Probabilistic finite-size transport models for fusion: Anomalous transport and scaling laws

2004 ◽  
Vol 11 (5) ◽  
pp. 2272-2285 ◽  
Author(s):  
B. Ph. van Milligen ◽  
R. Sánchez ◽  
B. A. Carreras
Keyword(s):  
Scaling Laws ◽  
Finite Size ◽  
Anomalous Transport ◽  
Transport Models

KINETIC RESPONSE OF SURFACES DEFINED BY FINITE FRACTALS

Fractals ◽  
2010 ◽  
Vol 18 (04) ◽  
pp. 461-476 ◽  
Author(s):  
PRADEEP R. NAIR ◽  
MUHAMMAD A. ALAM
Keyword(s):  
Scaling Laws ◽  
Finite Size ◽  
Critical Dimension ◽  
The Novel ◽  
Scale Invariant ◽  
Fractal Surfaces ◽  
Dimension Formula ◽  
Diffusion Limited ◽  
Engineered Systems ◽  
Size Limits

Historically, fractal analysis has been remarkably successful in describing wide ranging kinetic processes on (idealized) scale invariant objects in terms of elegantly simple universal scaling laws. However, as nanostructured materials find increasing applications in energy storage, energy conversion, healthcare, etc., one must reexamine the premise of traditional fractal scaling laws as it only applies to physically unrealistic infinite systems, while all natural/engineered systems are necessarily finite. In this article, we address the consequences of the 'finite-size' problem in the context of time dependent diffusion towards fractal surfaces via the novel technique of Cantor-transforms to (i) illustrate how finiteness modifies its classical scaling exponents; (ii) establish that for finite systems, the diffusion-limited reaction is decelerated below a critical dimension [Formula: see text] and accelerated above it; and (iii) to identify the crossover size-limits beyond which a finite system can be considered (practically) infinite and redefine the very notion of 'finiteness' of fractals in terms of its kinetic response. Our results have broad implications regarding dynamics of systems defined by the same fractal dimension, but differentiated by degree of scaling iteration or morphogenesis, e.g. variation in lung capacity between a child and adult.

scholarly journals Determining the nonequilibrium criticality of a Gardner transition via a hybrid study of molecular simulations and machine learning

2021 ◽  
Vol 118 (11) ◽  
pp. e2017392118
Author(s):  
Huaping Li ◽  
Yuliang Jin ◽  
Ying Jiang ◽  
Jeff Z. Y. Chen
Keyword(s):  
Machine Learning ◽  
Phase Transition ◽  
Critical Exponents ◽  
Spin Glasses ◽  
Scaling Laws ◽  
Finite Size ◽  
Three Dimensions ◽  
Aging Effects ◽  
Correlation Lengths ◽  
Nonequilibrium Phase

Apparent critical phenomena, typically indicated by growing correlation lengths and dynamical slowing down, are ubiquitous in nonequilibrium systems such as supercooled liquids, amorphous solids, active matter, and spin glasses. It is often challenging to determine if such observations are related to a true second-order phase transition as in the equilibrium case or simply a crossover and even more so to measure the associated critical exponents. Here we show that the simulation results of a hard-sphere glass in three dimensions are consistent with the recent theoretical prediction of a Gardner transition, a continuous nonequilibrium phase transition. Using a hybrid molecular simulation–machine learning approach, we obtain scaling laws for both finite-size and aging effects and determine the critical exponents that traditional methods fail to estimate. Our study provides an approach that is useful to understand the nature of glass transitions and can be generalized to analyze other nonequilibrium phase transitions.

