Spiral Growth Research Articles

Multi-Objective Low-Thrust Interplanetary Trajectory Optimization Based on Generalized Logarithmic Spirals

The multi-objective optimal design of low-thrust multigravity-assist trajectories is formulated within the hybrid optimal control framework. A new automated solution strategy for this problem is proposed in this Paper based on a two-step algorithm. In the first step, the trajectory is assumed to be a generalized logarithmic spiral. A heuristic global search algorithm combined with nonlinear programming are in charge of optimizing the set of parameters defining the spirals as well as the number, sequence, and configuration of the gravity assists. In the second step, candidate solutions are regarded as initial guesses for a direct collocation method, in which the problem is transcribed into a nonlinear programming problem by discretization, considering the full dynamics and the complete set of constraints. The presented approach is tested on a rendezvous mission to the asteroid Ceres, allowing a Mars flyby, and on a flyby mission to Jupiter, allowing multiple flybys on different bodies. Pareto-optimal solutions in terms of time of flight and propellant mass consumed are obtained for both cases. Results outperform those found in the literature in terms of optimality while showing the effectiveness of the proposed methodology to generate quick performance estimates for preliminary studies and accurate solutions for the detailed design.

Morphological dissection and cellular and transcriptome characterizations of bamboo pith cavity formation reveal a pivotal role of genes related to programmed cell death.

SummaryPith cavity formation is critical for bamboo to overcome the bending force during its fast growth; however, the underlying molecular mechanisms remain largely unknown. Multiple approaches, including anatomical dissection, mathematical modelling and transcriptome profiling, were employed in this study to investigate the biology of pith cavity formation in bamboo Pseudosasa japonica. We found that the corruption of pith tissue occurred sequentially and asymmetrically from the top‐centre of the internode down to the bottom, which might be caused by the combined effects of asymmetrical radial and axial tensile forces during shoot‐wall cell elongation and spiral growth of bamboo internodes. Programmed cell death (PCD) in pitch manifested by TUNEL positive nuclei, DNA cleavage and degraded organelles, and potentially regulated by ethylene and calcium signalling pathway, ROS burst, cell wall modification, proteolysis and nutrient recycle genes, might be responsible for pith tissue corruption of Ps. japonica. Although similar physiological changes and transcriptome profiles were found in different bamboo species, different formation rates of pith cavity were observed, which might be caused by different pith cells across the internode that were negatively correlated with the culm diameter. These findings provided a systematical view on the formation of bamboo pith cavity and revealed that PCD plays an important role in the bamboo pith cavity formation.

Spiral growth of a crystal due to chemical reaction

The article is devoted to the study of crystal growth due to chemical reactions in multicomponent media via terrace-kink-step mechanism. The theory of Burton, Cabrera and Frank is developed and applied to multicomponent case. Equations are obtained for speed of movement of single step, group of steps at certain interstep distance. Growth spirals caused by screw dislocations are considered. Growth rate of the crystal is found. Impact of partial pressures of reaction products on diffusion length of adatoms and growth rate is analyzed.

An iterative microphone removal method for acoustic beamforming array design

This paper presents a beamforming array design method that uses a large array of microphones and systematically reduces it to a predetermined number of microphones. The microphone, while included in the array, that results in the smallest (defined as Φ in this paper) product of frequency-averaged Main Lobe Width (MLW) and Maximum Sidelobe Level (MSL) of the point spread function using the cross-spectral beamforming algorithm is identified and removed. The reduction method is implemented in two ways: one-by-one microphone removal and an accelerated procedure that removes several microphones per iteration, where the removed number of microphones decreases in an exponential manner with increasing iterations. Multi-frequency array reductions, using 841 and 961-channel equi-and-non-equispaced grid initial arrays, are conducted over the frequency range of 2000 Hz–8000 Hz to replicate typical conditions in a small scale anechoic facility. These reduced arrays are compared against several logarithmic spiral and randomised pattern arrays and in most cases, reveal superior values of MSL, MLW and Φ. Single-frequency array reductions, using both 961 and 169-channel initial arrays, at the best-case frequencies for the logarithmic spirals, also display superior performance. Both the multi-and-single-frequency arrays can be used practically: the multi-frequency arrays possess an even performance across the simulated frequency range, whereas the single-frequency arrays possess excellent performance over narrowband frequency ranges and can be modified within an array stencil for each acoustic experiment.

