A nonlinear evolution equation for surface-diffusion-driven Asaro-Tiller-Grinfeld instability of an epitaxially strained thin solid film on a solid substrate is derived in the case where the film wets the substrate. It is found that the presence of a weak wetting interaction between the film and the substrate can substantially retard the instability and modify its spectrum in such a way that the formation of spatially regular arrays of islands or pits on the film surface becomes possible. It is shown that the self-organization dynamics is significantly affected by the presence of the Goldstone mode associated with the conservation of mass.

Self-Organization of Quantum Dots in Epitaxially-Strained Solid Films

Predicting and designing systems with dynamic self-assembly properties in a spatiotemporal fashion is an important research area across disciplines ranging from understanding the fundamental non-equilibrium features of life to the fabrication of next-generation materials with life-like properties. Herein, we demonstrate a spatiotemporal dynamics pattern in the self-assembly behavior of a surfactant from an unorganized assembly, induced by adenosine triphosphate (ATP) and enzymes responsible for the degradation or conversion of ATP. We report the different behavior of two enzymes, alkaline phosphatase (ALP) and hexokinase (HK), towards adenosine triphosphate (ATP)-driven surfactant assembly, which also results in contrasting spatiotemporal dynamic assembly behavior. Here, ALP acts antagonistically, resulting in transient self-assemblies, whereas HK shows agonistic action with the ability to sustain the assemblies. This dynamic assembly behavior was then used to program the time-dependent emergence of a self-assembled structure in a two-dimensional space by maintaining concentration gradients of the enzymes and surfactant at different locations, demonstrating a new route for obtaining 'spatial' organizational adaptability in a self-organized system of interacting components for the incorporation of programmed functionality. 

Spatiotemporal dynamics of self-assembled structures in enzymatically induced agonistic and antagonistic conditions

Although two-dimensional (2D) parabolic integro-differential equations (PIDEs) arise in many physical contexts, there is no generally available software that is able to solve them numerically. To remedy this situation, in this article, we provide a compact implementation for solving 2D PIDEs using the finite element method (FEM) on unstructured grids. Piecewise linear finite element spaces on triangles are used for the space discretization, whereas the time discretization is based on the backward-Euler and the Crank–Nicolson methods. The quadrature rules for discretizing the Volterra integral term are chosen so as to be consistent with the time-stepping schemes; a more efficient version of the implementation that uses a vectorization technique in the assembly process is also presented. The compactness of the approach is demonstrated using the software Matrix Laboratory (MATLAB). The efficiency is demonstrated via a numerical example on an L-shaped domain, for which a comparison is possible against the commercially available finite element software COMSOL Multiphysics. Moreover, further consideration indicates that COMSOL Multiphysics cannot be directly applied to 2D PIDEs containing more complex kernels in the Volterra integral term, whereas our method can. Consequently, the subroutines we present constitute a valuable open and validated resource for solving more general 2D PIDEs.

https://www.mdpi.com/1999-4893/13/10/242/pdf

A compact FEM implementation for parabolic integro-differential equations in 2D

Background/Objectives: The implementation of the “Cohen-Daubechies-Feauveau9/7” lifting algorithm on a NVIDIA GPU in order to accelerate the computation with single and double-precision of some test images. Methods/Statistical Analysis: The DWT “Cohen-Daubechies-Feauveau 9/7” filter is implemented on a GPU with MatLab using the in-house parallel computation toolbox (PCT). The performance of both CPU and GPU implantations are compared with single and double precision on some test image. Findings: The investigational results show that the speedup is proportional to the image size until reaching a maximum at 40962 pixels for single-precision and 20482 pixels for double-precision; beyond these values the speedup decreases. The performance with GPU is enhanced, compared to that with CPU, by a factor above 2 for a single-precision of 40962 pixels image size and by a factor above 3 for a double-precision of 20482 pixels image size. By computing the Peak Signal-to-Noise Ratio (PSNR) at critical points after compression, we concluded that with single-precision we can compress larger image sizes without altering the image quality. Applications/Improvements: An efficient parallel implementation of the algorithm on GPU may lead to higher performances. The proposed idea in this work could be also extended to provide high efficiency video coding.

MatLab-GPU-based 2D-DWT Acceleration for JPEG2000 with Single and Double-Precision

Chemical gradient sensing behavior of catalytically active colloids and enzymes is an area of immense interest owing to their importance in understanding fundamental spatiotemporal complexity patterns in living systems and designing dynamic materials. Herein, we have shown the peroxidase activity of DNAzyme (G‐quadruplex‐hemin complex tagged in a micron‐sized glass bead) can be modulated by metal ions and metal ion‐binding oligonucleotides. Next we demonstrated both experimentally and theoretically, that the localization and product formation ability of the DNAzyme‐containing particle remains biased to the more catalytically active zone where the concentration of metal ion (Hg2+) inhibitor is low. Interestingly, this biased localization can be broken by introduction of Hg2+ binding oligonucleotide in the system. Additionally, a macroscopically asymmetric catalytic product distributed zone has been achieved with this process, showing the possibility of regulation in autonomous spatially controlled chemical processes. This demonstration of autonomous modulation of the localization pattern and spatially specific enhanced product forming ability of DNAzymes will further enable the design of responsive nucleic acid‐based motile materials and surfaces.

Regulating Spatial Localization and Reactivity Biasness of DNAzymes by Metal Ions and Oligonucleotides

Time-stepping methods for the simulation of the self-assembly of nano-crystals in Matlab on a GPU

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Time-stepping methods for the simulation of the self-assembly of nano-crystals in Matlab on a GPU