scholarly journals Experimental Investigation of the Transition to Spatiotemporal Chaos with a System-Size Control Parameter

2008 ◽  
Vol 2008 ◽  
pp. 1-5
Author(s):  
Daniel R. Spiegel ◽  
Elliot R. Johnson
Keyword(s):  
Liquid Crystal ◽  
Control Parameter ◽  
Quantitative Measure ◽  
Building Blocks ◽  
System Size ◽  
Spatiotemporal Chaos ◽  
Length Scale ◽  
Fourth Moment ◽  
Pattern Size ◽  
Temporal Periodicity

Using a localized laser-heating method to allow the use of system size as a control parameter, we experimentally investigate, using liquid-crystal electroconvection with soft boundary conditions, the onset of spatial temporal chaos (STC) with increasing system size. We find that temporal periodicity is significantly quenched as the system size increases. The increase of the fourth moment (kurtosis) of the temporal Fourier transform provides a very useful quantitative measure of the loss of temporal periodicity (hence the onset of STC) as the pattern size increases, and also provides a simple means for determining a natural chaotic length scale. This length scale is comparable to the length of vertical rows observed in the original pattern. Our experiments, thus, imply that there are well-defined building blocks, which in our case are easily visualized, that control the dynamics in STC liquid crystal convection. The results of our experiments appear to be consistent with the conclusions of recent STC computer simulations carried out by Fishman and Egolf.

Reversible microscale assembly of nanoparticles driven by the phase transition of a thermotropic liquid crystal

2017 ◽  
Author(s):  
Niamh Mac Fhionnlaoich ◽  
Stephen Schrettl ◽  
Nicholas B. Tito ◽  
Ye Yang ◽  
Malavika Nair ◽  
...  
Keyword(s):  
Phase Transition ◽  
Liquid Crystal ◽  
Self Assembly ◽  
Nematic Phase ◽  
Hierarchical Control ◽  
Building Blocks ◽  
Model System ◽  
Microscopic Level ◽  
Reversible Process ◽  
Thermotropic Liquid Crystal

The arrangement of nanoscale building blocks into patterns with microscale periodicity is challenging to achieve via self-assembly processes. Here, we report on the phase transition-driven collective assembly of gold nanoparticles in a thermotropic liquid crystal. A temperature-induced transition from the isotropic to the nematic phase leads to the assembly of individual nanometre-sized particles into arrays of micrometre-sized aggregates, whose size and characteristic spacing can be tuned by varying the cooling rate. This fully reversible process offers hierarchical control over structural order on the molecular, nanoscopic, and microscopic level and is an interesting model system for the programmable patterning of nanocomposites with access to micrometre-sized periodicities.

scholarly journals Length scale of interaction in spatiotemporal chaos

2011 ◽  
Vol 83 (4) ◽  
Author(s):  
Dan Stahlke ◽  
Renate Wackerbauer
Keyword(s):  
Spatiotemporal Chaos ◽  
Length Scale

scholarly journals Improved mixing height monitoring through a combination of lidar and radon measurements

2012 ◽  
Vol 5 (5) ◽  
pp. 6835-6866 ◽  
Author(s):  
A. D. Griffiths ◽  
S. D. Parkes ◽  
S. D. Chambers ◽  
M. F. McCabe ◽  
A. G. Williams
Keyword(s):  
Boundary Layer ◽  
Time Series ◽  
Radon Concentration ◽  
Quantitative Measure ◽  
Potential Method ◽  
Length Scale ◽  
Mixing Length ◽  
Mixing Height ◽  
Lidar Measurements ◽  
Radon Measurements

Abstract. Surface-based radon (222Rn) measurements can be combined with lidar backscatter to obtain a higher quality time series of mixing height within the Planetary Boundary-Layer (PBL) than is possible from lidar alone, and a more quantitative measure of mixing height than is possible from only radon. The lidar measurements benefit because even when aerosol layers are detected, reliably attributing the mixing height to the correct layer presents a challenge. By combining lidar with a mixing length scale derived from a time series of radon concentration, automated and robust attribution is possible during the morning transition. Radon measurements also provide mixing information during the night and with the addition of lidar these measurements become insensitive to night-to-night changes in radon emissions. After calibration with lidar, the radon-derived equivalent mixing height agrees with other measures of mixing on daily and hourly time scales and is a potential method for studying intermittent mixing in nocturnal boundary layers.

