Reaction-Diffusion Modeling of Photopolymerization During Femtosecond Projection Two-Photon Lithography

2021 ◽  
Author(s):  
Rushil Pingali ◽  
Sourabh K. Saha
Keyword(s):  
Diffusion Mechanism ◽  
Chemical Properties ◽  
Reaction Diffusion ◽  
Element Model ◽  
Polymerization Process ◽  
Layer By Layer ◽  
Length Scales ◽  
Two Photon ◽  
Reaction Diffusion Model ◽  
Direct Laser

Abstract Two-photon lithography (TPL) is a polymerization-based direct laser writing process that is capable of fabricating arbitrarily complex three-dimensional (3D) structures with submicron features. Traditional TPL techniques have limited scalability due to the slow point-by-point serial writing scheme. The femtosecond projection TPL (FP-TPL) technique increases printing rate by a thousand times by enabling layer-by-layer parallelization. However, parallelization alters the time and the length scales of the underlying polymerization process. It is therefore challenging to apply the models of serial TPL to accurately predict process outcome during FP-TPL. To solve this problem, we have generated a finite element model of the polymerization process on the time and length scales relevant to FP-TPL. The model is based on the reaction-diffusion mechanism that underlies polymerization. We have applied this model to predict the geometry of nanowires printed under a variety of conditions and compared these predictions against empirical data. Our model accurately predicts the nanowire widths. However, accuracy of aspect ratio prediction is hindered by uncertain values of the chemical properties of the photopolymer. Nevertheless, our results demonstrate that the reaction-diffusion model can accurately capture the effect of controllable parameters on FP-TPL process outcome and can therefore be used for process control and optimization.

Reaction-Diffusion Modeling of Photopolymerization during Femtosecond Projection Two-Photon Lithography

2021 ◽  
pp. 1-13
Author(s):  
Rushil Pingali ◽  
Sourabh K. Saha
Keyword(s):  
Diffusion Mechanism ◽  
Chemical Properties ◽  
Reaction Diffusion ◽  
Element Model ◽  
Polymerization Process ◽  
Layer By Layer ◽  
Length Scales ◽  
Two Photon ◽  
Reaction Diffusion Model ◽  
Direct Laser

Abstract Two-photon lithography (TPL) is a polymerization-based direct laser writing process that is capable of fabricating arbitrarily complex three-dimensional (3D) structures with submicron features. Traditional TPL techniques have limited scalability due to the slow point-by-point serial writing scheme. The femtosecond projection TPL (FP-TPL) technique increases printing rate by a thousand times by enabling layer-by-layer parallelization. However, parallelization alters the time and the length scales of the underlying polymerization process. It is therefore challenging to apply the models of serial TPL to accurately predict process outcome during FP-TPL. To solve this problem, we have generated a finite element model of the polymerization process on the time and length scales relevant to FP-TPL. The model is based on the reaction-diffusion mechanism that underlies polymerization. We have applied this model to predict the geometry of nanowires printed under a variety of conditions and compared these predictions against empirical data. Our model accurately predicts the nanowire widths. However, accuracy of aspect ratio prediction is hindered by uncertain values of the chemical properties of the photopolymer. Nevertheless, our results demonstrate that the reaction-diffusion model can accurately capture the effect of controllable parameters on FP-TPL process outcome and can therefore be used for process control and optimization.

scholarly journals Reaction Diffusion and Chemotaxis for Decentralized Gathering on FPGAs

2009 ◽  
Vol 2009 ◽  
pp. 1-15 ◽  
Author(s):  
Bernard Girau ◽  
César Torres-Huitzil ◽  
Nikolaos Vlassopoulos ◽  
José Hugo Barrón-Zambrano
Keyword(s):  
Large Scale ◽  
Complex Dynamics ◽  
Diffusion Mechanism ◽  
Reaction Diffusion ◽  
Fpga Implementation ◽  
Cellular Slime Mold ◽  
Reaction Diffusion Model ◽  
Cellular Slime ◽  
Computational Resources ◽  
Embedded Implementation

We consider here the feasibility of gathering multiple computational resources by means of decentralized and simple local rules. We study such decentralized gathering by means of a stochastic model inspired from biology: the aggregation of theDictyostelium discoideumcellular slime mold. The environment transmits information according to a reaction-diffusion mechanism and the agents move by following excitation fronts. Despite its simplicity this model exhibits interesting properties of self-organization and robustness to obstacles. We first describe the FPGA implementation of the environment alone, to perform large scale and rapid simulations of the complex dynamics of this reaction-diffusion model. Then we describe the FPGA implementation of the environment together with the agents, to study the major challenges that must be solved when designing a fast embedded implementation of the decentralized gathering model. We analyze the results according to the different goals of these hardware implementations.

