Line-shaped Patterns Research Articles

Pattern formation in the Cucker-Smale model

In this paper, we study the pattern formation phenomenon in the Cucker-Smale model with short-range communication weight under the interaction with introduced driving force. We show that the multi-cluster flocking and multi-cluster alignment emerge, and each flock achieves a line-shaped motion pattern for a given class of admissible initial configurations if the coupling strength and driving force strengths satisfy certain conditions. We also show the emergence of the global flocking, the global alignment, and the line-shaped motion pattern in the Cucker-Smale model with short-range communication weight if the coupling strength has a lower bound.

Enhancing Dental Cement Bond Strength with Autofocus-Laser-Cutter-Generated Grooves on Polyetheretherketone Surfaces.

Polyetheretherketone (PEEK) is widely used in dentistry owing to its exceptional properties, including its natural appearance; however, existing surface treatment methods for bonding PEEK have limitations. Autofocus laser cutters, known for their precise engraving and cutting capabilities, offer potential for surface treatment of PEEK; thus, the objective of this study was to investigate the creation of laser groove structures on PEEK to enhance its bonding capability with dental resin cement. A dental computer-aided design and manufacturing system was used to fabricate PEEK samples, and three groove patterns (circle, line, and grid) were generated on PEEK surfaces, with air-abrasion used as the control group. The surface characteristics, cell viability, and bond strength were evaluated, and the data were statistically analyzed using one-way analysis of variance and post hoc Tukey's tests (α = 0.05). Laser-treated PEEK exhibited a uniform texture with a groove depth of approximately 39.4 µm, hydrophobic properties with a contact angle exceeding 90°, a surface roughness of 7.3-12.4 µm, consistent topography, and comparable cell viability compared with untreated PEEK. Despite a decrease in bond strength after thermal cycling, no significant intergroup differences were observed, except for the line-shaped laser pattern. These findings indicate that the autofocus laser cutter effectively enhances the surface characteristics of PEEK by creating a uniform texture and grooves, showing promise in improving bonding properties, even considering the impact of thermal cycling effects.

Light-Controlled Particle Enrichment Patterns in Droplets.

Precision manipulation of particle-enrichment patterns in droplets is challenging but important in biochemical analysis and clinical diagnosis. Herein, a light strategy for precisely manipulating particle enrichment patterns is reported. Focused laser irradiation to the droplet induces a Marangoni flow owing to a localized photothermal effect, which carries in-droplet particles and concentrates them at the laser-spot-acted region. Owing to high flexibility of light, multiple particle-enriched sites are formed in a droplet, and the concentrated particles can be transported and reconstructed on demand. In addition to the island-like enrichment pattern, this optical particle manipulation strategy enables the formation of various particle-enriched patterns, such as the line-shape and circle-shape patterns. Further, light directly acts on the working fluid instead of target particles, considerably weakening dependence on particle properties. For particles whose density is similar to that of the working fluid, a portion of particles can still be concentrated. It is also found that only a small portion of submicron particles can be concentrated, while nanoparticles are hardly concentrated by this light strategy. Moreover, high reconfigurability of light enables in-parallel high-throughput operations, which is demonstrated using two laser beams to form two particle enrichment sites in a droplet simultaneously. Finally, this light strategy is also demonstrated by concentrating cells and nucleic acid molecules. This work paves the way for the applications of optofluidics in cell sorting, point-of-care analysis, and drug screening.

Scalable fabrication of renal spheroids and nephron-like tubules by bioprinting and controlled self-assembly of epithelial cells

