Extending two-dimensional human-inspired bipedal robotic walking to three dimensions through geometric reduction

2012 ◽  
Author(s):  
R. W. Sinnet ◽  
A. D. Ames
Keyword(s):  
Three Dimensions ◽  
Two Dimensional ◽  
Geometric Reduction

scholarly journals BMS field theories and Weyl anomaly

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Arjun Bagchi ◽  
Sudipta Dutta ◽  
Kedar S. Kolekar ◽  
Punit Sharma
Keyword(s):  
Three Dimensions ◽  
Field Theories ◽  
Partition Functions ◽  
Two Dimensional ◽  
Speed Of Light ◽  
Asymptotically Flat ◽  
Weyl Invariance ◽  
Flat Spacetimes ◽  
Liouville Action ◽  
Null Surfaces

Abstract Two dimensional field theories with Bondi-Metzner-Sachs symmetry have been proposed as duals to asymptotically flat spacetimes in three dimensions. These field theories are naturally defined on null surfaces and hence are conformal cousins of Carrollian theories, where the speed of light goes to zero. In this paper, we initiate an investigation of anomalies in these field theories. Specifically, we focus on the BMS equivalent of Weyl invariance and its breakdown in these field theories and derive an expression for Weyl anomaly. Considering the transformation of partition functions under this symmetry, we derive a Carrollian Liouville action different from ones obtained in the literature earlier.

Dynamic Contrast-Enhanced MRI and Fractal Characteristics of Percolation Clusters in Two-Dimensional Tumor Blood Perfusion

1999 ◽  
Vol 121 (5) ◽  
pp. 480-486 ◽  
Author(s):  
O. I. Craciunescu ◽  
S. K. Das ◽  
S. T. Clegg
Keyword(s):  
Tumor Tissue ◽  
Blood Perfusion ◽  
Percolation Cluster ◽  
Three Dimensions ◽  
Invasion Percolation ◽  
Two Dimensional ◽  
Tumor Perfusion ◽  
Dynamic Contrast Enhanced ◽  
Contrast Enhanced ◽  
Fractal Characteristics

Dynamic contrast-enhanced magnetic resonance imaging (DE-MRI) of the tumor blood pool is used to study tumor tissue perfusion. The results are then analyzed using percolation models. Percolation cluster geometry is depicted using the wash-in component of MRI contrast signal intensity. Fractal characteristics are determined for each two-dimensional cluster. The invasion percolation model is used to describe the evolution of the tumor perfusion front. Although tumor perfusion can be depicted rigorously only in three dimensions, two-dimensional cases are used to validate the methodology. It is concluded that the blood perfusion in a two-dimensional tumor vessel network has a fractal structure and that the evolution of the perfusion front can be characterized using invasion percolation. For all the cases studied, the front starts to grow from the periphery of the tumor (where the feeding vessel was assumed to lie) and continues to grow toward the center of the tumor, accounting for the well-documented perfused periphery and necrotic core of the tumor tissue.

scholarly journals General up to next-nearest-neighbour elasticity of triangular lattices in three dimensions

2006 ◽  
Vol 462 (2073) ◽  
pp. 2695-2713 ◽  
Author(s):  
Cyril Dubus ◽  
Ken Sekimoto ◽  
Jean-Baptiste Fournier
Keyword(s):  
Blood Cell ◽  
Red Blood Cell ◽  
Triangular Lattice ◽  
Soft Matter ◽  
Rotational Symmetry ◽  
Three Dimensions ◽  
Nearest Neighbour ◽  
Two Dimensional ◽  
Biological Physics ◽  
Crystalline System

We establish the most general form of the discrete elasticity of a two-dimensional triangular lattice embedded in three dimensions, taking into account up to next-nearest-neighbour interactions. Besides crystalline system, this is relevant to biological physics (e.g. red blood cell cytoskeleton) and soft matter (e.g. percolating gels, etc.). In order to correctly impose the rotational invariance of the bulk terms, it turns out to be necessary to take into account explicitly the elasticity associated with the vertices located at the edges of the lattice. We find that some terms that were suspected in the literature to violate rotational symmetry are, in fact, admissible.

