arXiv subjects

Sergey V. Dmitriev

Publications and source records attributed to Sergey V. Dmitriev.

At least 37 records · Page 2Linked to original sources

arXiv2017

Extreme values of elastic strain and energy in sine-Gordon multi-kink collisions

In our recent study the maximal values of kinetic and potential energy densities that can be achieved in the collisions of $N$ slow kinks in the sine-Gordon model were calculated analytically (for $N=1,2$, and 3) and numerically (for $4\le N\le 7$). However, for many physical applications it is important to know not only the total potential energy density but also its two components (the on-site potential energy density and the elastic strain energy density) as well as the extreme values of the elastic strain, tensile (positive) and compressive (negative). In the present study we give (i) the two components of the potential energy density and (ii) the extreme values of elastic strain. Our results suggest that in multi-soliton collisions the main contribution to the potential energy density comes from the elastic strain, but not from the on-site potential. It is also found that tensile strain is usually larger than compressive strain in the core of multi-soliton collision.

nlin.PS↗

arXiv2017

Crossover from ballistic to normal heat transport in the $ϕ^{4}$ lattice: If nonconservation of momentum is the reason, what is the mechanism?

Anomalous (non-Fourier's) heat transport is no longer just a theoretical issue since it has been observed experimentally in a number of low-dimensional nanomaterials, such as SiGe nanowires, carbon nanotubes, and others. To understand these anomalous behaviors, exploring the microscopic origin of normal (Fourier's) heat transport is a fascinating theoretical topic. However, this issue has not yet been fully understood even for one-dimensional (1D) model chains, in spite of a great amount of thorough studies done to date. From those studies it has been widely accepted that the conservation of momentum is a key ingredient to induce anomalous heat transport, while momentum-nonconserving systems usually support normal heat transport where Fourier's law is valid. But if the nonconservation of momentum is the reason, what is the underlying microscopic mechanism for the observed normal heat transport? Here we carefully revisit a typical 1D momentum-nonconserving $ϕ^{4}$ model and present evidence that the mobile discrete breathers or, in other words, the moving intrinsic localized modes with frequency components above the linear phonon band can be responsible for that.

cond-mat.stat-mech↗

arXiv2017

Multi-kink collisions in the $ϕ^6$ model

We study simultaneous collisions of two, three, and four kinks and antikinks of the $ϕ^6$ model at the same spatial point. Unlike the $ϕ^4$ kinks, the $ϕ^6$ kinks are asymmetric and this enriches the variety of the collision scenarios. In our numerical simulations we observe both reflection and bound state formation depending on the number of kinks and on their spatial ordering in the initial configuration. We also analyze the extreme values of the energy densities and the field gradient observed during the collisions. Our results suggest that very high energy densities can be produced in multi-kink collisions in a controllable manner. Appearance of high energy density spots in multi-kink collisions can be important in various physical applications of the Klein-Gordon model.

hep-th↗

arXiv2017

Energy transfer in strained graphene assisted by discrete breathers excited by external ac driving

In the present molecular dynamics study, external ac driving is used at frequencies outside the phonon spectrum to excite gap DBs in uniformly strained graphene nanoribbon. Harmonic displacement or harmonic force is applied to a zigzag atomic chain of graphene. In the former case non-propagating DBs are excited on the atoms next to the driven atoms, while in the latter case the excited DBs propagate along the nanoribbon. The energy transfer along the nanoribbon assisted by the DBs is investigated in detail and the differences between harmonic displacement driving and harmonic force driving are discussed. It is concluded that the amplitude of external driving at out of phonon spectrum frequencies should not necessarily be large to obtain a noticeable energy transfer to the system. Overall, our results suggest that external harmonic driving even at relatively small driving amplitudes can be used to control excitation of DBs and consequently the energy transfer to the system.

cond-mat.mes-hall↗

arXiv2016

Resonant interaction of $ϕ^4$ kink with spatially periodic $\mathcal{PT}$-symmetric perturbation

The resonant interaction of the $ϕ^4$ kink with a periodic $\mathcal{PT}$-symmetric perturbation is observed in the frame of the continuum model and with the help of a two degree of freedom collective variable model derived in PRA 89, 010102(R). When the kink interacts with the perturbation, the kink's internal mode is excited with the amplitude varying in time quasiperiodically. The maximal value of the amplitude was found to grow when the kink velocity is such that it travels one period of perturbation is nearly one period of the kink's internal mode. It is also found that the kink's translational and vibrational modes are coupled in a way that an increase in the kink's internal mode amplitude results in a decrease in kink velocity. The results obtained with the collective variable method are in a good qualitative agreement with the numerical simulations for the continuum model. The results of the present study suggest that kink dynamics in open systems with balanced gain and loss can have new features in comparison with the case of conservative systems.