Length Scale Dependent Deformation in Polymers

2012 ◽  
Author(s):  
F. Alisafaei ◽  
Seyed Hamid Reza Sanei ◽  
Chung-Souk Han
Keyword(s):  
Liquid Crystal ◽  
Size Effects ◽  
Liquid Crystal Polymers ◽  
Length Scale ◽  
Indentation Testing ◽  
Indentation Size ◽  
Length Scales ◽  
Indentation Tests ◽  
Length Scale Dependent Deformation ◽  
Beam Bending

Length scale dependent deformation of polymers has been observed in different experiments including micro-beam bending and indentation tests. Here the length scale dependent deformation of polydimethylsiloxane is examined in indentation testing at length scales from microns down to hundreds of nanometers. Strong indentation size effects have been observed in these experiments which are rationalized with rotation gradients that can be related to Frank elasticity type molecular energies known from liquid crystal polymers. To support this notion additional experiments have been conducted where Berkovich and spherical indenter tips results have been compared with each other.

scholarly journals Electrically powered motions of toron crystallites in chiral liquid crystals

2020 ◽  
Vol 117 (12) ◽  
pp. 6437-6445 ◽  
Author(s):  
Hayley R. O. Sohn ◽  
Ivan I. Smalyukh
Keyword(s):  
Liquid Crystal ◽  
Electric Field ◽  
Soft Matter ◽  
Building Blocks ◽  
Rigid Particles ◽  
Deformable Particle ◽  
External Stresses ◽  
Oscillating Electric Field ◽  
Experimental Geometry ◽  
Chiral Liquid Crystals

Malleability of metals is an example of how the dynamics of defects like dislocations induced by external stresses alters material properties and enables technological applications. However, these defects move merely to comply with the mechanical forces applied on macroscopic scales, whereas the molecular and atomic building blocks behave like rigid particles. Here, we demonstrate how motions of crystallites and the defects between them can arise within the soft matter medium in an oscillating electric field applied to a chiral liquid crystal with polycrystalline quasi-hexagonal arrangements of self-assembled topological solitons called “torons.” Periodic oscillations of electric field applied perpendicular to the plane of hexagonal lattices prompt repetitive shear-like deformations of the solitons, which synchronize the electrically powered self-shearing directions. The temporal evolution of deformations upon turning voltage on and off is not invariant upon reversal of time, prompting lateral translations of the crystallites of torons within quasi-hexagonal periodically deformed lattices. We probe how these motions depend on voltage and frequency of oscillating field applied in an experimental geometry resembling that of liquid crystal displays. We study the interrelations between synchronized deformations of the soft solitonic particles and their arrays, and the ensuing dynamics and giant number fluctuations mediated by motions of crystallites, five–seven defects pairs, and grain boundaries in the orderly organizations of solitons. We discuss how our findings may lead to technological and fundamental science applications of dynamic self-assemblies of topologically protected but highly deformable particle-like solitons.

Linear Software Models: Standard Modularity Highlights Residual Coupling

2014 ◽  
Vol 24 (02) ◽  
pp. 183-210 ◽  
Author(s):  
Iaakov Exman
Keyword(s):  
Case Studies ◽  
Design Patterns ◽  
Linear Models ◽  
Formal Theory ◽  
Building Blocks ◽  
System Size ◽  
Software Systems ◽  
Software Models ◽  
Software Modules ◽  
Long Time

Modularity — the decoupling of software units — is essential for composition of real software systems from ready-made components. But for a long time one lacked a formal theory of modularity. Recently we have been developing Linear Software Models as rigorous theoretical modularity standards based upon plain Linear Algebra. By these models, decoupling means just linear independence, within a modularity matrix. This paper applies Linear Software Models to software systems, obtaining three consequences: (1) besides decoupling, various informal notions of software engineering, such as software modules, cohesion, and single responsibility, have for the first time a well-defined formal counterpart; (2) canonical building blocks like Software Design Patterns strictly obey the Linear Software Models; (3) larger software systems obey bordered Linear Models, allowing precise location and visualization of residual coupling. The latter consequences are demonstrated by case studies of software systems from the literature. The applicability of the Linear Software Models is quantitatively shown to scale well with system size, for the given case studies.

Transition to Chaos: From Small to Large Systems in the Nikolaevskiy Model

2020 ◽  
Vol 30 (01) ◽  
pp. 2030002
Author(s):  
Steffen Richters-Finger ◽  
Simon Hartmann ◽  
Stefan J. Linz
Keyword(s):  
Soft Mode ◽  
Domain Size ◽  
Periodic Boundary Conditions ◽  
System Size ◽  
Spatiotemporal Chaos ◽  
Numerical Continuation ◽  
Partial Differential ◽  
Rich Variety ◽  
Transition To Chaos ◽  
Large Systems

We investigate the dynamics and the transitions to spatiotemporal chaos observed in a partial differential equation known as Nikolaevskiy equation in the regime of small domains while applying periodic boundary conditions. In contrast to generic chaotic solutions in large domains called soft-mode turbulence, the Nikolaevskiy model exhibits a rich variety of different chaotic and nonchaotic dynamics if the considered domain size is constrained to only a few characteristic wavelengths. Extending the work by Tanaka, we provide (i) an in-depth numerical analysis including maps of solution types for several parameter subspaces and (ii) results from the numerical continuation of selected types of regular dynamics. Doing this, we detect and classify the highly elaborate scenario of different transitions from regular dynamics to chaos that occur if the system size is varied. Due to the model’s simplicity, we expect those results to be adaptable in similar partial differential equations.

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