Micro-structural phenomena in agate/chalcedony: spiral growth

AbstractAgates with spectacular micro-structural features were found in volcanic rocks at several occurrences in the Saar-Nahe region (Germany). These agates include spirals of several tens up to several hundreds of μm in size within zones lacking the characteristic structural agate banding. A combined mineralogical study by polarising microscopy, scanning electron microscopy, cathodoluminescence microscopy and spectroscopy, and electron backscatter diffraction provided evidence that the spirals consist of well-ordered trigonal α-quartz, whereas the surrounding matrix is composed of strongly disordered or amorphous SiO2phases. The quartz micro-crystals show a systematic rotation of the crystal orientation perpendicular to the direction of the spiral loops indicating helical growth.It is assumed that the spiral growth is initiated by dislocations with a screw component. The lacking symmetry of the strongly disordered or amorphous matrix initiated a curved development by a screw dislocation in a system far from equilibrium. The atoms/molecules are packed into spiral layers, which is energetically favoured in comparison with the incorporation into plane crystal faces. Such self-organisation growth and polymerisation initiated by a screw dislocation can produce variable spiral morphologies sometimes resembling living forms.

Quasicrystal nucleation and \u2124 module twin growth in an intermetallic glass-forming system

While quasicrystals possess long-range orientational order they lack translation periodicity. Considerable advancements in the elucidation of their structures and formative principles contrast with comparatively uncharted interrelations, as studies bridging the spatial scales from atoms to the macroscale are scarce. Here, we report on the homogeneous nucleation of a single quasicrystalline seed from the undercooled melt of glass-forming NiZr and its continuous growth into a tenfold twinned dendritic microstructure. Observing a series of crystallization events on electrostatically levitated NiZr confirms homogeneous nucleation. Mapping the microstructure with electron backscatter diffraction suggests a unique, distortion-free structure merging a common structure type of binary alloys with a spiral growth mechanism resembling phyllotaxis. A general geometric description, relating all atomic loci, observed by atomic resolution electron microscopy, to a pentagonal {Bbb Z} module, explains how the seed’s decagonal long-range orientational order is conserved throughout the symmetry breaking steps of twinning and dendritic growth.

Structure Transformations in Broken Symmetry Groups—Abstraction and Visualization

The work reports the finding and the study of transformation groups with two conditional elements (binary transformations of abstract structures of the finite numerical sets with broken symmetry). The term Broken Symmetry Group (BSG) is introduced. Transformation examples of relevant structures are studied with computer visualization and application in real structure study. A special type of BSG was discovered, which describes the subsets of “evolutionary trees” with convergent and divergent properties of the oriented graph (orgraph) with structure-development direction edges and “growth spirals”.

In situ observations of spiral growth on ice crystal surfaces

The spiral growth of crystals, mediated by their screw dislocations, is a general crystal-growth mechanism observed over a large variety of crystalline solids. Despite its general nature, direct observations of the spiral growth of ice have been rarely reported so far. Here, with the aid of advanced optical microscopy, we succeed in making in situ observations of the perfect spiral growth during the vapor growth of ice. We find that the spiral steps observed are well described by the classical Burton--Cabrera--Frank theory, taking into account surface diffusion of water admolecules between adjacent steps. This is distinct from the dominant growth mode that we have assigned as spiral in our recent studies, which accompanies fluctuations of the adjacent step interval. We also successfully capture the birth of a screw dislocation and the ensuing spiral growth, originating in the lattice mismatch arising from the coalescence of single ice crystals. Furthermore, we demonstrate that the nucleation of quasi-liquid layers (QLLs) takes place at the spiral center immediately after the birth of the dislocation, which suggests a link between screw dislocations and the generation of QLLs near the ice melting point.

