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Updated: Jul 18, 2025

Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion
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线性和非线性系统的动态粗粒度:莫里-兹万齐格形式主义和超越

Bernd Jung1, Gerhard Jung2

  • 1Independent Scholar, Eltville, Germany.

The Journal of chemical physics
|August 24, 2023
PubMed
概括

非线性相互作用显著影响动态粗粒度. 使用非线性投影运算符可以准确地捕捉粗的动态,与线性方法不同,特别是对于具有非线性潜力的复杂系统.

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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
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A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
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