Development of a three dimensional, lattice-free multiscale model of the mammary terminal end bud

2016 ◽  
Author(s):  
Joseph D. Butner ◽  
Vittorio Cristini ◽  
Zhihui Wang
Keyword(s):  
Three Dimensional ◽  
Multiscale Model ◽  
Dimensional Lattice ◽  
Terminal End Bud

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

scholarly journals Flux tubes in three-dimensional lattice gauge theories

1993 ◽  
Vol 48 (5) ◽  
pp. 2290-2298 ◽  
Author(s):  
Howard D. Trottier ◽  
R. M. Woloshyn
Keyword(s):  
Gauge Theories ◽  
Three Dimensional ◽  
Flux Tubes ◽  
Dimensional Lattice ◽  
Lattice Gauge ◽  
Lattice Gauge Theories

scholarly journals Multiscale Coupling of Transcranial Direct Current Stimulation to Neuron Electrodynamics: Modeling the Influence of the Transcranial Electric Field on Neuronal Depolarization

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Edward T. Dougherty ◽  
James C. Turner ◽  
Frank Vogel
Keyword(s):  
Electric Field ◽  
Direct Current ◽  
Transcranial Direct Current Stimulation ◽  
Three Dimensional ◽  
Human Head ◽  
Multiscale Model ◽  
Medical Intervention ◽  
Medical Community ◽  
Computational Grids ◽  
Direct Current Stimulation

Transcranial direct current stimulation (tDCS) continues to demonstrate success as a medical intervention for neurodegenerative diseases, psychological conditions, and traumatic brain injury recovery. One aspect of tDCS still not fully comprehended is the influence of the tDCS electric field on neural functionality. To address this issue, we present a mathematical, multiscale model that couples tDCS administration to neuron electrodynamics. We demonstrate the model’s validity and medical applicability with computational simulations using an idealized two-dimensional domain and then an MRI-derived, three-dimensional human head geometry possessing inhomogeneous and anisotropic tissue conductivities. We exemplify the capabilities of these simulations with real-world tDCS electrode configurations and treatment parameters and compare the model’s predictions to those attained from medical research studies. The model is implemented using efficient numerical strategies and solution techniques to allow the use of fine computational grids needed by the medical community.

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