Lagrangian Formalism in Perturbed Nonlinear Klein-Gordon Equations

We develop an alternative approach to study the effect of the generic perturbation (in addition to explicitly considering the loss term) in the nonlinear Klein-Gordon equations. By a change of the variables that cancel the dissipation term we are able to write the Lagrangian density and then, calculate the Lagrangian as a function of collective variables. We use the Lagrangian formalism together with the Rice {\it Ansatz} to derive the equations of motion of the collective coordinates (CCs) for the perturbed sine-Gordon (sG) and $\phi^{4}$ systems. For the $N$ collective coordinates, regardless of the {\it Ansatz} used, we show that, for the nonlinear Klein-Gordon equations, this approach is equivalent to the {\it Generalized Traveling Wave Ansatz} ({\it GTWA})Comment: 9 page

ac driven sine-Gordon solitons: dynamics and stability

The ac driven sine-Gordon equation is studied analytically and numerically, with the aim of providing a full description of how soliton solutions behave. To date, there is much controversy about when ac driven dc motion is possible. Our work shows that kink solitons exhibit dc or oscillatory motion depending on the relation between their initial velocity and the force parameters. Such motion is proven to be impossible in the presence of damping terms. For breathers, the force amplitude range for which they exist when dissipation is absent is found. All the analytical results are compared with numerical simulations, which in addition exhibit no dc motion at all for breathers, and an excellent agreement is found. In the conclusion, the generality of our results and connections to others systems for which a similar phenomenology may arise are discussed.Comment: 10 pages, latex, PostScript figures included with epsfig, to appear in European Physical Journal B, see GISC homepage at http://valbuena.fis.ucm.es/ for related wor

AuNx stabilization with interstitial nitrogen atoms: A Density Functional Theory Study

Researchers have been studying 4d and 5d Series Transition Metal Nitrides lately as a result of the experimental production of AuN, PtN, CuN. In this paper, we used the Density Functional Theory (DFT) implementing a pseudopotential plane-wave method to study the incorporation of nitrogen atoms in the face-centered cube (fcc) lattice of gold (Au). First, we took the fcc structure of gold, and gradually located the nitrogen atoms in tetrahedral (TH) and octahedral (OH) interstitial sites. AuN stabilized in: 2OH (30%), 4OH and 4TH (50%), 4OH - 2TH (close to the wurtzite structure) and 6TH (60%). This leads us to think that AuN behaves like a Transition Metal Nitride since the nitrogen atoms look for tetrahedral sites. © Published under licence by IOP Publishing Ltd

Obtaining Au thin films in atmosphere of reactive nitrogen through magnetron sputtering

4d and 5d series of the transition metals are used to the obtaining nitrides metallic, due to the synthesis of PtN, AgN and AuN in the last years. Different nitrides are obtained in the Plasma Assisted Physics Vapour Deposition system, due to its ionization energy which is necessary for their formation. In this paper a Magnetron Sputtering system was used to obtain Au thin films on Si wafers in Nitrogen atmosphere. The substrate temperature was varied between 500 to 950°C. The samples obtained at high temperatures (>500°C) show Au, Si and N elements, as it is corroborated in the narrow spectrum obtained for X-Ray Photoelectron Spectroscopy; besides the competition of orientation crystallographic texture between (111) and (311) directions was present in the X-Ray Diffraction analysis to the sample heated at 950°C

Non-sinusoidal current and current reversals in a gating ratchet

In this work, the ratchet dynamics of Brownian particles driven by an external sinusoidal (harmonic) force is investigated. The gating ratchet effect is observed when another harmonic is used to modulate the spatially symmetric potential in which the particles move. For small amplitudes of the harmonics, it is shown that the current (average velocity) of particles exhibits a sinusoidal shape as a function of a precise combination of the phases of both harmonics. By increasing the amplitudes of the harmonics beyond the small-limit regime, departures from the sinusoidal behavior are observed and current reversals can also be induced. These current reversals persist even for the overdamped dynamics of the particles.Comment: 11 pages, 9 figure

Reply to Comment on "Existence of Internal Modes of sine-Gordon Kinks"

In this reply to the comment by C. R. Willis, we show, by quoting his own statements, that the simulations reported in his original work with Boesch [Phys. Rev. B 42, 2290 (1990)] were done for kinks with nonzero initial velocity, in contrast to what Willis claims in his comment. We further show that his alleged proof, which assumes among other approximations that kinks are initially at rest, is not rigorous but an approximation. Moreover, there are other serious misconceptions which we discuss in our reply. As a consequence, our result that quasimodes do not exist in the sG equation [Phys. Rev. E 62, R60 (2000)] remains true.Comment: Reply to a comment by C. R. Willis on Phys. Rev. E 62, R60 (2000), to appear in Physical Review

Exact stationary solutions of the parametrically driven and damped nonlinear Dirac equation

Two exact stationary soliton solutions are found in the parametrically driven and damped nonlinear Dirac equation. The parametric force considered is a complex ac force. The solutions appear when their frequencies are locked to half the frequency of the parametric force, and their phases satisfy certain conditions depending on the force amplitude and on the damping coe cient. Explicit expressions for the charge, the energy, and the momentum of these solutions are provided. Their stability is studied via a variational method using an ansatz with only two collective coordinates. Numerical simulations con rm that one of the solutions is stable, while the other is an unstable saddle point. Consequently, the stabilization of damped Dirac solitons can be achieved via time-periodic parametric excitations.Junta de Andalucía and Ministerio de Economía y Competitividad of Spain FIS2017-89349-PMinisterio de Ciencia, Innovación y Universidades of Spain PGC2018-093998-BI0

Anomalies of ac driven solitary waves with internal modes: Nonparametric resonances induced by parametric forces

We study the dynamics of kinks in the $\phi^4$ model subjected to a parametric ac force, both with and without damping, as a paradigm of solitary waves with internal modes. By using a collective coordinate approach, we find that the parametric force has a non-parametric effect on the kink motion. Specifically, we find that the internal mode leads to a resonance for frequencies of the parametric driving close to its own frequency, in which case the energy of the system grows as well as the width of the kink. These predictions of the collective coordinate theory are verified by numerical simulations of the full partial differential equation. We finally compare this kind of resonance with that obtained for non-parametric ac forces and conclude that the effect of ac drivings on solitary waves with internal modes is exactly the opposite of their character in the partial differential equation.Comment: To appear in Phys Rev