Scalable fabrication concepts of 3D kidney tissue models are required to enable their application in pharmaceutical high-throughput screenings. Yet the reconstruction of complex tissue structures remains technologically challenging. We present a novel concept reducing the fabrication demands, by using controlled cellular self-assembly to achieve higher tissue complexities from significantly simplified construct designs. We used drop-on-demand bioprinting to fabricate locally confined patterns of renal epithelial cells embedded in a hydrogel matrix. These patterns provide defined local cell densities (cell count variance <11%) with high viability (92 ± 2%). Based on these patterns, controlled self-assembly leads to the formation of renal spheroids and nephron-like tubules with a predefined size and spatial localization. With this, we fabricated scalable arrays of hollow epithelial spheroids. The spheroid sizes correlated with the initial cell count per unit and could be stepwise adjusted, ranging from Ø = 84, 104, 120–131 µm in diameter (size variance <9%). Furthermore, we fabricated scalable line-shaped patterns, which self-assembled to hollow cellular tubules (Ø = 105 ± 22 µm). These showed a continuous lumen with prescribed orientation, lined by an epithelial monolayer with tight junctions. Additionally, upregulated expression of kidney-specific functional genes compared to 2D cell monolayers indicated increased tissue functionality, as revealed by mRNA sequencing. Furthermore, our concept enabled the fabrication of hybrid tubules, which consisted of arranged subsections of different cell types, combining murine and human epithelial cells. Finally, we integrated the self-assembled fabrication into a microfluidic chip and achieved fluidic access to the lumen at the terminal sites of the tubules. With this, we realized flow conditions with a wall shear stress of 0.05 ± 0.02 dyne cm−2 driven by hydrostatic pressure for scalable dynamic culture towards a nephron-on-chip model.

Stencil-masked phosphorus-implanted silicon for solar cell applications

Stencil-masked phosphorus implantation on silicon wafers is demonstrated for solar cell applications. Line-shaped window patterns with areas of 156 mm × 156 mm and 125 mm × 125 mm are laid out in the silicon stencil mask with diameters of 200 and 300 mm, respectively. According to laser optical microscopy and scanning electron microscopy observation, the phosphorus-implanted line is 100 μm wide with an edge roughness of a few micrometers. Based on the silicon-stencil-masked phosphorus implantation, the fabrication process of alternative phosphorus-implanted and boron-diffused patterns on silicon wafers is proposed. During the post-implantation wet oxidation process, a thick oxide layer is grown on the phosphorus-implanted silicon, acting as a protective layer for the subsequent diffusion of boron. Scanning capacitance microscopy observation reveals the p-type polarity in boron-diffused silicon and the n-type in phosphorus-implanted silicon with homogeneous contrast along the textured surface. Silicon-stencil-masked ion implantation has potential as a selective doping method on silicon wafers for solar cells.

Pattern Formation and Tropical Geometry

Sandpile models exhibit fascinating pattern structures: patches, characterized by quadratic functions, and line-shaped patterns (also called solitons, webs, or linear defects). It was predicted by Dhar and Sadhu that sandpile patterns with line-like features may be described in terms of tropical geometry. We explain the main ideas and technical tools—tropical geometry and discrete superharmonic functions—used to rigorously establish certain properties of these patterns. It seems that the aforementioned tools have great potential for generalization and application in a variety of situations.

Flocking and line-shaped spatial configuration to delayed Cucker-Smale models

<p style='text-indent:20px;'>As we known, it is popular for a designed system to achieve a prescribed performance, which have remarkable capability to regulate the flow of information from distinct and independent components. Also, it is not well understand, in both theories and applications, how self propelled agents use only limited environmental information and simple rules to organize into an ordered motion. In this paper, we focus on analysis the flocking behaviour and the line-shaped pattern for collective motion involving time delay effects. Firstly, we work on a delayed Cucker-Smale-type system involving a general communication weight and a constant delay <inline-formula><tex-math id="M1">\begin{document}$ \tau&gt;0 $\end{document}</tex-math></inline-formula> for modelling collective motion. In a result, by constructing a new Lyapunov functional approach, combining with two delayed differential inequalities established by <inline-formula><tex-math id="M2">\begin{document}$ L^2 $\end{document}</tex-math></inline-formula>-analysis, we show that the flocking occurs for the general communication weight when <inline-formula><tex-math id="M3">\begin{document}$ \tau $\end{document}</tex-math></inline-formula> is sufficiently small. Furthermore, to achieve the prescribed performance, we introduce the line-shaped inner force term into the delayed collective system, and analytically show that there is a flocking pattern with an asymptotic flocking velocity and line-shaped pattern. All results are novel and can be illustrated by numerical simulations using some concrete influence functions. Also, our results significantly extend some known theorems in the literature.

Fabrication of ZnO Nanowire Field-Emitter Arrays With Focusing Capability

ZnO nanowire field-emitter arrays (FEAs) show great application potentials in large-area vacuum microelectronics devices. However, the electron divergence is an issue which should be addressed. In this paper, ZnO nanowire FEAs with co-planar focus electrode were designed. A four-mask fabrication process and lift-off process were adopted to achieve the integration of focus electrode. The device demonstrated line-addressing and focusing capability with a spacing of 5 mm between anode and cathode, and the linewidth of field-emission images was reduced from 2.25 to 1.35 mm when the focus voltage changed from 50 to −50 V. Besides, line-shaped emission patterns were observed during focusing process, which was attributed to the emission pattern from the ZnO nanowire and the asymmetrical focusing electrical field.

