A Huygens principle for diffusion and anomalous diffusion in spatially extended systems.
Ontology highlight
ABSTRACT:
SUBMITTER: Gottwald GA
PROVIDER: S-EPMC3666731 | biostudies-literature | 2013 May
REPOSITORIES: biostudies-literature
Publications
A Huygens principle for diffusion and anomalous diffusion in spatially extended systems.
Gottwald Georg A GA Melbourne Ian I
Proceedings of the National Academy of Sciences of the United States of America 20130507 21
We present a universal view on diffusive behavior in chaotic spatially extended systems for anisotropic and isotropic media. For anisotropic systems, strong chaos leads to diffusive behavior (Brownian motion with drift) and weak chaos leads to superdiffusive behavior (Lévy processes with drift). For isotropic systems, the drift term vanishes and strong chaos again leads to Brownian motion. We establish the existence of a nonlinear Huygens principle for weakly chaotic systems in isotropic media w ...[more]
Similar Datasets
Project description:Recent years have witnessed an extraordinary spurt in attention toward the wave-manipulating strategies revealed by phase-amplitude metasurfaces. Recently, it has been shown that, when two different phase-encoded metasurfaces responsible for doing separate missions are added together based on the superposition theorem, the mixed digital phase distribution will realize both missions at the same time. In this paper, via a semi-analytical procedure, we demonstrate that such a theorem is not necessarily valid when using phase-only metasurfaces or ignoring the element pattern functions. We introduce the concept of asymmetric spatial power divider (ASPD) with arbitrary power ratio levels in which modulating both amplitude and phase of the meta-atoms is inevitable to fully control the power intensity pattern of a reflective metasurface. Numerical simulations illustrate that the proposed ASPD designed by proper phase and amplitude distribution over the surface can directly generate a desired number of beams with predetermined orientations and power budgets. The C-shaped Pancharatnam-Berry meta-atoms locally realize the optimal phase and amplitude distribution in each case, and the good conformity between simulations and theoretical predictions verifies the presented formalism. A prototype of our ASPD designs is also fabricated and measured, and the experimental results corroborate well our numerical and semi-analytical predictions. Our findings not only offer possibilities to realize arbitrary spatial power dividers over subwavelength scale but also reveal an economical and simple alternative for a beamforming array antenna.
| S-EPMC6733224 | biostudies-literature
Project description:Huygens' Principle (1678) implies that every point on a wave front serves as a source of secondary wavelets, and the new wave front is the tangential surface to all the secondary wavelets. But two problems arise: portions of wavelets that exist outside of the new wave front combine to form a wake. Also there are two tangential surfaces so wave fronts are propagated in both the forward and backward directions. These problems have not previously been resolved by using a geometrical theory with impulsive wavelets that are in harmony with Huygens' geometrical description. Doing so would provide deeper understanding of and greater intuition into wave propagation, in addition to providing a new model for wave propagation analysis. The interpretation, developed here, of Huygens' geometrical construction shows Huygens' Principle to be correct: as for the wake, the Huygens' wavelets disappear when combined except where they contact their common tangent surfaces, the new propagating wave fronts. As for the backward wave, a source propagates both a forward wave and a backward wave when it is stationary, but it propagates only the forward wave front when it is advancing with a speed equal to the propagation speed of the wave fronts.
| S-EPMC8511121 | biostudies-literature
Project description:Measurements on physical systems result from the systems' activity being converted into sensor measurements by a forward model. In a number of cases, inversion of the forward model is extremely sensitive to perturbations such as sensor noise or numerical errors in the forward model. Regularization is then required, which introduces bias in the reconstruction of the systems' activity. One domain in which this is particularly problematic is the reconstruction of interactions in spatially-extended complex systems such as the human brain. Brain interactions can be reconstructed from non-invasive measurements such as electroencephalography (EEG) or magnetoencephalography (MEG), whose forward models are linear and instantaneous, but have large null-spaces and high condition numbers. This leads to incomplete unmixing of the forward models and hence to spurious interactions. This motivated the development of interaction measures that are exclusively sensitive to lagged, i.e. delayed interactions. The drawback of such measures is that they only detect interactions that have sufficiently large lags and this introduces bias in reconstructed brain networks. We introduce three estimators for linear interactions in spatially-extended systems that are uniformly sensitive to all lags. We derive some basic properties of and relationships between the estimators and evaluate their performance using numerical simulations from a simple benchmark model.
