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Related Concept Videos

Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

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In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
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Entropy Changes Accompanying Specific Processes01:21

Entropy Changes Accompanying Specific Processes

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Entropy, a measure of disorder in a system, changes during phase transitions like freezing or boiling. At the transition temperature Ttrs, where two phases are in equilibrium, the phase transition is a reversible process. The entropy change can be calculated from a substance's enthalpy of transition using the equation ΔStrs = ΔtrsH /Ttrs.When a perfect gas expands isothermally from one volume to another, entropy increases logarithmically with volume. Conversely, isothermal compression...
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Basic Discrete Time Signals01:16

Basic Discrete Time Signals

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The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is...
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Limits with Oscillating Discontinuities01:19

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An oscillating discontinuity is a type of discontinuity in which a function’s values fluctuate infinitely often as the input approaches a particular point. Unlike jump discontinuities, where the function suddenly shifts between two values, or infinite discontinuities, where the function diverges without bound, an oscillating discontinuity arises from rapid back-and-forth variation. Because the function never stabilizes toward a single value, no finite limit exists at that point.One of the...
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Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

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In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis.
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Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

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The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
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Related Experiment Video

Updated: Apr 29, 2026

A Simple Stimulatory Device for Evoking Point-like Tactile Stimuli: A Searchlight for LFP to Spike Transitions
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Bursting transition in a linear self-exciting point process.

Tomokatsu Onaga1, Shigeru Shinomoto1

  • 1Department of Physics, Kyoto University, Kyoto 606-8502, Japan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 16, 2014
PubMed
Summary

Self-exciting point processes show bursts due to event facilitation. A critical transition point, independent of excitation profile, governs this bursting behavior in complex systems.

Area of Science:

  • * Statistical Physics
  • * Network Science
  • * Dynamical Systems

Background:

  • * Self-exciting point processes model event sequences where past events influence future occurrences.
  • * These processes are relevant to phenomena like epidemics and human activity patterns.
  • * Increased excitability can lead to spontaneous bursting behavior.

Purpose of the Study:

  • * To identify the critical threshold for bursting in self-exciting point processes.
  • * To investigate the role of the average number of events per event.
  • * To extend the theory to multidimensional processes for network analysis.

Main Methods:

  • * Theoretical analysis of self-exciting point processes.
  • * Derivation of the transition condition for bursting.

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  • * Extension of the model to multidimensional and network contexts.

    • Main Results:

    • * The transition to bursting is determined by a universal constant (1 - 1/√2 ≈ 0.2929).
    • * This critical value is independent of the specific temporal excitation profile.
    • * The theory was extended to multidimensional processes, enabling control over network bursting.

    Conclusions:

    • * A fundamental threshold governs bursting in self-exciting point processes.
    • * The findings offer insights into emergent behaviors in complex systems.
    • * The multidimensional extension provides tools for manipulating network dynamics.