Crystal defects observed by the etch-pit method and their effects on Schottky-barrier-diode characteristics on β-Ga2O3

A pixel array of vertical Schottky-barrier diodes (SBDs) was fabricated and measured on the surface of a β-Ga2O3 single crystal. Subsequently, etch pits and patterns were observed on the same surface. Three types of etch pits were discovered: (1) a line-shaped etch pattern originating from a void and extending toward the [010] direction, (2) an arrow-shaped etch pit whose arrow’s head faces toward the [102] direction and, (3) a gourd-shaped etch pit whose point head faces toward the [102] direction. Their average densities were estimated to be 5 × 102, 7 × 104, and 9 × 104 cm−2, respectively. We confirmed no clear relationship between the leakage current in SBDs and these crystalline defects. Such results are obtained because threading dislocations run mainly in the [010] growth direction and do not go through the sample plate.

Analytical design of refractive optical elements generating one-parameter intensity distributions.

We calculate a refractive surface to generate a one-parameter intensity distribution described by a vector function of one argument from an incident beam with a plane wavefront. The calculation of the refractive surface is reduced to the solution of two explicit ordinary differential equations of the first order. An approach to solving the problem of the existence of solutions for various one-parameter intensity distributions is proposed. Optical elements that form a variety of intensity distributions (a line, a circular arc, and a double-arc) are designed. The results of numerical simulations of the designed optical elements demonstrate the high quality of the generated line-shaped patterns.

Thermoplastic nanoimprint lithography of electroactive polymer poly(vinylidene fluoride-trifluoroethylene-chlorofluoroethylene) for micro/nanoscale sensors and actuators

Thermoplastic nanoimprint lithography has been used for the first time, to the best of our knowledge, as a method for transferring nanoscale patterns to electroactive polymer poly(vinylidene fluoride-trifluoroethylene-chlorofluoroethylene) [P(VDF-TrFE-CFE)]. PVDF, its copolymers, and terpolymers cannot be processed using conventional lithography techniques because of their solubility in most organic solvents and photoresist developers. In this work, line-shaped patterns with widths of 60 to 100 nm were formed in the thermoplastic polymer by thermal compression using a previously patterned and treated silicon (Si) stamp. Annealing of the polymer under compression in a nanoimprinter following imprint resulted in a 10-fold improvement in the surface roughness of the polymer relative to spin-coated layers of P(VDF-TrFE-CFE). Patterning of distinct polymer structures on Si substrates (without residual layer) was achieved for micron scale structures. The processes presented here comprise a basis for the integration of P(VDF-TrFE-CFE) as an active material in nanoscale sensors and actuators.

An efficient framework for estimation of muscle fiber orientation using ultrasonography

BackgroundMuscle fiber orientation (MFO) is an important parameter related to musculoskeletal functions. The traditional manual method for MFO estimation in sonograms was labor-intensive. The automatic methods proposed in recent years also involved voting procedures which were computationally expensive.MethodsIn this paper, we proposed a new framework to efficiently estimate MFO in sonograms. We firstly employed Multi-scale Vessel Enhancement Filtering (MVEF) to enhance fascicles in the sonograms and then the enhanced images were binarized. Finally, line-shaped patterns in the binary map were detected one by one, according to their shape properties. Specifically speaking, for the long-and-thinner regions, the orientation of the targeted muscle fibre was directly computed, without voting procedures, as the orientation of the ellipse that had the same normalized second central moments as the region. For other cases, the Hough voting procedure might be employed for orientation estimation. The performance of the algorithm was evaluated using four various group of sonograms, which are a dataset used in previous reports, 33 sonograms of gastrocnemius from 11 young healthy subjects, one sonogram sequence including 200 frames from a subject and 256 frames from an aged subject with cerebral infarction respectively.ResultsIt was demonstrated in the experiments that measurements of the proposed method agreed well with those of the manual method and achieved much more efficiency than the previous Re-voting Hough Transform (RVHT) algorithm.ConclusionsResults of the experiments suggested that, without compromising the accuracy, in the proposed framework the previous orientation estimation algorithm was accelerated by reduction of its dependence on voting procedures.

