 Award ID(s):
 1907620
 Publication Date:
 NSFPAR ID:
 10285198
 Journal Name:
 Applicable Analysis
 Page Range or eLocationID:
 1 to 20
 ISSN:
 00036811
 Sponsoring Org:
 National Science Foundation
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The dynamics of initially truncated and bent line solitons for the Kadomtsev–Petviashvili (KPII) equation modelling internal and surface gravity waves is analysed using modulation theory. In contrast to previous studies on obliquely interacting solitons that develop from acute incidence angles, this work focuses on initial value problems for the obtuse incidence of two or three partial line solitons, which propagate away from one another. Despite counterpropagation, significant residual soliton interactions are observed with novel physical consequences. The initial value problem for a truncated line soliton – describing the emergence of a quasionedimensional soliton from a wide channel – is shown to be related to the interaction of oblique solitons. Analytical descriptions for the development of weak and strong interactions are obtained in terms of interacting simple wave solutions of modulation equations for the local soliton amplitude and slope. In the weak interaction case, the longtime evolution of truncated and large obtuse angle solitons exhibits a decaying, parabolic wave profile with temporally increasing focal length that asymptotes to a cylindrical Korteweg–de Vries soliton. In contrast, the strong interaction case of slightly obtuse interacting solitons evolves into a steady, onedimensional line soliton with amplitude reduced by an amount proportional to the incidencemore »

Twodimensional materials composed of transition metal carbides and nitrides (MXenes) are poised to revolutionize energy conversion and storage. In this work, we used density functional theory (DFT) to investigate the adsorption of Mg and Na adatoms on five M 2 CS 2 monolayers (where M = Mo, Nb, Ti, V, and Zr) for battery applications. We assessed the stability of the adatom ( i.e. Na and Mg)monolayer systems by calculating adsorption and formation energies, as well as voltages as a function of surface coverage. For instance, we found that Mo 2 CS 2 cannot support a full layer of Na nor even a single Mg atom. Na and Mg exhibit the strongest binding on Zr 2 CS 2 , followed by Ti 2 CS 2 , Nb 2 CS 2 and V 2 CS 2 . Using the nudged elastic band method (NEB), we computed promising diffusion barriers for both dilute and nearly full ion surface coverage cases. In the dilute ion adsorption case, a single Mg and Na atom on Ti 2 CS 2 experience ∼0.47 eV and ∼0.10 eV diffusion barriers between the lowest energy sites, respectively. For a nearly full surface coverage, a Na ion moving onmore »

A compact Green's function for general dispersive anisotropic poroelastic media in a fullfrequency regime is presented for the first time. First, starting in a frequency domain, the anisotropic dispersion is exactly incorporated into the constitutive relationship, thus avoiding fractional derivatives in a time domain. Then, based on the Radon transform, the original threedimensional differential equation is effectively reduced to a onedimensional system in space. Furthermore, inspired by the strategy adopted in the characteristic analysis of hyperbolic equations, the eigenvector diagonalization method is applied to decouple the onedimensional vector problem into several independent scalar equations. Consequently, the fundamental solutions are easily obtained. A further derivation shows that Green's function can be decomposed into circumferential and spherical integrals, corresponding to static and transient responses, respectively. The procedures shown in this study are also compatible with other pertinent multiphysics coupling problems, such as piezoelectric, magnetoelectroelastic and thermoelastic materials. Finally, the verifications and validations with existing analytical solutions and numerical solvers corroborate the correctness of the proposed Green's function.

We consider the time evolution in two spatial dimensions of a double vorticity layer consisting of two contiguous, infinite material fluid strips, each with uniform but generally differing vorticity, embedded in an otherwise infinite, irrotational, inviscid incompressible fluid. The potential application is to the wake dynamics formed by two boundary layers separating from a splitter plate. A thinlayer approximation is constructed where each layer thickness, measured normal to the common centre curve, is small in comparison with the local radius of curvature of the centre curve. The threecurve equations of contour dynamics that fully describe the doublelayer dynamics are expanded in the small thickness parameter. At leading order, closed nonlinear initialvalue evolution equations are obtained that describe the motion of the centre curve together with the time and spatial variation of each layer thickness. In the special case where the layer vorticities are equal, these equations reduce to the singlelayer equation of Moore ( Stud. Appl. Math. , vol. 58, 1978, pp. 119–140). Analysis of the linear stability of the firstorder equations to smallamplitude perturbations shows Kelvin–Helmholtz instability when the farfield fluid velocities on either side of the double layer are unequal. Equal velocities define a circulationfree double vorticity layer,more »

Abstract The complete physical understanding of the optimization of the thermodynamic work still is an important open problem in stochastic thermodynamics. We address this issue using the Hamiltonian approach of linear response theory in finite time and weak processes. We derive the Euler–Lagrange equation associated and discuss its main features, illustrating them using the paradigmatic example of driven Brownian motion in overdamped regime. We show that the optimal protocols obtained either coincide, in the appropriate limit, with the exact solutions by stochastic thermodynamics or can be even identical to them, presenting the wellknown jumps. However, our approach reveals that jumps at the extremities of the process are a good optimization strategy in the regime of fast but weak processes for any driven system. Additionally, we show that fastbutweak optimal protocols are timereversal symmetric, a property that has until now remained hidden in the exact solutions far from equilibrium.