl$ and homodimer $I_2, O_2,H_2$. The calculated energy and momentum spectra are tabulated and analysed.

Has a fully three-dimensional space map never evolved in any species? A comparative imperative for studies of spatial cognition

2013 ◽  
Vol 36 (5) ◽  
pp. 557-557 ◽  
Author(s):  
Cynthia F. Moss
Keyword(s):  
Spatial Cognition ◽  
Dimensional Space ◽  
Large Body ◽  
Three Dimensional ◽  
Comparative Data ◽  
Dimensional Representation ◽  
Three Dimensional Representation ◽  
Space Coding ◽  
Three Dimensional Space

AbstractI propose that it is premature to assert that a fully three-dimensional map has never evolved in any species, as data are lacking to show that space coding in all animals is the same. Instead, I hypothesize that three-dimensional representation is tied to an animal's mode of locomotion through space. Testing this hypothesis requires a large body of comparative data.

The Brain Stem Saccadic Burst Generator Encodes Gaze in Three-Dimensional Space

2008 ◽  
Vol 99 (5) ◽  
pp. 2602-2616 ◽  
Author(s):  
Marion R. Van Horn ◽  
Pierre A. Sylvestre ◽  
Kathleen E. Cullen
Keyword(s):  
Eye Movements ◽  
Brain Stem ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Saccadic Eye Movements ◽  
Three Dimensions ◽  
Related Information ◽  
Computer Based ◽  
Different Depths ◽  
The Brain

When we look between objects located at different depths the horizontal movement of each eye is different from that of the other, yet temporally synchronized. Traditionally, a vergence-specific neuronal subsystem, independent from other oculomotor subsystems, has been thought to generate all eye movements in depth. However, recent studies have challenged this view by unmasking interactions between vergence and saccadic eye movements during disconjugate saccades. Here, we combined experimental and modeling approaches to address whether the premotor command to generate disconjugate saccades originates exclusively in “vergence centers.” We found that the brain stem burst generator, which is commonly assumed to drive only the conjugate component of eye movements, carries substantial vergence-related information during disconjugate saccades. Notably, facilitated vergence velocities during disconjugate saccades were synchronized with the burst onset of excitatory and inhibitory brain stem saccadic burst neurons (SBNs). Furthermore, the time-varying discharge properties of the majority of SBNs (>70%) preferentially encoded the dynamics of an individual eye during disconjugate saccades. When these experimental results were implemented into a computer-based simulation, to further evaluate the contribution of the saccadic burst generator in generating disconjugate saccades, we found that it carries all the vergence drive that is necessary to shape the activity of the abducens motoneurons to which it projects. Taken together, our results provide evidence that the premotor commands from the brain stem saccadic circuitry, to the target motoneurons, are sufficient to ensure the accurate control shifts of gaze in three dimensions.

scholarly journals Development and assessment of CootVR, a virtual reality computer program for model building

2021 ◽  
Vol 77 (1) ◽  
pp. 19-27
Author(s):  
Hamish Todd ◽  
Paul Emsley
Keyword(s):  
Virtual Reality ◽  
Computer Program ◽  
Model Building ◽  
Three Dimensional ◽  
Specific Model ◽  
Three Dimensions ◽  
Biological Macromolecules ◽  
Data Set ◽  
X Ray Crystallography ◽  
Order Of Magnitude

Biological macromolecules have complex three-dimensional shapes that are experimentally examined using X-ray crystallography and electron cryo-microscopy. Interpreting the data that these methods yield involves building 3D atomic models. With almost every data set, some portion of the time put into creating these models must be spent manually modifying the model in order to make it consistent with the data; this is difficult and time-consuming, in part because the data are `blurry' in three dimensions. This paper describes the design and assessment of CootVR (available at http://hamishtodd1.github.io/cvr), a prototype computer program for performing this task in virtual reality, allowing structural biologists to build molecular models into cryo-EM and crystallographic data using their hands. CootVR was timed against Coot for a very specific model-building task, and was found to give an order-of-magnitude speedup for this task. A from-scratch model build using CootVR was also attempted; from this experience it is concluded that currently CootVR does not give a speedup over Coot overall.