Nonlinear three-dimensional diffusion models of porous medium in the presence of non-stationary source or absorption and some exact solutions

We study a general three-dimensional nonlinear diffusion model of porous medium with non-stationary source or absorption. We found nine basic models of the original model of the porous medium with non-stationary source or absorption, having different symmetry properties. For the model, admitting the widest group Lie of the transformations we found all invariant submodels. We found explicitly all essentially distinct invariant solutions describing invariant submodels of rank 0 of this model. In particular, we obtained the solutions, which we called “a layered circular pie”, “a layered spiral pie”, “ layered plane pie” and “a layered spherical pie”. The solution “a layered circular pie” describes a motion of the liquid or gas in a porous medium, for which at each fixed moment of a time at all points of each circle from the family of concentric circles a pressure is the same. The solution “a layered spiral pie” describes a motion of the liquid or gas in a porous medium, for which at each fixed moment of a time at all points of each logarithmic spiral, from the obtained family of logarithmic spirals a pressure is the same . The solution “a layered spherical pie” describes a motion of the liquid or gas in a porous medium, for which at each fixed moment of a time at all points of each sphere , from the family of concentric spheres a pressure is the same. A set of the solutions “a layered circular pie”, “a layered spiral pie” and “a layered spherical pie” contains the solutions describing a distribution of the pressure in a porous medium after a point blast or a point hydraulic shock. Also this set contains the solutions describing a stratified with respect to the pressure a motion of liquid or gas in a porous medium, with a very high pressure at infinity in a presence of a very strong absorption at a point. The solution “a layered plane pie” describes a motion of the liquid or gas in a porous medium, for which at each fixed moment of a time at all points of each plane, from the family of parallel planes a pressure is the same. A set of the solutions “a layered plane pie” contains the solutions describing a motion of the liquid or gas in a porous medium with a very high pressure near a fixed plane in a presence of a very strong absorption at infinity. Also this set contains the solutions describing a motion of the liquid or gas in a porous medium with a very high pressure at infinity in a presence of a very strong absorption on a fixed plane. The obtained results can be used to study to describe the processes associated with a underground fluid or gas flow, with water filtration, with the engineering surveys in the construction of the buildings, and also with shale oil and gas production.

Texture analysis and epitaxial relationships in Bi2Te3 thin film grown by physical vapor transport on silicon substrates

Controlling the film/substrate crystallographic relationships is of great interest since a good interface results in an improved crystal homogeneity and quality. In this work, texture analysis on Bi2Te3 films grown by physical vapor transport was carried out in order to study the influence of growth conditions such as time and substrate orientation. Two types of substrates were used: Si (1 0 0) and Si (1 1 1). It was found that the c-axis of the hexagonal structure of Bi2Te3 is always perpendicular to the substrate surface, while the orientation of the a-axes depends on the growth parameters. The in-plane orientation of the Bi2Te3 crystallites was improved as the growth time increased and textured epitaxial growth was achieved. The epitaxial relationships between the cubic Si and the hexagonal Bi2Te3 lattices were studied through pole diagrams. It was found that the a-axes of the Bi2Te3 lattice are oriented along the 〈1 1 0〉 directions of the Si surface in both types of substrates. In contrast to other reports, the observed growth rate was not constant, but it decreased with time. This effect is discussed in relation with the characteristic spiral growth mechanism.

Concentric and Spiral Few-Layer Graphene: Growth Driven by Interfacial Nucleation vs Screw Dislocation

Spiral growth of various nanomaterials including some two-dimensional (2D) transition metal dichalcogenides had recently been experimentally realized using chemical vapor deposition (CVD). However, such growth that is driven by screw dislocation remained elusive for graphene and is rarely discussed because of the use of metal catalysts. In this work, we show that formation of few-layer graphene (FLG) with a spiral structure driven by screw dislocation can be obtained alongside FLG having a concentric layered structure formed by interfacial nucleation (nucleation at the graphene/Cu interface) using Cu-catalyzed ambient pressure CVD. Unlike commonly reported FLG grown by interfacial nucleation where the second layer is grown independently beneath the first, the growth of a spiral structure adopts a top growth mechanism where the top layers are an extension from the initial monolayer which spirals around an axial dislocation in self-perpetuating steps. Since the same atomic orientation is preserved, the subs...