| S-EPMC7732350 | biostudies-literature
Project description:The principle of vinylogy states that the electronic effects of a functional group in a molecule are possibly transmitted to a distal position through interposed conjugated multiple bonds. As an emblematic case, the nucleophilic character of a π-extended enolate-type chain system may be relayed from the legitimate α-site to the vinylogous γ, ε, ..., ω remote carbon sites along the chain, provided that suitable HOMO-raising strategies are adopted to transform the unsaturated pronucleophilic precursors into the reactive polyenolate species. On the other hand, when "unnatural" carbonyl ipso-sites are activated as nucleophiles (umpolung), vinylogation extends the nucleophilic character to "unnatural" β, δ, ... remote sites. Merging the principle of vinylogy with activation modalities and concepts such as iminium ion/enamine organocatalysis, NHC-organocatalysis, cooperative organo/metal catalysis, bifunctional organocatalysis, dicyanoalkylidene activation, and organocascade reactions represents an impressive step forward for all vinylogous transformations. This review article celebrates this evolutionary progress, by collecting, comparing, and critically describing the achievements made over the nine year period 2010-2018, in the generation of vinylogous enolate-type donor substrates and their use in chemical synthesis.
| S-EPMC7993750 | biostudies-literature
Project description:Interface diffusion along a metal/ceramic interface present in numerous energy and electronic devices can critically affect their performance and stability. Hole formation in a polycrystalline Ni film on an ?-Al2O3 substrate coupled with a continuum diffusion analysis demonstrates that Ni diffusion along the Ni/?-Al2O3 interface is surprisingly fast. Ab initio calculations demonstrate that both Ni vacancy formation and migration energies at the coherent Ni/?-Al2O3 interface are much smaller than in bulk Ni, suggesting that the activation energy for diffusion along coherent Ni/?-Al2O3 interfaces is comparable to that along (incoherent/high angle) grain boundaries. Based on these results, we develop a simple model for diffusion along metal/ceramic interfaces, apply it to a wide range of metal/ceramic systems and validate it with several ab initio calculations. These results suggest that fast metal diffusion along metal/ceramic interfaces should be common, but is not universal.
| S-EPMC6286315 | biostudies-literature
Project description:The dynamics of water exhibits anomalous behavior in the presence of different electrolytes. Recent experiments [Kim JS, Wu Z, Morrow AR, Yethiraj A, Yethiraj A (2012) J Phys Chem B 116(39):12007-12013] have found that the self-diffusion of water (Dw) can either be enhanced or suppressed around CsI and NaCl, respectively, relative to that of neat water. Here we show that unlike classical empirical potentials, ab initio molecular dynamics simulations successfully reproduce the qualitative trends observed experimentally. These types of phenomena have often been rationalized in terms of the "structure-making" or "structure-breaking" effects of different ions on the solvent, although the microscopic origins of these features have remained elusive. Rather than disrupting the network in a significant manner, the electrolytes studied here cause rather subtle changes in both structural and dynamical properties of water. In particular, we show that water in the ab initio molecular dynamics simulations is characterized by dynamic heterogeneity, which turns out to be critical in reproducing the experimental trends.
