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Continuity equation for the flow of Fisher information in wave scattering
Using waves to explore our environment is a widely used paradigm, ranging from seismology to radar technology, and from biomedical imaging to...
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Cosmology with modified continuity equation in asymptotically safe gravity
We study FLRW cosmology, taking into account quantum gravitational corrections in the formalism of the exact renormalization group flow of the...
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Solution of Schrödinger Equation: Boundary and Continuity Conditions in Coordinate Representation
In this chapter, it is shown in general how boundary and continuity conditions lead to eigen solutions: discrete for localized and continuous for...
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Changes in Residual Stresses in the Vicinity of a Continuity Defect in an Elastoviscoplastic Material under Repeated Loading
AbstractThe results of calculations of the stress-strain states of an elastoplastic material containing a single cylindrical continuity defect and...
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Comparison of continuity equation and Gaussian mixture model for long-term density propagation using semi-analytical methods
This paper compares the continuum evolution for density equation modelling and the Gaussian mixture model on the 2D phase space long-term density...
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Close-to-optimal continuity bound for the von Neumann entropy and other quasi-classical applications of the Alicki–Fannes–Winter technique
We consider a quasi-classical version of the Alicki–Fannes–Winter technique widely used for quantitative continuity analysis of characteristics of...
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Reguera and Rubi Kinetic Equation
This chapter is devoted to the in-depth study of the mesoscopic non-equilibrium thermodynamics theory in the presence of entropic barriers, as well...
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The Adjoint Transport Equation—The Equation of Neutron Importance
Consideration will be given to the equation which is adjoint to the neutron transport equation. The solutions to an adjoint equation will be seen to...
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The Klein–Gordon Equation
From the early works on the constitution of the atom made by pioneers like A. Sommerfeld[aut]Sommerfeld, Arnold Johannes Wilhelm, the need to...
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Relativistic Boltzmann Equation
The special and general relativistic generalizations of the Boltzmann equation are considered as well as the methods to solve this equation—the...
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The Dirac equation as a linear tensor equation for one component
The Dirac equation is one of the most fundamental equations of modern physics. It is a spinor equation, but some tensor equivalents of the equation...
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Quaternion Klein–Gordon equation in the electromagnetic field
A pure quaternionic Klein–Gordon equation is developed in terms of quaternion operators and wave functions. The equivalence between quaternion and...
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Schrödinger’s Equation
This chapter develops Schrödinger’s equation, the fundamental law of quantum physics. Schrödinger’s equation is a type of “wave” equation, so this...
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Lipschitz Continuity of Solutions to Drift-Diffusion Equations in the Presence of Nonlocal Terms
We analyze the propagation of Lipschitz continuity of solutions to various linear and nonlinear drift-diffusion systems, with and without...
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Solution of the Diffusion Equation in Free Space
In this chapter, we focus on solving the diffusion equation under no spatial constraints, that is, in free space, to find a unique solution that will...
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A Non-local Quasi-Equilibrium State in the Bhatnagar–Gross–Krook Boltzmann Equation for Thermo-hydrodynamics: Conservation Laws, The Boltzmann H-Theorem, and the Fluctuation-Dissipation Theorem
The Bhatnagar–Gross–Krook (BGK) Boltzmann equation with the Maxwellian–Boltzmann-type equilibrium state leads to the set of thermo-hydrodynamic...
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Investigation of Brownian motion in stochastic Schrödinger wave equation using the modified generalized Riccati equation map** method
This work investigates the stochastic nonlinear Schrödinger equation in a more extended form, influenced by multiplicative noise which represents the...
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Nowhere-Uniform Continuity of the Data-to-Solution Map for the Two-Component Fornberg–Whitham
In this paper, we present a new method to prove that the data-to-solution map for the two-component Fornberg–Whitham is not uniformly continuous from...