Journal of Mathematical Physics

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ISSN / EISSN : 0022-2488 / 1089-7658
Published by: AIP Publishing (10.1063)
Total articles ≅ 24,840
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Journal of Mathematical Physics, Volume 63; https://doi.org/10.1063/5.0088228

Abstract:
In loop quantum gravity, states of quantum geometry are represented by classes of knotted graphs, equivalent under diffeomorphisms. Thus, it is worthwhile to enumerate and distinguish these classes. This paper looks at the case of 4-regular graphs, which have an interpretation as objects dual to triangulations of three-dimensional manifolds. Two different polynomial invariants are developed to characterize these graphs—one inspired by the Kauffman bracket relations and the other based on quandles. How the latter invariant changes under the Pachner moves acting on the graphs is then studied.
Wen-Shuo Yuan, Bin Ge
Journal of Mathematical Physics, Volume 63; https://doi.org/10.1063/5.0077842

Abstract:
The main goal of this work is to investigate the initial boundary value problem for a class of pseudo-parabolic p-Laplacian equations with singular potential and logarithmic nonlinearity. First of all, we prove the local existence of weak solutions. Second, we show the existence of the global solution and the weak solution converging to the stationary solution when the time tends to infinity, and we show blow-up phenomena of solutions with the initial energy less than the mountain pass level d by using the potential well method. Finally, we parallelly stretch all the conclusions for the subcritical case to the critical case.
, Martin Fraas, Jürg Fröhlich
Journal of Mathematical Physics, Volume 63; https://doi.org/10.1063/5.0088668

Abstract:
The appearance of tracks, close to classical orbits, left by charged quantum particles propagating inside a detector, such as a cavity periodically illuminated by light pulses, is studied for a family of idealized models. In the semi-classical regime, which is reached when one considers highly energetic particles, we present a detailed, mathematically rigorous analysis of this phenomenon. If the Hamiltonian of the particles is quadratic in position- and momentum operators, as in the examples of a freely moving particle or a particle in a homogeneous external magnetic field, we show how symmetries, such as spherical symmetry, of the initial state of a particle are broken by tracks consisting of infinitely many approximately measured particle positions and how, in the classical limit, the initial position and velocity of a classical particle trajectory can be reconstructed from the observed particle track.
Yang Liu, Shan Ma,
Journal of Mathematical Physics, Volume 63; https://doi.org/10.1063/5.0057973

Abstract:
In this paper, we use the method of evolutionary systems introduced by Cheskidov and Foias to describe the existence of global attractor for 2D incompressible Navier–Stokes flow coupled with time-dependent Darcy flow. Furthermore, stationary statistical solutions of this system are constructed from the global attractor.
Sohail A. Khan, T. Hayat, A. Alsaedi, B. Ahmad
Journal of Mathematical Physics, Volume 63; https://doi.org/10.1063/5.0067167

Abstract:
Here, we investigate magnetohydrodynamic flow of an incompressible Reiner–Philippoff fluid over a stretched surface. The stretching property of the sheet induced flow. Joule heating and dissipation effects are considered in energy communication. The energy equation is developed through the first law of thermodynamics. Irreversibility analysis is constructed. Furthermore, the first-order chemical reaction is also accounted. Adequate transformation is used to get the ordinary differential system tackled through a local non-similar technique via the built-in Matlab function bvp4c. Prominent characteristics of flow parameters on the entropy rate, temperature, velocity, and concentration are studied. Thermal and solutal transport rates are studied. Reverse impacts for velocity and temperature are noted for the Reiner–Philippoff liquid parameter. Reduction in velocity is seen for the Bingham number. A larger Prandtl number reduces temperature distribution. Concentration is decreased for both the Lewis number and chemical reaction parameter. A reverse trend is observed for the entropy rate against Brinkman and Bingham numbers. A larger magnetic variable enhances entropy generation.
Journal of Mathematical Physics, Volume 63; https://doi.org/10.1063/5.0065739

Abstract:
In this paper, we consider the restricted four-body problem on S2 and the restricted three-body problem on H2. In the first case, the primary particles are considered to be rotating around the vertical axis. In the latter case, the primaries move at a hyperbolic relative equilibrium. If the primary particles locate at height z0 = 0 and they form an isosceles triangle on S2, then the number of symmetric equilibrium points of the restricted four-body problem depends on the angular velocity, the configuration, and the masses of the primaries. For this case, the number of equilibrium points is 0, 2, 4, 6, or 8. If the primaries are at height z0 ∈ (0, 1), then the primaries form an equilateral triangle and the number of symmetric equilibrium points is 8, 11, 14, 17, or 20. The number depends on the position of the primaries, and it is higher than the previous case due to the higher number of symmetry axes of the triangle formed by the primaries. On the other hand, for the restricted three-body problem on H2, the number of equilibrium points is 3, considering that the primaries move at a hyperbolic relative equilibrium. We analyzed the general (non-symmetric) case, showing the locations of the equilibrium points for the given positions of the primaries. We also studied the stability of these equilibrium points.
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