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¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

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The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene...
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¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

1.4K
Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
1.4K
Limitations of Friedel–Crafts Reactions01:26

Limitations of Friedel–Crafts Reactions

6.7K
Several restrictions limit the use of Friedel–Crafts reactions. First, the halogen in the alkyl halide must be attached to an sp3-hybridized carbon for the Friedel–Crafts reactions to occur. Vinyl or aryl halides do not react since the carbocations formed are unstable under the reaction conditions. Second, Friedel–Crafts alkylation is susceptible to carbocation rearrangement, and the major products obtained have a rearranged carbon skeleton. In contrast, the acylium ion is...
6.7K
Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

1.4K
Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
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Coupled Reactions01:17

Coupled Reactions

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Cellular processes such as building and breaking down complex molecules occur through stepwise chemical reactions. Some of these chemical reactions are spontaneous and release energy, whereas others require energy to proceed. Cells often couple the energy-releasing reaction with the energy-requiring one to carry out important cell functions. 
Energy in adenosine triphosphate or ATP molecules is easily accessible to do work. ATP powers the majority of energy-requiring cellular reactions....
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Fundamental Mathematical Principles in Pharmacokinetics: Rate and Order of Reaction01:15

Fundamental Mathematical Principles in Pharmacokinetics: Rate and Order of Reaction

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In pharmacokinetics, the rates and order of reactions play a crucial role in understanding how the body processes drugs and help us comprehend drug absorption, distribution, metabolism, and elimination. A critical concept in pharmacokinetics is the rate constant, which quantifies the speed of a reaction. It provides valuable information about the kinetics of drug elimination. The rate constant allows us to determine the rate at which drugs are eliminated from the body.
Pharmacokinetic reactions...
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Updated: Jan 8, 2026

Setting Limits on Supersymmetry Using Simplified Models
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Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

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Grandes órdenes y límite de acoplamiento fuerte en la renormalización funcional

Mikhail N Semeikin1, Kay Jörg Wiese1

  • 1Sorbonne Université, ENS, PSL, Laboratoire de Physique de l'Ecole Normale Supérieure, CNRS-, Université Paris Cité, 24 rue Lhomond, 75005 Paris, France.

Physical review. E
|December 23, 2025
PubMed
Resumen
Este resumen es generado por máquina.

Establecemos la sumabilidad de Borel para el grupo de renormalización funcional (FRG) en cero dimensiones. En el límite de acoplamiento fuerte, los desórdenes microscópicos fluyen hacia un punto fijo universal, relevante para sistemas elásticos.

Palabras clave:
grupo de renormalización funcionalsumabilidad de Borelpuntos fijos universalessistemas desordenadossistemas elásticoslímite de acoplamiento fuerte

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Área de la Ciencia:

  • Física Teórica
  • Física de la Materia Condensada

Sus antecedentes:

  • El grupo de renormalización funcional (FRG) es una herramienta poderosa para estudiar teorías cuánticas de campos.
  • Comprender el comportamiento de orden superior de FRG es crucial para su aplicación confiable.
  • Los sistemas desordenados, en particular los sistemas elásticos, presentan desafíos teóricos significativos.

Objetivo del estudio:

  • Investigar el comportamiento de orden superior del grupo de renormalización funcional (FRG).
  • Establecer condiciones para la sumabilidad de Borel en un modelo de dimensión cero.
  • Analizar el flujo de desórdenes microscópicos en el límite de acoplamiento fuerte.

Principales métodos:

  • Análisis matemático de las ecuaciones FRG.
  • Aplicación de técnicas de sumación de Borel.
  • Representación integral de contorno de las derivadas y series FRG.
  • Investigación del límite de acoplamiento fuerte.

Principales resultados:

  • Se establece la sumabilidad de Borel para un amplio rango de acoplamientos microscópicos en un modelo de dimensión cero.
  • La transformada de Borel y la serie FRG original se expresan como integrales.
  • Se demuestra que todos los desórdenes microscópicos de corto alcance fluyen hacia el mismo punto fijo universal en el límite de acoplamiento fuerte.

Conclusiones:

  • El estudio proporciona un marco matemático riguroso para FRG en presencia de desorden.
  • El punto fijo universal identificado ofrece información sobre el comportamiento de los sistemas elásticos desordenados.
  • Estos hallazgos avanzan la aplicabilidad de FRG a fenómenos físicos complejos.