Collective Coordinates Theory for Discrete Soliton Ratchets in the sine-Gordon Model

A collective coordinate theory is develop for soliton ratchets in the damped discrete sine-Gordon model driven by a biharmonic force. An ansatz with two collective coordinates, namely the center and the width of the soliton, is assumed as an approximated solution of the discrete non-linear equation. The evolution of these two collective coordinates, obtained by means of the Generalized Travelling Wave Method, explains the mechanism underlying the soliton ratchet and captures qualitatively all the main features of this phenomenon. The theory accounts for the existence of a non-zero depinning threshold, the non-sinusoidal behaviour of the average velocity as a function of the difference phase between the harmonics of the driver, the non-monotonic dependence of the average velocity on the damping and the existence of non-transporting regimes beyond the depinning threshold. In particular it provides a good description of the intriguing and complex pattern of subspaces corresponding to different dynamical regimes in parameter space

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

Soliton ratchets in homogeneous nonlinear Klein-Gordon systems

We study in detail the ratchet-like dynamics of topological solitons in homogeneous nonlinear Klein-Gordon systems driven by a bi-harmonic force. By using a collective coordinate approach with two degrees of freedom, namely the center of the soliton, $X(t)$, and its width, $l(t)$, we show, first, that energy is inhomogeneously pumped into the system, generating as result a directed motion; and, second, that the breaking of the time shift symmetry gives rise to a resonance mechanism that takes place whenever the width $l(t)$ oscillates with at least one frequency of the external ac force. In addition, we show that for the appearance of soliton ratchets, it is also necesary to break the time-reversal symmetry. We analyze in detail the effects of dissipation in the system, calculating the average velocity of the soliton as a function of the ac force and the damping. We find current reversal phenomena depending on the parameter choice and discuss the important role played by the phases of the ac force. Our analytical calculations are confirmed by numerical simulations of the full partial differential equations of the sine-Gordon and $\phi^4$ systems, which are seen to exhibit the same qualitative behavior. Our results are in agreement with recent experimental work on dissipation induced symmetry breaking.Comment: Minor corrections, several references added, accepted for publication in Chao

Internal mode mechanism for collective energy transport in extended systems

We study directed energy transport in homogeneous nonlinear extended systems in the presence of homogeneous ac forces and dissipation. We show that the mechanism responsible for unidirectional motion of topological excitations is the coupling of their internal and translation degrees of freedom. Our results lead to a selection rule for the existence of such motion based on resonances that explains earlier symmetry analysis of this phenomenon. The direction of motion is found to depend both on the initial and the relative phases of the two harmonic drivings, even in the presence of noise.Comment: Final version, to appear in Physical Review Letter

Anomalous resonance phenomena of solitary waves with internal modes

We investigate the non-parametric, pure ac driven dynamics of nonlinear Klein-Gordon solitary waves having an internal mode of frequency $\Omega_i$. We show that the strongest resonance arises when the driving frequency $\delta=\Omega_i/2$, whereas when $\delta=\Omega_i$ the resonance is weaker, disappearing for nonzero damping. At resonance, the dynamics of the kink center of mass becomes chaotic. As we identify the resonance mechanism as an {\em indirect} coupling to the internal mode due to its symmetry, we expect similar results for other systems.Comment: 4 pages, 4 figures, to appear in Phys Rev Let

On the existence of internal modes of sine-Gordon kinks

We study whether or not sine-Gordon kinks exhibit internal modes or ``quasimodes.'' By considering the response of the kinks to ac forces and initial distortions, we show that neither intrinsic internal modes nor ``quasimodes'' exist in contrast to previous reports. However, we do identify a different kind of internal mode bifurcating from the bottom edge of the phonon band which arises from the discretization of the system in the numerical simulations, thus confirming recent predictions.Comment: 4 pages, 2 figures, REVTeX, to appear as a Rapid Communication in Phys Rev E (July 1st

Overdamped sine-Gordon kink in a thermal bath

We study the sine-Gordon kink diffusion at finite temperature in the overdamped limit. By means of a general perturbative approach, we calculate the first- and second-order (in temperature) contributions to the diffusion coefficient. We compare our analytical predictions with numerical simulations. The good agreement allows us to conclude that, up to temperatures where kink-antikink nucleation processes cannot be neglected, a diffusion constant linear and quadratic in temperature gives a very accurate description of the diffusive motion of the kink. The quadratic temperature dependence is shown to stem from the interaction with the phonons. In addition, we calculate and compute the average value $$ of the wave function as a function of time and show that its width grows with $\sqrt{t}$. We discuss the interpretation of this finding and show that it arises from the dispersion of the kink center positions of individual realizations which all keep their width.Comment: REVTeX, 12 pages, 10 figures, to appear in Phys Rev

Sustancias tóxicas y antinutricionales de Amaranthus dubius Mart. ex Thell. Efecto de la parte de la planta y la época de recolecta