Axial Control of Two-Photon Polymerization With Femtosecond Bessel Beam

2017 ◽  
Author(s):  
Xiaoming Yu ◽  
Meng Zhang ◽  
Shuting Lei
Keyword(s):  
3D Printing ◽  
Bessel Beam ◽  
Average Diameter ◽  
Axial Direction ◽  
Polymerization Process ◽  
Layer By Layer ◽  
Light Modulator ◽  
Simultaneous Generation ◽  
Two Photon ◽  
Two Photon Polymerization

Stereolithography of three-dimensional, arbitrarily-shaped objects is achieved by successively curing photopolymer on multiple 2D planes and then stacking these 2D slices into 3D objects. Often as a bottleneck for speeding up the fabrication process, this layer-by-layer approach originates from the lack of axial control of photopolymerization. In this paper, we present a novel stereolithography technology with which two-photon polymerization can be dynamically controlled in the axial direction using Bessel beam generated from a spatial light modulator (SLM) and an axicon. First, we use unmodulated Bessel beam to fabricate micro-wires with an average diameter of 100 μm and a length exceeding 10 mm, resulting in an aspect ratio > 100:1. A study on the polymerization process shows that a fabrication speed of 2 mm/s can be achieved. Defect and deformation are observed, and the micro-wires consist of multiple narrow fibers which indicate the existence of the self-writing effect. A test case is presented to demonstrate fast 3D printing of a hollow tube within one second. Next, we modulate the Bessel beam with an SLM and demonstrate the simultaneous generation of multiple focal spots along the laser propagation direction. These spots can be dynamically controlled by loading an image sequence on the SLM. The theoretical foundation of this technology is outlined, and computer simulation is conducted to verify the experimental results. The presented technology extends current stereolithography into the third dimension, and has the potential to significantly increase 3D printing speed.

Pyrolysis behaviors dominated by the reaction–diffusion mechanism in the fluorine-free metal–organic decomposition process

2020 ◽  
Vol 8 (48) ◽  
pp. 17417-17428
Author(s):  
Jiangtao Shi ◽  
Yue Zhao ◽  
Yue Wu ◽  
Jingyuan Chu ◽  
Xiao Tang ◽  
...  
Keyword(s):  
Diffusion Model ◽  
Diffusion Mechanism ◽  
Reaction Diffusion ◽  
Decomposition Process ◽  
One Dimensional ◽  
Reaction Diffusion Model ◽  
Metal Organic ◽  
Free Metal ◽  
Organic Decomposition

In this work, pyrolysis behaviors dominated by the reaction–diffusion mechanism were investigated. And one-dimensional reaction–diffusion model is proposed.

scholarly journals Studies of Turing pattern formation in zebrafish skin

2021 ◽  
Vol 379 (2213) ◽  
Author(s):  
Shigeru Kondo ◽  
Masakatsu Watanabe ◽  
Seita Miyazawa
Keyword(s):  
Pattern Formation ◽  
Diffusion Mechanism ◽  
Model Organism ◽  
Reaction Diffusion ◽  
Cell Interactions ◽  
Pigment Cells ◽  
Turing Pattern ◽  
Reaction Diffusion Model ◽  
Experimental Findings ◽  
Cell Cell

Skin patterns are the first example of the existence of Turing patterns in living organisms. Extensive research on zebrafish, a model organism with stripes on its skin, has revealed the principles of pattern formation at the molecular and cellular levels. Surprisingly, although the networks of cell–cell interactions have been observed to satisfy the ‘short-range activation and long-range inhibition’ prerequisites for Turing pattern formation, numerous individual reactions were not envisioned based on the classical reaction–diffusion model. For example, in real skin, it is not an alteration in concentrations of chemicals, but autonomous migration and proliferation of pigment cells that establish patterns, and cell–cell interactions are mediated via direct contact through cell protrusions. Therefore, the classical reaction–diffusion mechanism cannot be used as it is for modelling skin pattern formation. Various studies are underway to adapt mathematical models to the experimental findings on research into skin patterns, and the purpose of this review is to organize and present them. These novel theoretical methods could be applied to autonomous pattern formation phenomena other than skin patterns. This article is part of the theme issue ‘Recent progress and open frontiers in Turing's theory of morphogenesis’.

