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Quadratic Models01:23

Quadratic Models

Quadratic models are mathematical representations used to describe relationships in which the rate of change changes at a constant rate. These models appear in a wide variety of natural and engineered systems, especially those involving motion, forces, and optimization. One common application is analyzing the vertical motion of objects influenced by gravity, such as a ball thrown into the air.In such scenarios, the object's height changes over time in a curved pattern, rising to a maximum point...
Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model01:13

Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model

Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
Gauss's Law01:07

Gauss's Law

If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
Debye–Huckel–Onsager Conductance Equation01:28

Debye–Huckel–Onsager Conductance Equation

The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect. According to this equation,...
Pharmacodynamic Models: Additive and Proportional Drug Effect Model01:09

Pharmacodynamic Models: Additive and Proportional Drug Effect Model

Drug response models describe how pharmacological agents interact with biological systems to produce measurable effects. Baseline responses are inherent physiological activities without a drug significantly influencing the observed pharmacological outcomes. Depending on the drug response model employed, these baseline responses may combine with the drug's effect in either an additive or proportional manner.Additive Drug Response ModelIn the additive model, the drug effect is independent of the...
Equations of Equilibrium in Three Dimensions01:30

Equations of Equilibrium in Three Dimensions

When analyzing structures or systems at rest, it is necessary to ensure they are in equilibrium. This is where the vector and scalar equations of equilibrium come into play. These equations are crucial in ensuring a structure is stable and will not collapse or fall apart. The vector and scalar equations of equilibrium provide a framework for analyzing the forces acting on a body.
According to the vector equations of equilibrium, the vector sum of all the external forces acting on a body must...

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Related Experiment Video

Updated: Jun 23, 2026

Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

General two-order-parameter Ginzburg-Landau model with quadratic and quartic interactions.

I P Ivanov1

  • 1Interactions Fondamentales en Physique et en Astrophysique, Université de Liège, Allée du 6 Août 17, bâtiment B5a, B-4000 Liège, Belgium. Igor.Ivanov@ulg.ac.be

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 28, 2009
PubMed
Summary

We present a geometric method to analyze the complex Ginzburg-Landau model with multiple order parameters. This approach simplifies studying its minima, symmetries, and phase diagrams in condensed matter physics.

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Area of Science:

  • Condensed Matter Physics
  • Theoretical Physics
  • Mathematical Physics

Background:

  • The Ginzburg-Landau model is crucial for understanding phase transitions in condensed matter systems.
  • The general U(1)-symmetric Landau potential, even for scalar order parameters, involves 13 coefficients, complicating direct minimization.
  • Existing algebraic methods struggle with minimizing complex Landau potentials.

Purpose of the Study:

  • To develop a novel geometric approach for analyzing the Ginzburg-Landau model with two-order parameters.
  • To overcome the computational challenges associated with minimizing complex Landau potentials.
  • To provide a framework for studying the model's properties without explicit minimization.

Main Methods:

  • Development of a geometric analysis technique.
  • Application of the geometric approach to the U(1)-symmetric Landau potential.
  • Systematic classification of model properties based on geometric insights.

Main Results:

  • Determination of the number of minima for the Ginzburg-Landau potential.
  • Classification of possible symmetries within the model.
  • Identification of conditions and mechanisms for spontaneous symmetry breaking.
  • Explicit description of the model's phase diagram.

Conclusions:

  • The geometric approach offers a powerful alternative to direct algebraic minimization for complex Ginzburg-Landau models.
  • This method facilitates a deeper understanding of symmetry breaking and phase transitions in condensed matter.
  • The findings provide a comprehensive framework for analyzing diverse condensed-matter phenomena described by this model.