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Abstract This article presents the displacement field produced by a point force acting on an athermal random fiber network (the Green function for the network). The problem is defined within the limits of linear elasticity and the field is obtained numerically for nonaffine networks characterized by various parameter sets. The classical Green function solution applies at distances from the point force larger than a threshold which is independent of the network parameters in the range studied. At smaller distances, the nonlocal nature of fiber interactions modifies the solution.

Abstract The anti-trigonometric function is used to strictly solve the uniaxial anisotropic Stoner-Wohlfarth (SW) model, which can obtain the relation of the angle α (θ) between the magnetization (the anisotropy field) and the applied magnetic field. Using this analytic solution, the hysteresis loops of uniaxial anisotropic SW particles magnetized in typical directions could be numerically calculated. Then, the hysteresis loops are obtained in randomly distributed SW particle ensembles while ignoring the dipole interaction among them with the analytic solution. Finally, the correctness of the analytic solution is verified by the exact solutions of remanence, switching field, and coercivity from SW model. The analytic solution provides an important reference for understanding the magnetizing and magnetization reversal processes of magnetic materials.

In this paper, we obtain the stationary elliptic- and hyperbolic-function solutions of the nonlocal reverse-time and reverse-space-time nonlinear Schrödinger (NLS) equations based on their connection with the standard Weierstrass elliptic equation. The reverse-time NLS equation possesses the bounded dn-, cn-, sn-, sech-, and tanh-function solutions. Of special interest, the tanh-function solution can display both the dark- and antidark-soliton profiles. The reverse-space-time NLS equation admits the general Jacobian elliptic-function solutions (which are exponentially growing at one infinity or display the periodical oscillation in x), the bounded dn- and cn-function solutions, as well as the K-shifted dn- and sn-function solutions. At the degeneration, the hyperbolic-function solutions may exhibit an exponential growth behavior at one infinity, or show the gray- and bright-soliton profiles.

AbstractIn this paper, by using Fokas method, we study the initial-boundary value problems (IBVPs) of the fourth-order dispersive nonlinear Schrödinger (FODNLS) equation on the half-line, which can simulate the nonlinear transmission and interaction of ultrashort pulses in the high-speed optical fiber transmission system, and can also describe the nonlinear spin excitation phenomenon of one-dimensional Heisenberg ferromagnetic chain with eight poles and dipole interaction. By discussing the eigenfunctions of Lax pair of FODNLS equation and analyzing symmetry of the scattering matrix, we get a matrix Riemann–Hilbert (RH) problem from for the IBVPs of FODNLS equation. Moreover, we get the potential function solution u(x, t) of the FODNLS equation by solving this matrix RH problem. In addition, we also obtain that some spectral functions satisfy an important global relation.

In this paper, we first construct a symplectic Schur function solution to a newly defined two-component symplectic Kadomtsev–Petviashvili hierarchy. As a generalization of a two-component symplectic Schur function, we construct two-component symplectic universal characters which satisfy quadratic equations in an infinite-dimensional integrable dynamic system called a two-component symplectic universal character hierarchy. Then, we define a modified symplectic universal character hierarchy whose tau function can be represented by free fermions in Clifford algebras.

The Dirac delta function is a function that mathematically does not meet the criteria as a function, this is because the function has an infinite value at a point. However, in physics the Dirac Delta function is an important construction, one of which is in constructing the Green function. This research constructs the Green function by utilizing the Dirac Delta function and Green identity. Furthermore, the construction is directed at the Green function of the Poisson's equation which is equipped with the Dirichlet boundary condition. After the form of the Green function solution from the Poisson's equation is obtained, the Green function is determined by means of the expansion of the eigen functions in the Poisson's equation. These results are used to analyze the application of the Poisson equation in electrostatic.

<p>New heat flow measurements collected throughout the Auka and JaichMaa Ja' ag' hydrothermal vent fields in the central graben of the Southern Pescadero Basin, southern Gulf of California, indicate that upflow of hydrothermal fluids associated with active rifting dissipate heat in excess of 10 W/m<sup>2</sup> around faults that have a few tens-of-meters of displacement. Heat flow anomalies slowly decay to background values of ~2 W/m<sup>2</sup> at distances of ~1 km from these faults following an inverse square-root distance law. We develop a physical model of the Auka vent field based on the fundamental Green's function solution of the heat equation. The model includes the effects of circulation in the porous networks of faults and the lateral seepage of geothermal brines through the fault walls to surrounding hemipelagic sediments.  We use an optimal fitting method to estimate the reservoir depth, permeability, and circulation rate. Our model indicates the heat source is at a depth of ~5.7 km; permeability and flow rates in the fracture system are ~10<sup>-14</sup> m<sup>2</sup> and 10<sup>-7</sup> m/s, respectively, and ~10<sup>-16</sup> m<sup>2</sup> and 10<sup>-8</sup> m/s in the basin aquitards, respectively. Model scaling laws point to the importance of faults in controlling sediment-hosted vent fields and slow circulation throughout low permeability sediments in controlling the brine's chemistry. Although the fault model seems appropriate and straightforward for the Pescadero vents, it does seem to be the exception to the other known sediment-hosted vent fields in the Pacific.</p>