Depth-dependent Clustering Analysis of Fractures in Crystalline Basement Rocks

2021 ◽  
Author(s):  
Mohammad Javad Afshari Moein ◽  
Keith Evans ◽  
Benoît Valley ◽  
Kristian Bär ◽  
Albert Genter
Keyword(s):  
Fractal Dimension ◽  
Rock Mass ◽  
Scaling Laws ◽  
Tectonic Setting ◽  
Critical Role ◽  
Finite Size ◽  
Fracture Network ◽  
Crystalline Basement ◽  
Partial Fracture ◽  
Fracture Distribution

<p>Understanding the complex seismic, thermal, hydraulic and mechanical processes active during the hydraulic stimulation or continuous operation of Enhanced Geothermal Systems (EGS) requires an accurate description of the pre-existing fractures and faults. However, the three-dimensional characterization of the fracture network is challenging, as direct observation of the discontinuity network at great depth is limited. Fracture image logs and continuous core, which provide line samples through the fracture network, are most valuable in this regard as they provide the most precise option to place constraints on network attributes in stochastic realizations of the fractured rock mass. Among various geometrical attributes, the spatial clustering of fractures plays a critical role on the rock mass properties. </p><p>Here, we analyzed the spatial distribution of fractures derived from image log runs in six deep boreholes in crystalline basement rock. In one well, the fracture distribution from continuous core was also available. The wells were drilled to depths between 2-5 km, and were all located in the same tectonic setting of the Upper Rhine Graben, which is recognized for its high geothermal potential. The normalized correlation integral method was employed to define the scaling relationships of fracture patterns. This methodology is demonstrated to be less affected by the finite size effects, delivering reliable estimates of scaling laws.</p><p>Detailed analyses of image log datasets revealed fractal scaling with similar fractal dimensions (between 0.85 and 0.96), prevailed over almost two orders of magnitude of scale. The same was true for the fracture distribution derived from the continuous core, although this distribution was found to be more clustered than that derived from image logs in the same well (i.e. the fractal dimension was lower, which may be due to the partial fracture sampling of image logs which have a coarser resolution than continuous core analyses). Analysis of fractures in sub-sections of the core dataset from progressively increasing depths revealed no systematic depth-dependency for the fractal dimension, although a local variation at a scale of hundreds of meters was identified.</p>

scholarly journals Assessing the polymer coil-globule state from the very first spectral modes

2021 ◽  
Author(s):  
Timothy Földes ◽  
Antony Lesage ◽  
Maria Barbi
Keyword(s):  
Scaling Laws ◽  
Imaging Techniques ◽  
Interaction Strength ◽  
Finite Size ◽  
Point Of View ◽  
Fluorescent Imaging ◽  
Experimental Implementation ◽  
Wide Range ◽  
Polymer Coil

The determination of the coil-globule transition of a polymer is generally based on the reconstruction of scaling laws, implying the need for samples from a rather wide range of different polymer lengths N. The spectral point of view developed in this work allows for a very parsimonious description of all the aspects of the finite-size coil-globule transition on the basis of the first two Rouse (cosine) modes only, shedding new light on polymer theory. Capturing the relevant configuration path features, the proposed approach enables to determine the state of a polymer without the need of any information about the polymer length or interaction strength. Importantly, we propose an experimental implementation of our analysis that can be easily performed with modern fluorescent imaging techniques, and would allow differentiation of coil or globule conformations by simply recording the positions of three discernible loci on the polymer.

scholarly journals Polymer coil-globule phase transition is a universal folding principle of Drosophila epigenetic domains

2018 ◽  
Author(s):  
Antony Lesage ◽  
Vincent Dahirel ◽  
Jean-Marc Victor ◽  
Maria Barbi
Keyword(s):  
Scaling Laws ◽  
Persistence Length ◽  
Finite Size ◽  
Super Resolution ◽  
Structural Features ◽  
Polymer Physics ◽  
The Mean ◽  
Induced Changes ◽  
First Time