Mine Impact Burial Prediction From One to Three Dimensions

2008 ◽  
Vol 62 (1) ◽  
Author(s):  
Peter C. Chu
Keyword(s):  
Three Dimensional ◽  
Time History ◽  
Three Dimensions ◽  
Vertical Position ◽  
Burial Depth ◽  
Prediction Errors ◽  
Two Dimensional ◽  
Dimensional Model ◽  
One Dimensional ◽  
Dimensional Models

The Navy’s mine impact burial prediction model creates a time history of a cylindrical or a noncylindrical mine as it falls through air, water, and sediment. The output of the model is the predicted mine trajectory in air and water columns, burial depth/orientation in sediment, as well as height, area, and volume protruding. Model inputs consist of parameters of environment, mine characteristics, and initial release. This paper reviews near three decades’ effort on model development from one to three dimensions: (1) one-dimensional models predict the vertical position of the mine’s center of mass (COM) with the assumption of constant falling angle, (2) two-dimensional models predict the COM position in the (x,z) plane and the rotation around the y-axis, and (3) three-dimensional models predict the COM position in the (x,y,z) space and the rotation around the x-, y-, and z-axes. These models are verified using the data collected from mine impact burial experiments. The one-dimensional model only solves one momentum equation (in the z-direction). It cannot predict the mine trajectory and burial depth well. The two-dimensional model restricts the mine motion in the (x,z) plane (which requires motionless for the environmental fluids) and uses incorrect drag coefficients and inaccurate sediment dynamics. The prediction errors are large in the mine trajectory and burial depth prediction (six to ten times larger than the observed depth in sand bottom of the Monterey Bay). The three-dimensional model predicts the trajectory and burial depth relatively well for cylindrical, near-cylindrical mines, and operational mines such as Manta and Rockan mines.

Monkey superior colliculus represents rapid eye movements in a two-dimensional motor map

1993 ◽  
Vol 69 (3) ◽  
pp. 965-979 ◽  
Author(s):  
K. Hepp ◽  
A. J. Van Opstal ◽  
D. Straumann ◽  
B. J. Hess ◽  
V. Henn
Keyword(s):  
Eye Movements ◽  
Superior Colliculus ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Eye Position ◽  
Two Dimensional ◽  
Vestibular Nystagmus ◽  
Rapid Eye Movements ◽  
Q Model

1. Although the eye has three rotational degrees of freedom, eye positions, during fixations, saccades, and smooth pursuit, with the head stationary and upright, are constrained to a plane by ListingR's law. We investigated whether Listing's law for rapid eye movements is implemented at the level of the deeper layers of the superior colliculus (SC). 2. In three alert rhesus monkeys we tested whether the saccadic motor map of the SC is two dimensional, representing oculocentric target vectors (the vector or V-model), or three dimensional, representing the coordinates of the rotation of the eye from initial to final position (the quaternion or Q-model). 3. Monkeys made spontaneous saccadic eye movements both in the light and in the dark. They were also rotated about various axes to evoke quick phases of vestibular nystagmus, which have three degrees of freedom. Eye positions were measured in three dimensions with the magnetic search coil technique. 4. While the monkey made spontaneous eye movements, we electrically stimulated the deeper layers of the SC and elicited saccades from a wide range of initial positions. According to the Q-model, the torsional component of eye position after stimulation should be uniquely related to saccade onset position. However, stimulation at 110 sites induced no eye torsion, in line with the prediction of the V-model. 5. Activity of saccade-related burst neurons in the deeper layers of the SC was analyzed during rapid eye movements in three dimensions. No systematic eye-position dependence of the movement fields, as predicted by the Q-model, could be detected for these cells. Instead, the data fitted closely the predictions made by the V-model. 6. In two monkeys, both SC were reversibly inactivated by symmetrical bilateral injections of muscimol. The frequency of spontaneous saccades in the light decreased dramatically. Although the remaining spontaneous saccades were slow, Listing's law was still obeyed, both during fixations and saccadic gaze shifts. In the dark, vestibularly elicited fast phases of nystagmus could still be generated in three dimensions. Although the fastest quick phases of horizontal and vertical nystagmus were slower by about a factor of 1.5, those of torsional quick phases were unaffected. 7. On the basis of the electrical stimulation data and the properties revealed by the movement field analysis, we conclude that the collicular motor map is two dimensional. The reversible inactivation results suggest that the SC is not the site where three-dimensional fast phases of vestibular nystagmus are generated.(ABSTRACT TRUNCATED AT 400 WORDS)

scholarly journals ONSHORE-OFFSHORE SEDIMENT MOVEMENT ON A BEACH

1978 ◽  
Vol 1 (16) ◽  
pp. 87 ◽  
Author(s):  
P. Nielsen ◽  
I.A. Svensen ◽  
C. Staub
Keyword(s):  
Experimental Data ◽  
Diffusion Coefficient ◽  
Oscillatory Flow ◽  
Sediment Flux ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Present Formulation ◽  
Exact Analytical Solutions ◽  
Net Flux ◽  
Loose Sediments

A theoretical model is developed for the movement of loose sediments in oscillatory flow with or without a net current. In the present formulation the model is two-dimensional, but may readily be extended to three dimensions. It is assumed that all movement of sediments occurs in suspension, and exact analytical solutions are given for the time variation of the concentration profile, the instantaneous sediment flux and the net flux of sediment over a wave period. The model requires as empirical input a diffusion coefficient e and pick-up function p(t), for which experimental data are presented. Two examples are discussed in detail, illustrating important aspects of the onshore-offshore sediment motion.

