N-Dimensional Array Model for Geophysical Process Simulation
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Solution Overview
Problem
Current simulation models for dynamic processes and events in geophysical territories require extensive measurements of parameters, which can be burdensome, especially when dealing with numerous operative units, and struggle to effectively predict future dynamics over time and space.
Innovation Solution
A non-linear adaptive mathematical model that uses measured parameter values at multiple times to create an n-dimensional array of points, visualizing the evolution of events or processes by calculating displacements and distances between points, allowing for the prediction of future conditions and behavior.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If extensive measurements of parameters are taken at numerous operative units, then the accuracy and detail of the simulation model improves, but the burden and complexity of data collection increases significantly
Solution Approach 1:
The system segments the monitoring task by dividing the territory into discrete spatial locations represented in the n-dimensional array. Each location can be independently measured and updated, allowing the complex system to be broken down into manageable units that can be monitored separately and integrated into the overall simulation model
Solution Approach 2:
The patent transitions from traditional spatial mapping to an n-dimensional state space where each point represents a combination of multiple parameters (pressure, volume, temperature, etc.). This dimensional transformation allows the system to capture complex multi-parameter relationships without requiring proportional increases in measurement infrastructure, as the same physical measurements can be represented in multiple dimensional contexts
2Loss of information
If measurements are taken at many different locations to capture complete dynamics, then the comprehensiveness of the model improves, but the time and resources required for measurement increase
Solution Approach 1:
The n-dimensional array structure serves multiple functions simultaneously: it stores current state information, tracks temporal evolution, identifies patterns across different parameters, and enables predictive modeling. This multi-functionality reduces the need for separate measurement and analysis systems, thereby reducing overall time and resource requirements while maintaining comprehensive dynamics information
Solution Approach 2:
The system creates a virtual copy of the physical system in the form of the n-dimensional array model. Once the physical measurements are taken, the model can be updated and simulated repeatedly without requiring additional physical measurements, allowing comprehensive analysis of system dynamics to be performed on the digital copy rather than requiring continuous physical monitoring
Data Source
AI summary
A model simulating the evolutionary dynamics of events or processes includes a non-linear adaptive mathematical system simulating spatial and temporal dynamics by using measured values of parameters describing the evolutionary condition of an event or process at different times. The model enables the definition of a n-dimensional array of points in a n-dimensional reference system having an axis that represents the values of the parameters being measured. The displacements of each of the points are computed as a function of their displacements in the array of points between a first time a second time and as a function of the distance of each of the points of the array from each of the points representing the measured parameters. The evolution of the event and or the model in time is visualized by displaying the points of the array of points at different times.