Amaranth species are gaining increasing interest for human and animal nutrition, although its use is limited due to their toxic and antinutritional substances contents. The contents of toxic and antinutritionals substances (oxalates, phytates, total phenols, condensate tannins, hydrolysable tannins and cyanide) in the leaves, stems, and panicles of Amaranthus dubius Mart. ex Thell., not yet investigated, were evaluated in both rainy and dry seasons. The plants were cultivated in El Néctar Hacienda, located in Merecure, in the municipality of Acevedo, Miranda State, Venezuela (10º31’38" N, 66º33’16" W). The concentration of oxalates, phytates, total phenols, condensate and hydrolysable tannins were determined by classic colorimetric techniques, the cyanide being determined by silver nitrate titration. The content of toxic and antinutrients in A. dubius ranged from 169.6 to 368.5 mg of oxalates.kg-1 DM, 0.771 to 7.482 mg of phytates.g-1 DM, 0.47 to 1.77 mg of total phenols.g-1 DM, and 0.22 to 1.20 mg of condensate tannins.g-1 DM. Cyanide and hydrolysable tannins were not detected. The values of most of these substances presented differences according to harvesting seasons and plant part (P<0.001), as well as an interaction between both factors. The content of toxic and antinutrients was generally higher in the dry than in the rainy season for all parts of the plant. The harvesting season and the plant part affect the content of toxic and antinutritional substances in A.dubius, whose values were, however, below the maximum levels allowed by regulators for human consumption. Therefore, as raw material it does not need to be processed in order to guarantee its harmlessnessLas especies de amaranto están generando creciente interés para la nutrición humana y animal, aunque su uso es limitado debido al contenido de sustancias tóxicas y antinutricionales. El contenido de sustancias tóxicas y antinutrientes (oxalatos, fitatos, fenoles totales, taninos condensados, taninos hidrolizables y cianuro) en las hojas, tallos y panículas de Amaranthus dubius Mart. ex Thell., no ha sido investigado, por ello se evaluaron en época lluviosa y seca. Las plantas fueron cultivadas en la hacienda El Néctar, localizada en Merecure, municipio Acevedo, estado Miranda, Venezuela (10º31’38'’ N, 66º33’16'’ O). La concentración de oxalatos, fitatos, fenoles totales, taninos condensados y taninos hidrolizables se determinaron mediante técnicas colorimétricas clásicas y el cianuro se determinó por titulación con nitrato de plata. El contenido de tóxicos y antinutrientes en A. dubius osciló entre 169,6-368,5 mg de oxalatos.kg-1 en biomasa seca (BS); 0,771-7,482 mg de fitatos.g-1 BS; 0,47-1,77 mg de fenoles totales.g-1 BS y 0,22-1,20 mg de taninos condensados.g-1 BS. No se detectó cianuro ni taninos hidrolizables. Los valores de la mayoría de estas sustancias presentaron diferencias de acuerdo a la época de recolecta y partes de la planta (P<0,001), así como interacción entre ambos factores. El contenido de tóxicos y antinutrientes fue generalmente mayor en la época seca que en la época lluviosa para todas las partes de la planta. La época de recolecta y la parte de la planta afectaron el contenido de sustancias tóxicas y antinutricionales de A. dubius; sin embargo, los valores estuvieron por debajo de los niveles máximos permitidos regulados para el consumo humano. Por lo tanto, la materia prima no necesita ser procesada para garantizar su inocuida

Recombination reduction on lead halide perovskite solar cells based on low temperature synthesized hierarchical TiO2 nanorods

Intensive research on the electron transport material (ETM) has been pursued to improve the efficiency of perovskite solar cells (PSCs) and decrease their cost. More importantly, the role of the ETM layer is not yet fully understood, and research on new device architectures is still needed. Here, we report the use of three-dimensional (3D) TiO2 with a hierarchical architecture based on rutile nanorods (NR) as photoanode material for PSCs. The proposed hierarchical nanorod (HNR) films were synthesized by a two-step low temperature (180 °C) hydrothermal method, and consist of TiO2 nanorod trunks with optimal lengths of 540 nm and TiO2 nanobranches with lengths of 45 nm. Different device configurations were fabricated with TiO2 structures (compact layer, NR and HNR) and CH3NH3PbI3, using different synthetic routes, as the active material. PSCs based on HNR-CH3NH3PbI3 achieved the highest power conversion efficiency compared to PSCs with other TiO2 structures. This result can be ascribed mainly to lower charge recombination as determined by impedance spectroscopy. Furthermore, we have observed that the CH3NH3PbI3 perovskite deposited by the two-step route shows higher efficiency, surface coverage and infiltration within the structure of 3D HNR than the one-step CH3NH3PbI3−xClx perovskite.This work was supported by the Universitat Jaume I (project 12I361.01/1), the Spanish MINECO (project MAT2013-47192- C3-1-R), CONACYT-México (project CB-2010/153270) and UNAM (PAPIIT-IN1030

Resonances in the dynamics of ϕ4\phi^4 kinks perturbed by ac forces

We study the dynamics of $\phi^4$ kinks perturbed by an ac force, both with and without damping. We address this issue by using a collective coordinate theory, which allows us to reduce the problem to the dynamics of the kink center and width. We carry out a careful analysis of the corresponding ordinary differential equations, of Mathieu type in the undamped case, finding and characterizing the resonant frequencies and the regions of existence of resonant solutions. We verify the accuracy of our predictions by numerical simulation of the full partial differential equation, showing that the collective coordinate prediction is very accurate. Numerical simulations for the damped case establish that the strongest resonance is the one at half the frequency of the internal mode of the kink. In the conclusion we discuss on the possible relevance of our results for other systems, especially the sine-Gordon equation. We also obtain additional results regarding the equivalence between different collective coordinate methods applied to this problem.Comment: 23 pages, 7 figures, REVTeX, accepted for publication in Phys. Rev.