Unmixing Dynamic Fluorescence Diffuse Optical Tomography Images With Independent Component Analysis

Dynamic fluorescence diffuse optical tomography (D-FDOT) is important for drug delivery research. However, the low spatial resolution of FDOT and the complex kinetics of drug limit the ability of D-FDOT in resolving metabolic processes of drug throughout whole body of small animals. In this paper, we propose an independent component analysis (ICA)-based method to perform D-FDOT studies. When applied to D-FDOT images, ICA not only generates a set of independent components (ICs) which can illustrate functional structures with different kinetic behaviors, but also provides a set of associated time courses (TCs) which can represent normalized time courses of drug in corresponding functional structures. Further, the drug concentration in specific functional structure at different time points can be recovered by an inverse ICA transformation. To evaluate the performance of the proposed algorithm in the study of drug kinetics at whole-body level, simulation study and phantom experiment are both performed on a full-angle FDOT imaging system with line-shaped excitation pattern. In simulation study, the nanoparticle delivery of indocynaine green (ICG) throughout whole body of a digital mouse is simulated and imaged. In phantom experiment, four tubes containing different ICG concentrations are imaged and used to imitate the uptake and excretion of ICG in organs. The results suggest that we can not only illustrate ICG distributions in different functional structures, but also recover ICG concentrations in specific functional structure at different time points, when ICA is applied to D-FDOT images.

Estimation of muscle pennation angle in ultrasound images using the beamlet transform

Ultrasound imaging has been widely used to investigate the architecture properties of skeletal muscle, including the measurement of the pennation angle. In this study, we propose a beamlet-based algorithm to detect the straight line-shaped patterns of aponeurosis, fascicle or bone, and then to quantify the pennation angle in ultrasound images. The results demonstrate that the proposed algorithm can well detect the pennatoin angles in thirty ultrasound images with the correlation coefficient of 0.945, the standard root mean square error of 0.682°, and the relative root mean square error of 3.498%. The results suggest that this beamlet-based algorithm provides an alternative approach for the orientation estimation in musculoskeletal ultrasound images.

Root uptake and reduction of hexavalent chromium by aquatic macrophytes as assessed by high-resolution X-ray emission

Aquatic macrophytes Salvinia auriculata, Pistia stratiotes and Eichhornia crassipes were chosen to investigate the Cr(VI) reduced by root-based biosorption in a chromium uptake experiment, using a high-resolution XRF technique. These plants were grown in hydroponics medium supplied with non-toxic Cr concentrations during a 27-day metal uptake experiment. The high-resolution Cr-Kβ fluorescence spectra for dried root tissues and Cr reference material (100% Cr, Cr 2O 3, and CrO 3) were measured using an XRF spectrometer. For all species of aquatic plant treated with Cr(VI), the energy of the Cr-Kβ 2,5 line was shifted around 8 eV below the same spectral line identified for the Cr(VI) reference, but it was also near to the line identified for the Cr(III) reference. Moreover, there was a lack of the strong Cr-Kβ″ line assigned to the Cr(VI) reference material within the Cr(VI)-treated plant spectra, suggesting the reduction of Cr(VI) for other less toxic oxidation states of Cr. As all Cr-Kβ spectra of root tissue species were compared, the peak energies and lineshape patterns of the Cr-Kβ 2,5 line are coincident for the same aquatic plant species, when they were treated with Cr(III) and Cr(VI). Based on the experimental evidence, the Cr(VI) reduction process has happened during metal biosorption by these plants.

A novel jet-based nano-hydroxyapatite patterning technique for osteoblast guidance

Surface topography is well known to play a crucial role in influencing cellular responses to an implant material and is therefore important in bone tissue regeneration. A novel jet-based patterning technique, template-assisted electrohydrodynamic atomization spraying, was recently devised to control precisely the surface structure as well as its dimensions. In the present study, a detailed investigation of this patterning process was carried out. A range of nano-hydroxyapatite (nHA) line-shaped patterns <20 microm in width were successfully deposited on a commercially pure Ti surface by controlling the flow of an nHA suspension in an electric field. In vitro studies showed that the nHA patterns generated are capable of regulating the human osteoblast cell attachment and orientation.

