Spatio-Temporal Modeling of Saltatory Conduction in Neurons Using Poisson-Nernst-Planck Treatment and Estimation of Conduction Velocity

Gulati, Rahul; Rudraraju, Shiva

doi:10.2139/ssrn.4258219

Cited by 3 publications

(3 citation statements)

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“…This framework is build on top of the deal.II open source finite element library [30]. Following the standard practise in our group to release all research codes as open source [31,32,33,34,35], the complete code base for this work is made available to the wider research community as an open-source library [36].…”

Section: Computational Implementationmentioning

confidence: 99%

A Novel Phase-Field Based Formulation of Interface Evolution during Mechanical Compaction of Sedimentary Basins

Bhagat¹,

Jin²,

Rudraraju³

2022

Preprint

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A novel phase-field method based numerical approach to modeling the compaction process of sedi- ments is presented. Water-logged rock or soil sediments are deposited on the water basins over time and the increasing volume of the sediment compacts under its own weight and external pressure. Coupled evolution of mass conservation, Darcy flow, and the viscoelastic constitutive response, in conjunction with the evolution of porosity and permeability, make this problem highly non-linear and involve moving boundaries. We adopt a phase-field approach to represent the moving sediment interface, and the underlying multiphasic model permits for studying compaction in dynamically evolving sediments. This approach does not necessitate a change of domain sizes as is the case of existing traditional models of sedimentation but rather treats sedimentation growth as a problem of interface motion. We first model a classical compaction problem in 1D to compare with existing results in the literature, and then extend the framework to 2D to model the compaction process taking place under the influence of gravity. The model is then extensively applied to understand the effect of the sediment initial state and the sediment material properties on the compaction process and its spatiotemporal evolution. Lastly, a strong validation of our phase-field treatment results against predictions from traditional methods of solving open boundary sediment compaction problems, and a good agreement between the conventional understanding and the numerical predictions of porosity dependence on the fluid pore pressure for various cases of geological interest, are used to demonstrate the applicability and scalability of this novel numerical framework to model more advanced sediment compaction problems and geometries.

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Section: Computational Implementationmentioning

confidence: 99%

A Novel Phase-Field Based Formulation of Interface Evolution during Mechanical Compaction of Sedimentary Basins

Bhagat¹,

Jin²,

Rudraraju³

2022

Preprint

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“…The coupled Navier-Stokes equations are solved using Chorin's projection method [51]. Following the standard practice in our group to release all research codes as open source [43,52,53,54,55], the complete code base for this work is made available to the wider research community as an open-source library [56]. A representative schematic of the computational domain and the relevant boundary conditions are shown in Figure 2.…”

Section: Computational Implementationmentioning

confidence: 99%

A Numerical Investigation of Dimensionless Numbers Characterizing Meltpool Morphology of the Laser Powder Bed Fusion Process

Bhagat¹,

Rudraraju²

2022

Preprint

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Microstructure evolution in metal additive manufacturing (AM) is a complex multi-physics and multi-scale problem. Understanding the impact of AM process conditions on the microstructure evolution and the resulting mechanical properties of the printed part is an active area of research. At the meltpool scale, the thermo-fluidic governing equations have been extensively modeled in the literature to understand the meltpool conditions and the thermal gradients in its vicinity. In many phenomena governed by partial differential equations, dimensional analysis and identification of important dimensionless numbers can provide significant insights into the process dynamics. In this context, a novel strategy using dimensional analysis and the method of linear least squares regression to numerically investigate the thermo-fluidic governing equations of the Laser Powder Bed Fusion AM process is presented in this work. First, the governing equations are solved using the Finite Element Method, and the model predictions are validated by comparing with experimentally estimated cooling rates, and with numerical results from the literature. Then, through dimensional analysis, an important dimensionless quantity - interpreted as a measure of heat ab- sorbed by the powdered material and the meltpool, is identified. This dimensionless measure of heat absorbed, along with classical dimensionless quantities such as Peclet, Marangoni, and Stefan numbers, is used to investigate advective transport in the meltpool for different alloys. Further, the framework is used to study the variations of thermal gradients and the solidification cooling rate. Important correlations linking meltpool morphology and microstructure evolution related variables with classical dimensionless numbers are the key contribution of this work.

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“…The coupled Navier-Stokes equations are solved using Chorin's projection method[51]. Following the standard practise in our group to release all research codes as open source[43,52,53,54,55], the complete code base for this work is made available to the wider research community as an open-source library…”

mentioning

confidence: 99%

A Numerical Investigation of Dimensionless Numbers Characterizing Meltpool Morphology of the Laser Powder Bed Fusion Process

Bhagat¹,

Rudraraju²

2022

Preprint

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Microstructure evolution in metal additive manufacturing (AM) is a complex multi-physics and multi-scale problem. Understanding the impact of AM process conditions on microstructure evolution and the resulting mechanical properties of the printed part is an area of active research. In this context, high-fidelity numerical modeling of the AM process at various relevant length-scales has been finding favor. At the meltpool scale, the thermo-fluidic governing equations have been extensively modeled to understand the meltpool conditions and thermal gradients. In many phenomena governed by partial differential equations, dimensional analysis and identification of important dimensionless numbers can provide significant insights into the process dynamics. Hence, the use of dimensionless numbers to understand the complex multiphysics interactions active during metal AM is also gaining traction. In this context, we present a novel strategy using dimensional analysis and the least-squares regression approach, in conjunction with physics-based insights, to investigate the thermo-fluidic governing equations of the Laser Powder Bed Fusion AM process. Through this approach, we identify important dimensionless quantities influencing meltpool morphology. The governing equations are solved using the Finite Element Method, and the model predictions are validated by comparing with experimentally estimated cooling rates, and with numerical results from the literature. We then present our dimensional analysis and define an important dimensionless quantity - interpreted as a measure of heat absorbed by the powdered material and the resulting meltpool. We then use this dimensionless measure of heat absorbed, along with classical dimensionless quantities relevant to the thermo-fluidic governing equations, to investigate advective transport in the meltpool for different metal alloys. This understanding helps us characterize the meltpool aspect ratio and volume in terms of the Marangoni, and Stefan numbers. Further, we study the variations of thermal gradients and the solidification cooling rate using this framework and examine the effect of the Peclet number on the microstructure of the solidified meltpool region.

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Spatio-Temporal Modeling of Saltatory Conduction in Neurons Using Poisson-Nernst-Planck Treatment and Estimation of Conduction Velocity

Cited by 3 publications

References 0 publications

A Novel Phase-Field Based Formulation of Interface Evolution during Mechanical Compaction of Sedimentary Basins

A Novel Phase-Field Based Formulation of Interface Evolution during Mechanical Compaction of Sedimentary Basins

A Numerical Investigation of Dimensionless Numbers Characterizing Meltpool Morphology of the Laser Powder Bed Fusion Process

A Numerical Investigation of Dimensionless Numbers Characterizing Meltpool Morphology of the Laser Powder Bed Fusion Process

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