Estimating Three-Dimensional Space from Multiple Two-Dimensional Views

1993 ◽  
Vol 2 (1) ◽  
pp. 44-53 ◽  
Author(s):  
Kristinn R. Thorisson
Keyword(s):  
Visual Search ◽  
Eye Movement ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Simple Algorithm ◽  
Three Dimensions ◽  
Limiting Factor ◽  
Single Subject ◽  
Search Performance ◽  
Two Dimensional

The most common visual feedback technique in teleoperation is in the form of monoscopic video displays. As robotic autonomy increases and the human operator takes on the role of a supervisor, three-dimensional information is effectively presented by multiple, televised, two-dimensional (2-D) projections showing the same scene from different angles. To analyze how people go about using such segmented information for estimations about three-dimensional (3-D) space, 18 subjects were asked to determine the position of a stationary pointer in space; eye movements and reaction times (RTs) were recorded during a period when either two or three 2-D views were presented simultaneously, each showing the same scene from a different angle. The results revealed that subjects estimated 3-D space by using a simple algorithm of feature search. Eye movement analysis supported the conclusion that people can efficiently use multiple 2-D projections to make estimations about 3-D space without reconstructing the scene mentally in three dimensions. The major limiting factor on RT in such situations is the subjects' visual search performance, giving in this experiment a mean of 2270 msec (SD = 468; N = 18). This conclusion was supported by predictions of the Model Human Processor (Card, Moran, & Newell, 1983), which predicted a mean RT of 1820 msec given the general eye movement patterns observed. Single-subject analysis of the experimental data suggested further that in some cases people may base their judgments on a more elaborate 3-D mental model reconstructed from the available 2-D views. In such situations, RTs and visual search patterns closely resemble those found in the mental rotation paradigm (Just & Carpenter, 1976), giving RTs in the range of 5-10 sec.

scholarly journals On a set of quartic surfaces in space of four dimensions; and a certain involutory transformation

1926 ◽  
Vol 110 (756) ◽  
pp. 700-708
Keyword(s):  
Present Note ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Quartic Surface ◽  
Four Dimensions ◽  
Cubic Surfaces ◽  
Mutual Relations ◽  
Quartic Surfaces ◽  
Three Dimensional Space

There exists in space of four dimensions an interesting figure of 15 lines and 15 points, first considered by Stéphanos (‘Compt. Rendus,’ vol. 93, 1881), though suggested very clearly by Cremona’s discussion of cubic surfaces in three-dimensional space. In connection with the figure of 15 lines there arises a quartic surface, the intersection of two quadrics, which is of importance as giving rise by projection to the Cyclides, as Segre has shown in detail (‘Math. Ann.,’ vol. 24, 1884). The symmetry of the figure suggests, howrever, the consideration of 15 such quartic surfaces; and it is natural to inquire as to the mutual relations of these surfaces, in particular as to their intersections. In general, two surfaces in space of four dimensions meet in a finite number of points. It appears that in this case any two of these 15 surfaces have a curve in common; it is the purpose of the present note to determine the complete intersection of any two of these 15 surfaces. Similar results may be obtained for a system of cubic surfaces in three dimensions, corresponding to those here given for this system of quartic surfaces in four dimensions, since the surfaces have one point in common, which may be taken as the centre of a projection.

scholarly journals Glycoblocks: a schematic three-dimensional representation for glycans and their interactions

2016 ◽  
Vol 73 (2) ◽  
pp. 187-194 ◽  
Author(s):  
Stuart McNicholas ◽  
Jon Agirre
Keyword(s):  
Hydrogen Bonds ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Stacking Interactions ◽  
Molecular Graphics ◽  
Interacting Protein ◽  
Protein Residues ◽  
Three Dimensional Representation ◽  
Close Range ◽  
Covalently Linked

The close-range interactions provided by covalently linked glycans are essential for the correct folding of glycoproteins and also play a pivotal role in recognition processes. Being able to visualise protein–glycan and glycan–glycan contacts in a clear way is thus of great importance for the understanding of these biological processes. In structural terms, glycosylation sugars glue the protein together via hydrogen bonds, whereas non-covalently bound glycans frequently harness additional stacking interactions. Finding an unobscured molecular view of these multipartite scenarios is usually far from trivial; in addition to the need to show the interacting protein residues, glycans may contain many branched sugars, each composed of more than ten non-H atoms and offering more than three potential bonding partners. With structural glycoscience finally gaining popularity and steadily increasing the deposition rate of three-dimensional structures of glycoproteins, the need for a clear way of depicting these interactions is more pressing than ever. Here a schematic representation, named Glycoblocks, is introduced which combines a simplified bonding-network depiction (covering hydrogen bonds and stacking interactions) with the familiar two-dimensional glycan notation used by the glycobiology community, brought into three dimensions by the CCP4 molecular graphics project (CCP4mg).

