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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
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Exploring substitution random functions composed of stationary multi-Gaussian processes.

Julien Straubhaar1, Philippe Renard1

  • 1The Centre for Hydrogeology and Geothermics (CHYN), University of Neuchâtel, Emile-Argand 11, 2000 Neuchâtel, Switzerland.

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|May 3, 2024
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Summary
This summary is machine-generated.

Substitution random functions (SRFs) offer more flexible spatial modeling than traditional multi-Gaussian fields. This study introduces a method to control connectivity in SRFs, improving their application in Earth sciences for better forecasts.

Keywords:
Composition of Gaussian processesConditioningConnectivity propertiesStochastic simulation

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Area of Science:

  • Earth sciences
  • Geostatistics
  • Stochastic modeling

Background:

  • Simulation of random fields is crucial for Earth science modeling and uncertainty quantification.
  • Multi-Gaussian random fields are common but struggle to represent highly or poorly connected spatial structures.
  • Existing models often isolate low or high value regions, impacting flow and transport simulations.

Purpose of the Study:

  • To investigate the properties of Substitution Random Functions (SRFs) constructed from stationary multi-Gaussian fields.
  • To develop a technique for controlling the connectivity of specific value ranges (low, intermediate, high) within SRFs.
  • To enhance the flexibility of random field models for improved spatial feature representation.

Main Methods:

  • Utilizing stationary multi-Gaussian random fields for both the directing (T) and coding (Y) processes.
  • Combining these processes to form SRFs with bounded variograms.
  • Introducing a control point in the coding process (Y) to guide realizations and using a Gibbs sampler for local value conditioning.

Main Results:

  • The resulting SRFs (Z) are stationary but non-ergodic for mean and covariance due to the finite variance of the directing field (T).
  • Demonstrated a method to control connectivity of low, intermediate, or high values within SRF realizations.
  • Successfully conditioned SRFs to local values using a Gibbs sampler.

Conclusions:

  • SRFs provide a more flexible alternative to multi-Gaussian fields for modeling spatial structures with controlled connectivity.
  • The proposed control point technique enhances the practical applicability of SRFs in Earth sciences.
  • This approach improves the representation of crucial spatial features like connectivity in flow and transport problems.