| S-EPMC3948301 | biostudies-literature
Project description:Diffusion in cell membranes is not just simple two-dimensional Brownian motion but typically depends on the timescale of the observation. The physical origins of this anomalous subdiffusion are unresolved, and model systems capable of quantitative and reproducible control of membrane diffusion have been recognized as a key experimental bottleneck. Here, we control anomalous diffusion using supported lipid bilayers containing lipids derivatized with polyethylene glycol (PEG) headgroups. Bilayers with specific excluded area fractions are formed by control of PEG lipid mole fraction. These bilayers exhibit a switch in diffusive behavior, becoming anomalous as bilayer continuity is disrupted. Using a combination of single-molecule fluorescence and interferometric imaging, we measure the anomalous behavior in this model over four orders of magnitude in time. Diffusion in these bilayers is well described by a power-law dependence of the mean-square displacement with observation time. Anomaleity in this system can be tailored by simply controlling the mole fraction of PEG lipid, producing bilayers with diffusion parameters similar to those observed for anomalous diffusion in biological membranes.
| S-EPMC6428747 | biostudies-literature
Project description:The [Mo:7Fe:9S:C] iron-molybdenum cofactor (FeMoco) of nitrogenase is the largest known metal cluster and catalyses the 6-electron reduction of dinitrogen to ammonium in biological nitrogen fixation. Only recently its atomic structure was clarified, while its reactivity and electronic structure remain under debate. Here we show that for its resting S=3/2 state the common iron oxidation state assignments must be reconsidered. By a spatially resolved refinement of the anomalous scattering contributions of the 7 Fe atoms of FeMoco, we conclude that three irons (Fe1/3/7) are more reduced than the other four (Fe2/4/5/6). Our data are in agreement with the recently revised oxidation state assignment for the molybdenum ion, providing the first spatially resolved picture of the resting-state electron distribution within FeMoco. This might provide the long-sought experimental basis for a generally accepted theoretical description of the cluster that is in line with available spectroscopic and functional data.
| S-EPMC4793075 | biostudies-literature
Project description:Many biological and physical systems exhibit behaviour at multiple spatial, temporal or population scales. Multiscale processes provide challenges when they are to be simulated using numerical techniques. While coarser methods such as partial differential equations are typically fast to simulate, they lack the individual-level detail that may be required in regions of low concentration or small spatial scale. However, to simulate at such an individual level throughout a domain and in regions where concentrations are high can be computationally expensive. Spatially coupled hybrid methods provide a bridge, allowing for multiple representations of the same species in one spatial domain by partitioning space into distinct modelling subdomains. Over the past 20 years, such hybrid methods have risen to prominence, leading to what is now a very active research area across multiple disciplines including chemistry, physics and mathematics. There are three main motivations for undertaking this review. Firstly, we have collated a large number of spatially extended hybrid methods and presented them in a single coherent document, while comparing and contrasting them, so that anyone who requires a multiscale hybrid method will be able to find the most appropriate one for their need. Secondly, we have provided canonical examples with algorithms and accompanying code, serving to demonstrate how these types of methods work in practice. Finally, we have presented papers that employ these methods on real biological and physical problems, demonstrating their utility. We also consider some open research questions in the area of hybrid method development and the future directions for the field.
| S-EPMC5832735 | biostudies-literature
Project description:In 1665, Huygens observed that two identical pendulum clocks, weakly coupled through a heavy beam, soon synchronized with the same period and amplitude but with the two pendula swinging in opposite directions. This behaviour is now called anti-phase synchronization. This paper presents an analysis of the behaviour of a large class of coupled identical oscillators, including Huygens' clocks, using methods of equivariant bifurcation theory. The equivariant normal form for such systems is developed and the possible solutions are characterized. The transformation of the physical system parameters to the normal form parameters is given explicitly and applied to the physical values appropriate for Huygens' clocks, and to those of more recent studies. It is shown that Huygens' physical system could only exhibit anti-phase motion, explaining why Huygens observed exclusively this. By contrast, some more recent researchers have observed in-phase or other more complicated motion in their own experimental systems. Here, it is explained which physical characteristics of these systems allow for the existence of these other types of stable solutions. The present analysis not only accounts for these previously observed solutions in a unified framework, but also introduces behaviour not classified by other authors, such as a synchronized toroidal breather and a chaotic toroidal breather.
| S-EPMC5627120 | biostudies-literature