Symmetry-adapted digital modeling II. The double-helix B-DNA

2016 ◽  
Vol 72 (3) ◽  
pp. 312-323 ◽  
Author(s):  
A. Janner
Keyword(s):  
Dimensional Space ◽  
Double Helix ◽  
Three Dimensional ◽  
Reduction Factor ◽  
Lattice Points ◽  
Three Dimensions ◽  
Coarse Grained ◽  
Digital Modeling ◽  
Dna Strands ◽  
Dna Double Helix

The positions of phosphorus in B-DNA have the remarkable property of occurring (in axial projection) at well defined points in the three-dimensional space of a projected five-dimensional decagonal lattice, subdividing according to the golden mean ratio τ:1:τ [with τ = (1+\sqrt {5})/2] the edges of an enclosing decagon. The corresponding planar integral indicesn1,n2,n3,n4(which are lattice point coordinates) are extended to include the axial indexn5as well, defined for each P position of the double helix with respect to the single decagonal lattice ΛP(aP,cP) withaP= 2.222 Å andcP= 0.676 Å. A finer decagonal lattice Λ(a,c), witha=aP/6 andc=cP, together with a selection of lattice points for each nucleotide with a given indexed P position (so as to define a discrete set in three dimensions) permits the indexing of the atomic positions of the B-DNA d(AGTCAGTCAG) derived by M. J. P. van Dongen. This is done for both DNA strands and the single lattice Λ. Considered first is the sugar–phosphate subsystem, and then each nucleobase guanine, adenine, cytosine and thymine. One gets in this way a digital modeling of d(AGTCAGTCAG) in a one-to-one correspondence between atomic and indexed positions and a maximal deviation of about 0.6 Å (for the value of the lattice parameters given above). It is shown how to get a digital modeling of the B-DNA double helix for any given code. Finally, a short discussion indicates how this procedure can be extended to derive coarse-grained B-DNA models. An example is given with a reduction factor of about 2 in the number of atomic positions. A few remarks about the wider interest of this investigation and possible future developments conclude the paper.

scholarly journals BigTop: A Three-Dimensional Virtual Reality tool for GWAS Visualization

2019 ◽  
Author(s):  
Samuel T. Westreich ◽  
Maria Nattestad ◽  
Christopher Meyer
Keyword(s):  
Virtual Reality ◽  
Association Studies ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Gene Location ◽  
P Value ◽  
Genome Wide Association Studies ◽  
Two Dimensional ◽  
Three Dimensional Representation ◽  
Manhattan Plot

AbstractBackgroundGenome-wide association studies (GWAS) are typically visualized using a two-dimensional Manhattan plot, displaying chromosomal location of SNPs along the x-axis and the negative log-10 of their p-value on the y-axis. This traditional plot provides a broad overview of the results, but offers little opportunity for interaction or expansion of specific regions, and is unable to show additional dimensions of the dataset.ResultsWe created BigTop, a visualization framework in virtual reality (VR), designed to render a Manhattan plot in three dimensions, wrapping the graph around the user in a simulated cylindrical room. BigTop uses the z-axis to display minor allele frequency of each SNP, allowing for the identification of allelic variants of genes. BigTop also offers additional interactivity, allowing users to select any individual SNP and receive expanded information, including SNP name, exact values, and gene location, if applicable. BigTop is built in JavaScript using the React and A-Frame frameworks, and can be rendered using commercially available VR headsets or in a two-dimensional web browser such as Google Chrome. Data is read into BigTop in JSON format, and can be provided as either JSON or a tab-separated text file.ConclusionsUsing additional dimensions and interactivity options offered through VR, we provide a new, interactive, three-dimensional representation of the traditional Manhattan plot for displaying and exploring GWAS data.

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