Vorticity and curvature at a free surface

1998 ◽  
Vol 356 ◽  
pp. 149-153 ◽  
Author(s):  
MICHAEL S. LONGUET-HIGGINS
Keyword(s):  
Free Surface ◽  
Simple Relation ◽  
Surface Curvature ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Umbilical Point ◽  
Two Dimensional Flow ◽  
Principal Directions ◽  
Component Parallel

For two-dimensional flow there is a simple relation between the vorticity at a stress-free surface and the surface curvature. In this note the relation is generalized to flow in three dimensions. It is shown that in addition to a component of vorticity perpendicular to the flow there is also a component parallel to the direction of flow. The latter vanishes only at an umbilical point or when the flow is in one of the two principal directions of curvature.

Abstract 14952: Volumetric Echocardiographic Particle Image Velocimetry (V-Echo-PIV)

Circulation ◽  
2014 ◽  
Vol 130 (suppl_2) ◽  
Author(s):  
Ahmad Falahatpisheh ◽  
Arash Kheradvar
Keyword(s):  
Particle Image Velocimetry ◽  
Particle Image ◽  
Contrast Echocardiography ◽  
Ultrasound Contrast Agent ◽  
Three Dimensions ◽  
Small Scale ◽  
High Temporal Resolution ◽  
Two Dimensional ◽  
Particle Image Velocimetry Technique ◽  
Image Velocimetry

Introduction: The two-dimensional (2D) echocardiographic particle image velocimetry technique that was introduced in 2010 received much attention in clinical cardiology. Cardiac flow visualization based on contrast echocardiography results in images with high temporal resolution that are obtainable at relatively low cost. This makes it an ideal diagnostic and follow-up tool for routine clinical use. However, cardiac flow in a cardiac cycle is multidirectional with a tendency to spin in three dimensions rather than two-dimensional curl. Here, for the first time, we introduce a volumetric echocardiographic particle image velocimetry technique that robustly acquires the flow in three spatial dimensions and in time: Volumetric Echocardiographic Particle Image Velocimetry (V-Echo-PIV). Methods: V-Echo-PIV technique utilizes matrix array 3D ultrasound probes to capture the flow seeded with an ultrasound contrast agent (Definity). For this feasibility study, we used a pulse duplicator with a silicone ventricular sac along with bioprosthetic heart valves at the inlet and outlet. GE Vivid E9 system with an Active Matrix 4D Volume Phased Array probe at 30 Hz was used to capture the flow data (Figure 1). Results: The 3D particle field was obtained with excellent spatial resolution without significant noise (Figure 1). 3D velocity field was successfully captured for multiple cardiac cycles. Flow features are shown in Figure 2 where the velocity vectors in two selected slices and some streamlines in 3D space are depicted. Conclusions: We report successful completion of the feasibility studies for volumetric echocardiographic PIV in an LV phantom. The small-scale features of flow in the LV phantom were revealed by this technique. Validation and human studies are currently in progress.

Bringing Dynamic Geometry to Three Dimensions

2015 ◽  
pp. 68-99
Author(s):  
Nicholas H. Wasserman
Keyword(s):  
Teaching And Learning ◽  
Spatial Reasoning ◽  
Mathematics Classroom ◽  
Three Dimensional ◽  
Dynamic Geometry ◽  
State Standards ◽  
Three Dimensions ◽  
Two Dimensional ◽  
The Common ◽  
K 12

Contemporary technologies have impacted the teaching and learning of mathematics in significant ways, particularly through the incorporation of dynamic software and applets. Interactive geometry software such as Geometers Sketchpad (GSP) and GeoGebra has transformed students' ability to interact with the geometry of plane figures, helping visualize and verify conjectures. Similar to what GSP and GeoGebra have done for two-dimensional geometry in mathematics education, SketchUp™ has the potential to do for aspects of three-dimensional geometry. This chapter provides example cases, aligned with the Common Core State Standards in mathematics, for how the dynamic and unique features of SketchUp™ can be integrated into the K-12 mathematics classroom to support and aid students' spatial reasoning and knowledge of three-dimensional figures.

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