In Silico Crystal Growth Rate Prediction for NaCl from Aqueous Solution

The prediction of crystal growth rates from solution is a longstanding challenge and paramount opportunity for pharmaceuticals, materials science, biomineralization, and beyond. This work overcomes the key obstacle by calculating solute attachment rates to the crystal surface via atomistic simulations and rare-event methods. These rates are combined with the multiscale spiral growth model to produce the first parameter-free in silico crystal growth rate predictions. Our results are in excellent agreement with experimental measurements for sodium chloride grown from aqueous solution.

Control of Organic Crystal Shape by Femtosecond Laser Ablation

Control of organic crystal shape is crucial for various scientific and industrial fields, while it is still very challenging even with systematic optimization of environmental parameters such as temperature and concentration. Here we report an innovative approach for spatiotemporal control of organic crystal growth by directly modifying local crystal structures via femtosecond laser ablation. We found that a crystal face that is locally ablated only with a single laser pulse shows enhanced growth without the loss of crystal quality. The underlying mechanism can be explained by the generation of energetically favorable crystal growth mode (spiral growth mode), which is a fundamental growth mode for various organic crystals. We demonstrated that various crystal shapes can be achieved by femtosecond laser ablation. The fine-tuned, spatiotemporal cue given by femtosecond laser ablation will provide a facile means to obtain organic crystals with desired shape.

On Regional Differences in the Relationship among Stocks, Capital Siphons and Housing Prices

The current research on housing prices mainly concentrates on the cause of fluctuations from the view of the aggregate economy. However, the economic growth rates are relatively stable across time and even across regions, thus making it difficult to reconcile the tremendous yet persistent rising in housing prices. Though the concurring volatile financial factors can partly explain the overall growth of housing prices because of its similar rising trend, the factors taken into account are restricted within the macro perspectives, for example, by investigating the changes of a stock index（such as the Shanghai Composite Index）. The differences across regions of housing prices remain by and large unexplained. In fact, the literature of studying the relationship between financial development and the regional economic gap has been growing, but investigating from the micro perspectives still remains limited. For this reason, this paper attempts to find out the reason why the listed companies yield different effects on housing prices in different regions: capital siphons. The effect originates from the physical term phenomenon”, which refers to the one-way flow of water caused by different gravitational and potential forces. In this paper, we propose that the capital results in the flow of capital from less developed to relatively wealthier regions. Studying the effect after IPO is of great practical significance. First, previous literature pays little attention to capital siphons after IPO. Most of the related studies are qualitative analyses, or merely explore the relationship between stocks and GDP index without micro foundations. Second, capital siphons indeed have important effects on regional differences. This micro level analysis can be decomposed into two questions: First, how do listed companies funds to reserve money for the local real estate market and do capital siphons affect the housing price? Second, when the siphoned capital enters into the real estate market will affect the growth structure of the market value and housing prices? This study shows that financing from the primary market and insiders sell from the secondary market tend to siphon the national capital and increase the local currency, and then push up housing prices. Equivalently speaking, the area which is financing more or selling more will capital from other areas. The effect from insiders sell is different from that of financing: the former stimulates the accumulation of wealth, that is, the demand of rich strata drives housing prices mainly, while the latter has little impact on wealth accumulation. The price fluctuation in the secondary market determines the growth rhythm of housing prices, and spiral growth relationship is found between the market value of stocks and housing prices at the regional level. The substitution effect of stock markets is dominant in the bull market, in which the growth of the market value is negatively correlated with that of housing prices, while the wealth effect is dominant in the bear market, in which the relationship between the market value and housing prices is positive. In addition, the conclusion remained unchanged when we controlled some potential paths, which includes the population path, the favored economic boost policy path and the first-tier cities path. With the effect that siphoned capital exacerbates regional differences of housing prices is significant, the controversial Opinions for Poverty Alleviation enacted by China Securities Regulatory Commission（CSRC）in 2016 becomes reasonable and acceptable. In the future, the central and western regions, which are relatively backward in capital market development, should be offered certain favorable policies to encourage the capital to remain in the original area, in the hope that regional differences in housing prices can be mitigated. This study contributes to the literature in the following aspects: First, it is the leading study to verify the capital effect and to explain the financial causes and paths of regional differences in housing prices from the micro foundations. Second, it studies the influence of listed company on the regional economy from the perspectives of capital and housing prices. Third, it also clarifies the growth structure of stock markets and housing prices. Finally, this study provides a theoretical reference for regional economic coordination policies.

