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Related Concept Videos

The Delta-to-Delta Circuit01:17

The Delta-to-Delta Circuit

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In a delta-delta configuration, the source and the load are connected in a delta manner, forming a closed loop that divides the network into three distinct phases. This configuration makes the phase voltages identical to line voltages. Assuming the sources are in positive sequence, the phase voltages can be expressed directly without having a neutral wire.
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The distribution law or Nernst's distribution law is the law that governs the distribution of a solute between two immiscible solvents. This law, also known as the partition law, states that if a solute is added to the mixture of two immiscible solvents at a constant temperature, the solute is distributed between the two solvents in such a way that the ratio of solute concentrations in the solvents remains constant at equilibrium.
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One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

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This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
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The Y-to-Delta Circuit01:19

The Y-to-Delta Circuit

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A balanced wye-to-delta circuit comprises balanced Y-connected voltage sources and delta-connected loads with no neutral line connection.
The initial step in analyzing a wye-to-delta circuit is to assume a positive phase sequence. These phase voltages are then utilized to calculate the line voltages that occur directly across the delta-connected load impedances. Van, Vbn, and Vcn are the phase voltages in wye, and Vab, Vbc, and Vca are the line voltages for a delta circuit. The relation between...
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Aminoglycosides are a class of antibiotics used to treat various bacterial infections. Clinicians must determine the elimination rate constant (k) and volume of distribution (VD) to optimize therapeutic efficacy and minimize toxicity. The k value represents the rate at which the drug is removed from the body, and the VD reflects the degree to which the drug distributes into body tissues. Accurately estimating these parameters allows healthcare professionals to tailor drug dosing to individual...
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One-Compartment Open Model for IV Bolus Administration: Estimation of Elimination Rate Constant, Half-Life and Volume of Distribution01:09

One-Compartment Open Model for IV Bolus Administration: Estimation of Elimination Rate Constant, Half-Life and Volume of Distribution

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The one-compartment open model is a simplified approach used in pharmacokinetics to understand the distribution and elimination of a drug administered through an intravenous bolus. This model assumes rapid drug dispersal throughout the body and elimination using a first-order process. Key pharmacokinetic parameters, such as the elimination rate constant (k), half-life (t1/2), and the apparent volume of distribution (Vd), can be estimated from this model. The elimination rate is calculated...
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Related Experiment Video

Updated: Nov 27, 2025

Kinetic Analysis of Vasculogenesis Quantifies Dynamics of Vasculogenesis and Angiogenesis In Vitro
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Berry phases in the reconstructed KdV equation.

Blagoje Oblak1, Gregory Kozyreff2

  • 1Laboratoire de Physique Théorique et Hautes Energies, Sorbonne Université and CNRS UMR 7589, F-75005 Paris, France.

Chaos (Woodbury, N.Y.)
|December 2, 2020
PubMed
Summary

The KdV equation

Area of Science:

  • Nonlinear dynamics
  • Mathematical physics
  • Fluid mechanics

Background:

  • The Korteweg-de Vries (KdV) equation describes nonlinear wave phenomena.
  • Lie-Poisson reconstruction offers a fluid particle dynamics perspective.
  • Periodic waves on a circle exhibit complex iterated map dynamics.

Purpose of the Study:

  • To investigate the geometric origin of drift velocity in the KdV equation's reconstructed motion.
  • To analyze the contributions of dynamical, Berry, and anomalous phases.
  • To explore phenomena like orbital bifurcations in cnoidal wave solutions.

Main Methods:

  • Lie-Poisson reconstruction of the KdV equation.
  • Analysis of iterated maps and Poincaré rotation numbers.
  • Derivation of a uniformizing map for cnoidal waves.

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  • Investigation of Virasoro group structure implications.

    • Main Results:

    • Drift velocity is a sum of dynamical, Berry, and anomalous phases.
    • Berry and anomalous phases stem from Virasoro group structure.
    • Cnoidal waves allow closed-form evaluation of phases via a derived uniformizing map.
    • Orbital bifurcations occur in a resonance wedge of the cnoidal parameter space.

    Conclusions:

    • The drift velocity in the KdV equation has a universal geometric origin.
    • Virasoro group structure dictates Berry and anomalous phases.
    • Cnoidal waves provide a tractable model for studying these phase contributions and associated bifurcations.