Dissipative structures and morphogenetic pattern in unicellular algae

1981 ◽  
Vol 294 (1074) ◽  
pp. 547-588 ◽  
Keyword(s):  
Cell Wall ◽  
Cell Division ◽  
Diffusion Mechanism ◽  
Reaction Diffusion ◽  
Dissipative Structures ◽  
Two Dimensions ◽  
Unicellular Algae ◽  
Reaction Diffusion Model ◽  
Surface Ornamentation ◽  
Cell Wall Ingrowths

Patterns of cell wall growth and ornamentation in unicellular algae, mainly in desmids, are compared with patterns generated by Tyson’s Brusselator, a two-morphogen reaction-diffusion model. The model generates hexagonal arrays of points in two dimensions, according well with the observed patterns of surface ornamentation on desmid zygospores. Computed patterns in one dimension and of branching on a circular disc account both qualitatively and quantitatively for morphogenetic patterns that develop following cell division in several desmid genera. Cell wall ingrowths appear to be under similar pattern control to wall outgrowths during morphogenesis, which suggests the involvement of a reaction-diffusion mechanism in establishing and correctly positioning the cell division septum. The application of the model to morphogenesis in Acetabularia and diatoms is also discussed.

3D computer-aided nanoprinting for solid-state nanopores

2018 ◽  
Vol 3 (3) ◽  
pp. 312-316 ◽  
Author(s):  
Haibo Ding ◽  
Qiming Zhang ◽  
Zhongze Gu ◽  
Min Gu
Keyword(s):  
Solid State ◽  
Polymerization Process ◽  
Direct Laser Writing ◽  
Laser Writing ◽  
Two Photon ◽  
Direct Laser ◽  
Computer Aided ◽  
Two Photon Polymerization

Solid-state nanopores with controllable sizes and shapes were generated by direct laser writing using a computer-aided two-photon polymerization process.

scholarly journals Neuroepithelial organoid patterning is mediated by Wnt-driven Turing mechanism

2021 ◽  
Author(s):  
Abdel Rahman Abdel Fattah ◽  
Sergei Grebenyuk ◽  
Idris Salmon ◽  
Adrian Ranga
Keyword(s):  
In Silico ◽  
Interaction Analysis ◽  
Diffusion Mechanism ◽  
Reaction Diffusion ◽  
Model Systems ◽  
Ligand Interaction ◽  
Receptor Ligand ◽  
Length Scales ◽  
Multiple Length Scales

AbstractCell patterning in epithelia is critical for the establishment of tissue function during development. The organization of patterns in these tissues is mediated by the interpretation of signals operating across multiple length scales. How epithelial tissues coordinate changes in cell identity across these length scales to orchestrate cellular rearrangements and fate specification remains poorly understood. Here, we use human neural tube organoids as model systems to interrogate epithelial patterning principles that guide domain specification. In silico modeling of the patterning process by cellular automata, validated by in vitro experiments, reveal that the initial positions of floor plate cells, coupled with activator-inhibitor signaling interactions, deterministically dictate the patterning outcome according to a discretized Turing reaction-diffusion mechanism. This model predicts an enhancement of organoid patterning by modulating inhibitor levels. Receptor-ligand interaction analysis of scRNAseq data from multiple organoid domains reveals WNT-pathway ligands as the specific inhibitory agents, thereby allowing for the experimental validation of model predictions. These results demonstrate that neuroepithelia employ reaction-diffusion-based mechanisms during early embryonic human development to organize cellular identities and morphogen sources to achieve patterning. The wider implementation of such in vitro organoid models in combination with in-silico agent-based modeling coupled to receptor-ligand analysis of scRNAseq data opens avenues for a broader understanding of dynamic tissue patterning processes.

scholarly journals Formation of periodic pigment spots by the reaction-diffusion mechanism

2018 ◽  
Author(s):  
Baoqing Ding ◽  
Erin L. Patterson ◽  
Srinidhi V. Holalu ◽  
Jingjian Li ◽  
Grace A. Johnson ◽  
...  
Keyword(s):  
Long Range ◽  
Diffusion Model ◽  
Feedback Loop ◽  
Diffusion Mechanism ◽  
Reaction Diffusion ◽  
Pollinator Visitation ◽  
Reaction Diffusion Model ◽  
Inhibitory Feedback ◽  
R2r3 Myb ◽  
Diffusion Networks

AbstractMany organisms exhibit visually striking spotted or striped pigmentation patterns. Turing’s reaction-diffusion model postulates that such periodic pigmentation patterns form when a local autocatalytic feedback loop and a long-range inhibitory feedback loop interact. At its simplest, this network only requires one self-activating activator that also activates a repressor, which inhibits the activator and diffuses to neighboring cells. However, the molecular activators and repressors fully fitting this versatile model remain elusive. Here, we characterize an R2R3-MYB activator and an R3-MYB repressor in monkeyflowers that correspond to Turing’s model and explain how periodic anthocyanin spots form. Notably, disrupting this pattern impacts pollinator visitation. Thus, subtle changes in simple reaction-diffusion networks are likely essential contributors to the evolution of the remarkable diversity of periodic pigmentation patterns in flowers.

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