Controllable Growth and Formation Mechanisms of Dislocated WS2 Spirals.

Two-dimensional (2D) layered metal dichalcogenides can form spiral nanostructures by a screw-dislocation-driven mechanism, which leads to changes in crystal symmetry and layer stackings that introduce attractive physical properties different from their bulk and few-layer nanostructures. However, controllable growth of spirals is challenging and their growth mechanisms are poorly understood. Here, we report the controllable growth of WS2 spiral nanoplates with different stackings by a vapor phase deposition route and investigate their formation mechanisms by combining atomic force microscopy with second harmonic generation imaging. Previously not observed "spiral arm" features could be explained as covered dislocation spiral steps, and the number of spiral arms correlates with the number of screw dislocations initiated at the bottom plane. The supersaturation-dependent growth can generate new screw dislocations from the existing layers, or even new layers templated by existing screw dislocations. Different number of dislocations and orientation of new layers result in distinct morphologies, different layer stackings, and more complex nanostructures, such as triangular spiral nanoplates with hexagonal spiral pattern on top. This work provides the understanding and control of dislocation-driven growth of 2D nanostructures. These spiral nanostructures offer diverse candidates for probing the physical properties of layered materials and exploring new applications in functional nanoelectronic and optoelectronic devices.

Nucleation and growth mechanism of 2D SnS2 by chemical vapor deposition: initial 3D growth followed by 2D lateral growth

Tin disulfide (SnS2) is a n-type semiconductor with a hexagonally layered crystal structure and has promising applications in nanoelectronics, optoelectronics and sensors. Such applications require the deposition of SnS2 with controlled crystallinity and thickness control at monolayer level on large area substrate. Here, we investigate the nucleation and growth mechanism of two-dimensional (2D) SnS2 by chemical vapor deposition (CVD) using SnCl4 and H2S as precursors. We find that the growth mechanism of 2D SnS2 is different from the classical layer-by-layer growth mode, by which monolayer-thin 2D transition metal dichalcogenides can be formed. In the initial nucleation stage, isolated 2D SnS2 domains of several monolayers high are formed. Next, 2D SnS2 crystals grow laterally while keeping a nearly constant height until layer closure is achieved, due to the higher reactivity of SnS2 crystal edges than basal planes. We infer that the thickness of the 2D SnS2 crystals is determined by the height of initial SnS2 islands. After layer closure, SnS2 grows on grain boundaries and results in 3D growth mode, accompanied by spiral growth. Our findings suggest an approach to prepare 2D SnS2 with a controlled thickness of several monolayers and add more knowledge on the nucleation and growth mechanism of 2D materials.

Copper Pentagonal Micropyramids Grown by Mechanically Activated Electrodeposition

Abstract The formation of copper pentagonal micropyramids (PMPs) with high (multiatomic) spiral growth steps, which are grown by electrocrystallization with mechanical activation of the cathode, is studied experimentally. A new spiral-layer growth mechanism for the formation of such PMP is proposed. It is shown that PMPs grow on flat pentagonal microcrystals (PMCs) formed initially and containing fivefold twins with one of the twin boundaries being inclined by the angle of 35°16’ to the {110}-type substrate crystallographic plane. Such crystal geometry causes an inclined growth step on the PMC surface. The preferential deposition of metal atoms on this step leads to the spiral-layer PMC growth and the formation of PMPs with a structure inherited from the PMCs.