AbstractBackgroundLocalized functional domains within chromosomes, known as topologically associating domains (TADs), have been recently highlighted. In Drosophila, TADs are biochemically defined by epigenetic marks, this suggesting that the 3D arrangement may be the “missing link” between epigenetics and gene activity. Recent observations (Boettiger et al., Nature 2016) provide access to structural features of these domains with unprecedented resolution thanks to super-resolution experiments. In particular, they give access to the distribution of the radii of gyration for domains of different linear length and associated with different transcriptional activity states: active, inactive or repressed. Intriguingly, the observed scaling laws lack consistent interpretation in polymer physics.ResultsWe develop a new methodology conceived to extract the best information from such super-resolution data by exploiting the whole distribution of gyration radii, and to place these experimental results on a theoretical framework. We show that the experimental data are compatible with the finite-size behavior of a self-attracting polymer. The same generic polymer model leads to quantitative differences between active, inactive and repressed domains. Active domains behave as pure polymer coils, while inactive and repressed domains both lie at the coil-globule crossover. For the first time, the “colo-specificity” of both the persistence length and the mean interaction energy are estimated, leading to important differences between epigenetic states.ConclusionsThese results point toward a crucial role of criticality to enhance the system responsivity, resulting in both energy transitions and structural rearrangements. We get strong indications that epigenetically induced changes in nucleosome-nucleosome interaction can cause chromatin to shift between different activity states.

Analysis of anomalous transport based on radial fractional diffusion equation

2021 ◽  
Author(s):  
Kaibang Wu ◽  
Lai Wei ◽  
Zhengxiong Wang
Keyword(s):  
Fractional Diffusion ◽  
Local Effect ◽  
Anomalous Transport ◽  
Transport Models ◽  
Density Profiles ◽  
Confined Plasmas ◽  
Magnetically Confined ◽  
Non Local ◽  
Magnetically Confined Plasmas ◽  
Fractional Transport

Abstract The anomalous transport in magnetically confined plasmas is investigated by the radial fractional transport equations. It is shown that for fractional transport models, hollow density profiles are formed and uphill transports can be observed regardless of whether the fractional diffusion coefficients (FDCs) are radially dependent or not. When a radially dependent FDC Dα(r)<1 is imposed, compared with the case under Dα(r)=1.0, it is observed that the position of the peak of the density profile is closer to the core. Besides, it is found that when FDCs at the positions of source injections increase, the peak values of density profiles decrease. The non-local effect becomes significant as the order of fractional derivative α→1 and causes the uphill transport. However, as α→2, the fractional diffusion model returns to the standard model governed by Fick’s law.

scholarly journals Coexistence of Different Scaling Laws for the Entanglement Entropy in a Periodically Driven System

Proceedings ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 6
Author(s):  
Tony J. G. Apollaro ◽  
Salvatore Lorenzo
Keyword(s):  
Ground State ◽  
Scaling Laws ◽  
Entanglement Entropy ◽  
Finite Size ◽  
Simultaneous Occurrence ◽  
Many Body ◽  
Periodically Driven ◽  
Quantum Ising Model ◽  
Long Time ◽  
Many Body Systems

The out-of-equilibrium dynamics of many body systems has recently received a burst of interest, also due to experimental implementations. The dynamics of observables, such as magnetization and susceptibilities, and quantum information related quantities, such as concurrence and entanglement entropy, have been investigated under different protocols bringing the system out of equilibrium. In this paper we focus on the entanglement entropy dynamics under a sinusoidal drive of the tranverse magnetic field in the 1D quantum Ising model. We find that the area and the volume law of the entanglement entropy coexist under periodic drive for an initial non-critical ground state. Furthermore, starting from a critical ground state, the entanglement entropy exhibits finite size scaling even under such a periodic drive. This critical-like behaviour of the out-of-equilibrium driven state can persist for arbitrarily long time, provided that the entanglement entropy is evaluated on increasingly subsytem sizes, whereas for smaller sizes a volume law holds. Finally, we give an interpretation of the simultaneous occurrence of critical and non-critical behaviour in terms of the propagation of Floquet quasi-particles.

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