Entropy production in a two-dimensional reversible Gray-Scott system

The entropy production sigma is calculated in the time evolution processes toward a Turing-like pattern and a chaotic pattern in a two-dimensional reaction-diffusion system. The contributions of reaction and diffusion to the entropy production are evaluated separately. Though its contribution to total sigma is about 5%, the entropy production in diffusion foretells the moving direction of the dots (reaction spots) and the line-shaped patterns. The entropy production of the entire system sigma depicts well the cooperative dynamics and evolution of chaotic dot patterns. It is suggested that sigma can be a scalar measure for quantitative studies of hierarchic pattern dynamics. The relation is also discussed between the bifurcation parameter and the distance from thermodynamic equilibrium.

Mixed Self-Assembled Monolayers of Semirigid Tetrahydro-4H-thiopyran End-Capped Oligo(cyclohexylidenes)

Single-component and mixed self-assembled monolayers (SAMs) of one- and three-ring semirigid tetrahydro-4H-thiopyran end-capped oligo(cyclohexylidenes)-that is, thiopyran (1), 4-(4-cyclohexylidene-cyclohexylidene)tetrahydro-4H-thiopyran (2), and 4-(tetrahydro-4H-thiopyran-4-cyclohexylidene-4'-ylidene)tetrahydro-4H-thiopyran (3)--on Au(111) substrates have been prepared and studied by cyclic voltammetry (CV), atomic force microscopy (AFM), and scanning tunneling microscopy (STM). It was found that the shortest adsorbate 1 more readily forms a SAM than 2 or 3. Notwithstanding, the SAMs of 2 or 3 are thermodynamically more stable due to favorable intermolecular attractions. Holes were made with the AFM tip establishing tilt angles of 30-50 degrees with respect to the surface normal for all SAMs. STM imaging showed well-ordered, line-shaped packing patterns with molecular resolution for the SAM of 2. Similar patterned structures were not observed for 1 and 3. Mixed SAMs were prepared by exposing a SAM of 1 to ethanol solutions of either 2 or 3. STM imaging revealed that domains of molecules of 2 or 3 amidst a monolayer of 1 are formed in both cases. Whereas in the mixed SAM of 1 and 2 the domains are irregularly shaped, circular islands of uniform size are found in the mixed SAM of 1 and 3.

Micropatterning proteins and cells on polylactic acid and poly(lactide- co-glycolide)

Techniques for micropatterning proteins and cells on biomaterials are important in tissue engineering applications. Here, we present a method for patterning proteins and cells on poly(lactic acid) (PLA) and poly(lactide- co-glycolide) (PLGA) substrates that are routinely used as scaffolds in engineering tissues. Poly(oligoethyleneglycol methacrylate) (poly-OEGMA) or poly(oligoethyleneglycol methacrylate- co-methacrylic acid) (poly(OEGMA- co-MA)) was microcontact printed onto substrates to create cell resistant areas. Proteins adsorbed onto the unprinted regions whereas the polymer printed regions effectively repel non-specific protein adsorption. NIH 3T3 fibroblasts remain confined within the patterns on the PLGA and PLA films for up to 2 weeks and aligned their actin cytoskeleton along the line patterns. In comparison to unpatterned cells, fibroblasts confined within line-shaped patterns show fewer actin filaments. This method for controlling the spatial morphology and distribution of cells on synthetic biomaterials could have significant applications in tissue engineering.

Carr–Purcell echo spectra in the studies of lineshape effects. Nonclassical hindered rotation of methyl groups in 1,2,3,4-tetrachloro-9,10-dimethyltriptycene

In the standard NMR spectra, the lineshape patterns produced by a molecular rate process are often poorly structured. When alternative theoretical models of such a process are to be compared, even quantitative lineshape fits may then give inconclusive results. A detailed description is presented of an approach involving fits of the competing models to series of Carr–Purcell echo spectra. Its high discriminative power has already been exploited in a number of cases of practical significance. An explanation is given why it can be superior to methods based on the standard spectra. Its applicability in practice is now illustrated on example of the methyl proton spectra in 1,2,3,4-tetrachloro-9,10-dimethyltriptycene TCDMT. It is shown that, in the echo spectra, the recently discovered effect of nonclassical stochastic reorientation of the methyl group can be identified clearly while it is practically nondiscernible in the standard spectra of TCDMT. This is the first detection of the effect at temperatures above 200 K. It is also shown that in computer-assisted interpretation of exchange-broadened echo spectra, the usual description of the stimulating radiofrequency pulses in terms of rotation operators ought to be replaced by a more realistic pulse model.