scholarly journals Simulation of angiogenesis in three dimensions: Application to cerebral cortex

2021 ◽  
Vol 17 (6) ◽  
pp. e1009164
Author(s):  
Jonathan P. Alberding ◽  
Timothy W. Secomb
Keyword(s):  
Cerebral Cortex ◽  
Three Dimensional ◽  
Dynamic Structure ◽  
Three Dimensions ◽  
Vascular Response ◽  
Biological Responses ◽  
Dimensional Network ◽  
Partial Pressures ◽  
Essential Components ◽  
Mouse Cerebral Cortex

The vasculature is a dynamic structure, growing and regressing in response to embryonic development, growth, changing physiological demands, wound healing, tumor growth and other stimuli. At the microvascular level, network geometry is not predetermined, but emerges as a result of biological responses of each vessel to the stimuli that it receives. These responses may be summarized as angiogenesis, remodeling and pruning. Previous theoretical simulations have shown how two-dimensional vascular patterns generated by these processes in the mesentery are consistent with experimental observations. During early development of the brain, a mesh-like network of vessels is formed on the surface of the cerebral cortex. This network then forms branches into the cortex, forming a three-dimensional network throughout its thickness. Here, a theoretical model is presented for this process, based on known or hypothesized vascular response mechanisms together with experimentally obtained information on the structure and hemodynamics of the mouse cerebral cortex. According to this model, essential components of the system include sensing of oxygen levels in the midrange of partial pressures and conducted responses in vessel walls that propagate information about metabolic needs of the tissue to upstream segments of the network. The model provides insights into the effects of deficits in vascular response mechanisms, and can be used to generate physiologically realistic microvascular network structures.

scholarly journals Spin Waves in Two and Three Dimensional Magnetic Materials

2015 ◽  
Vol 49 ◽  
pp. 35-47 ◽  
Author(s):  
H.S. Wijesinhe ◽  
K.A.I.L. Wijewardena Gamalath
Keyword(s):  
Dynamic Properties ◽  
Equations Of Motion ◽  
Spin Waves ◽  
Three Dimensional ◽  
Dynamic Structure ◽  
Second Order ◽  
Three Dimensions ◽  
Operator Representation ◽  
Computer Based ◽  
Canonical Ensembles

The equations of motion for the dynamic properties of spin waves in three dimensions were obtained using Heisenberg model and solved for two and three dimensional lattices analytically up to an exponential operator representation. The second order Suzuki Trotter decomposition method was extended to incorporate second nearest interaction parameters into the numerical solution. Computer based simulations on systems in micro canonical ensembles in constant-energy states were used to check the applicability of this model for two dimensional lattice as well as three dimensional simple cubic and bcc lattices. In the magnon dispersion curves all or most of the spin wave components could be recognized as peaks in the dynamic structure factor presenting the variation of energy transfer with respect to momentum transfer of spin waves. Second order Suzuki Trotter algorithm used conserved the energy.

An Efficient Partitioning Algorithm Based on Hypergraph for 3D Network-On-Chip Architecture Floorplanning

2019 ◽  
Vol 28 (05) ◽  
pp. 1950075 ◽  
Author(s):  
Junyan Tan ◽  
Chunhua Cai
Keyword(s):  
Three Dimensional ◽  
Network On Chip ◽  
Three Dimensions ◽  
Layer By Layer ◽  
Task Partitioning ◽  
Silicon Area ◽  
Dimensional Network ◽  
3D Network ◽  
Partitioning Algorithm ◽  
On Chip

Network-on-Chip (NoC) supplies a scalable and fast interconnect for the communication between the different IP cores in the System-on-Chip (SoC). With the growing complexity in consumer embedded systems, the emerging SoC architectures integrate more and more components for the different signal processing tasks. Two dimensional Network-on-Chip (2D NoC) becomes a bottleneck for the development of the SoC architecture because of its limitation on the area of chip and the long latency. In this case, SoC research is forcing on the exploration of three dimensions (3D) technology for developing the next generation of large SoC which integrates three dimensional Network-on-Chip (3D NoC) for the communication architecture. 3D design technology resolves the vertical inter-layer connection issue by Through-Silicon Vias (TSVs). However, TSVs occupy significant silicon area which limits the inter-layer links of the 3D NoC. Therefore, the task partitioning on 3D NoC must be judicious in large SoC design. In this paper, we propose an efficient layer-aware partitioning algorithm based on hypergraph (named ELAP-NoC) for the task partitioning with TSV minimization for 3D NoC architecture floorplanning. ELAP-NoC contains divergence stage and convergence stage. ELAP-NoC supplies firstly a multi-way min-cut partitioning to gradually divide a given design layer by layer in the divergence stage in order to get an initial solution, then this solution is refined in convergence stage. The experiments show that ELAP-NoC performs a better capacity in the partitioning of the different numbers of cores which supplies the first step for the 3D NoC floorplanning.

scholarly journals Symplectic realization of two interacting spin-two fields in three dimensions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Omar Rodríguez-Tzompantzi
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Potential Gradient ◽  
Dynamic Structure ◽  
Three Dimensions ◽  
Dynamical Structure ◽  
Gauge Transformations ◽  
Zero Modes ◽  
New Perspective ◽  
Gauge Structure

Abstract We constructed a symplectic realization of the dynamic structure of two interacting spin-two fields in three dimensions. A significant simplification refers to the treatment of constraints: instead of performing a Hamiltonian analysis à la Dirac, we worked out a method that only uses properties of the pre-symplectic two-form matrix and its corresponding zero-modes to investigate the nature of constraints and the gauge structure of the theory. For instance, we demonstrate that the contraction of the zero-modes with the potential gradient, yields explicit expressions for the whole set of constraints on the dynamics of the theory, including the symmetrization condition and an explicit relationship between the coupling and cosmological constants. This way, we further identify the necessary conditions for the existence of a unique non-linear candidate for a partially massless theory, using only the expression for the interaction parameters of the model. In the case of gauge structure, the transformation laws for the entire set of dynamical variables are more straightforwardly derived from the structure of the remaining zero-modes; in this sense, the zero-modes must be viewed as the generators of the corresponding gauge transformations. Thereafter, we use an appropriate gauge-fixing procedure, the time gauge, to compute both the quantization brackets and the functional measure on the path integral associated with our model. Finally, we confirm that three-dimensional bi-gravity has two physical degrees of freedom per space point. With the above, we provide a new perspective for a better understanding of the dynamical structure of theories of interacting spin-two fields, which does not require the constraints to be catalogued as first- and second-class ones as in the case of Dirac’s standard method.

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.

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.

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