Development of biodegradable conductive cotton yarns by in-situ polymerisation of pyrrole

Cotton yarns were modified with pyrrole in the presence of ferric chloride following a dip-nip-dry technique. Treatment of cotton with 23.4% aqueous pyrrole followed by treatment with 40.6% aqueous ferric chloride and subsequent drying in atmospheric air produced balanced improvements in the properties of the yarn such as conductivity, tensile strength and extensibility. Among the three types of yarns such as ring spun, rotor spun and friction spun considered for such treatment, ring spun yarn performed best in respect of conductivity and retention of strength. Examination of surface morphology of yarns by scanning electron microscopy revealed a common discontinuity in the growth of polypyrrole along the length of the yarns spun using friction spinning and rotor spinning systems. Such discontinuity was caused by the wrapper fibres. Ring spun yarn, on the other hand, allowed a continuous spiral growth and deposition of polypyrrole in the inter-fibre space and on the surface of the yarn. Study of pyrrole modified ring spun yarn in a typical photoluminescence system indicated photoluminescence property of such pyrrole-treated cotton yarn.

Biopolymer Control on Calcite Precipitation

The influence of biopolymers, alginate (Alg) and polyaspartate (pAsp), on the kinetics of calcite precipitation was studied using the constant composition method for supersaturation states ranging from 2.4 to 4.5, at pH = 8.5. Biopolymer presence changes the mechanism of calcite precipitation and its inhibition depending on the system history. In a system without polymers, calcite precipitates by spiral growth. Introducing polymers during growth inhibits step movement by pinning at a number of kink sites along step edges. Polymer adsorption induces growth by two-dimensional nucleation. Both polymers inhibit calcite growth. Inhibition is stronger at higher concentration and lower solution supersaturation. The interfacial free energy, a key parameter in the control of nucleation and growth, was estimated from the analysis of the precipitation rates, as well as data obtained from vapor adsorption, which are quite identical for calcite with either alginate or polyaspartate adsorbed. This is confirmed by electrokinetic measurements, which show similar ζ- potential values for calcite with each of the polymers. Increasing polymer concentration and adsorption time led to a progressive decrease of the effective interface free energy, which could explain the much lower supersaturation needed for the onset of surface nucleation.

Analysis of growth and form in Aerothyris kerguelenensis (rhynchonelliform brachiopod) - Shell spiral deviations, microstructure, trace element contents and stable isotope ratios

Brachiopods are usually attached benthic marine invertebrates with a shell (exoskeleton) that archives modifications of the environment via chemical proxies. Growth lines regularly occurring (i.e. excluding random ones) at the shell's surface reflect phenotypically controlled interruptions or changes in secretion (Williams et al., 1997). Modifications in the secretion rate and reorientation of shell elements within the thickness of the shell induce marked changes in shell morphology providing elements for estimating age throughout ontogeny for specimens of Aerothyris kerguelenensis (Davidson 1880, formerly known as Waldheimia kerguelensis Davidson, 1978), from the Southern Indian Ocean. Maxima and minima of deviations from underlying shell spiral growth (SSD), plus maps (SEM-EDS) and Electron Microprobe (WDS) of Mg, S, Ca, Mn, Fe that are components of shells along with Scanning Electron Microscopy (SEM) all show evidence of rhythms at different time scales, including annual ones. Growth rates differ in young and adult forms as well as between dorsal and ventral valves; additionally the amplitudes of Mg peaks are higher early in ontogeny and in the primary shell layer, progressively decreasing with sporadic peaks. Anterior regions of shells are more informative regarding external growth (i.e. major growth marks) and mainly record later events in the life of the individual. Posterior regions are informative for internal morphology (cumulative growth) and reveal Mg bands and related concentrations that are consistent with the main extrema (maxima and minima) observed when using SSD and WDS analyses. Mg/Ca ratios indicate fluctuations in temperature and food supply during the growth period. Seawater temperatures calculated from the oxygen isotope compositions of the secondary layer of calcite in shells of A. kerguelenensis are close to those measured in situ in the environment in which they live. However, the difference in carbon isotope composition between the two studied shells reveal that these specimens record isotopic compositions most likely resulting from a combination of kinetic ‘vital’ isotope effects that may, sometimes, mimic equilibrium values.