nlin.PS↗

arXiv2016

Large Electronic Anisotropy and Enhanced Chemical Activity of Highly Rippled Phosphorene

We investigate the electronic structure and chemical activity of rippled phosphorene induced by large compressive strains via first-principles calculation. It is found that phosphorene is extraordinarily bendable, enabling the accommodation of ripples with large curvatures. Such highly rippled phosphorene shows a strong anisotropy in electronic properties. For ripples along the armchair direction, the band gap changes from 0.84 to 0.51 eV for the compressive strain up to -20% and further compression shows no significant effect, for ripples along the zigzag direction, semiconductor to metal transition occurs. Within the rippled phosphorene, the local electronic properties, such as the modulated band gap and the alignments of frontier orbitals, are found to be highly spatially dependent, which may be used for modulating the injection and confinement of carriers for optical and photovoltaic applications. The examination of the interaction of a physisorbed NO molecule with the rippled phosphorene under different compressive strains shows that the chemical activities of the phosphorene are significantly enhanced at the top and bottom peaks of the ripples, indicated by the enhanced adsorption and charge transfer between them. All these features can be ascribed to the effect of curvatures, which modifies the orbital coupling between atoms at the ripple peaks.

cond-mat.mtrl-sci↗

arXiv2016

High energy density spots and production of kink-antikink pairs in particle collisions

The maximal energy density that can be achieved in the collisions of the particle-like wave trains in the $ϕ^4$ model has been investigated numerically for different wave train parameters. From these results the prediction is made on how many kink-antikink pairs can be produced in wave train collisions taking into account that in collision of $N$ kinks maximal energy density is equal to $N^2/2$ for even $N$. Our numerical results are in a reasonably good agreement with the predicted maximal number of kink-antikink pairs formed in wave train collisions.

nlin.PS↗

arXiv2016

High energy density in the collision of $N$ kinks in the $ϕ^4$ model

Recently for the sine-Gordon equation it has been established that during collisions of $N$ slow kinks maximal energy density increases as $N^2$. In this numerical study, the same scaling rule is established for the non-integrable $ϕ^4$ model for $N\le 5$. For odd (even) $N$ the maximal energy density is in the form of potential (kinetic) energy density. Maximal elastic strain is also calculated. In addition, the effect of the kink's internal modes on the maximal energy density is analysed for $N=1, 2, 3$. Our results suggest that in multi-soliton collisions very high energy density can be achieved in a controllable manner.

nlin.PS↗

arXiv2015

On the spectral stability of kinks in 2D Klein-Gordon model with parity-time-symmetric perturbation

In a series of recent works by Demirkaya et al. stability analysis for the static kink solutions to the 1D continuous and discrete Klein-Gordon equations with a $\mathcal{PT}$-symmetric perturbation has been analysed. We consider the linear stability problem for the static kink in 2D Klein-Gordon field taking into account spatially localized $\mathcal{PT}$-symmetric perturbation. The perturbation is in the form of viscous friction, which does not affect the static solutions to the unperturbed Klein-Gordon equation. Small dynamic perturbation around the static kink solution is considered to formulate the linear stability problem. The effect of the small perturbation on the solutions to the corresponding eigenvalue problem is analysed. The main result is presented in the form of a theorem describing the behavior of the eigenvalues corresponding to the extended and localised eigenmodes as the functions of the perturbation parameter.

math-ph↗

arXiv2015

Nonlinear switching and solitons in PT-symmetric photonic systems

One of the challenges of the modern photonics is to develop all-optical devices enabling increased speed and energy efficiency for transmitting and processing information on an optical chip. It is believed that the recently suggested Parity-Time (PT) symmetric photonic systems with alternating regions of gain and loss can bring novel functionalities. In such systems, losses are as important as gain and, depending on the structural parameters, gain compensates losses. Generally, PT systems demonstrate nontrivial non-conservative wave interactions and phase transitions, which can be employed for signal filtering and switching, opening new prospects for active control of light. In this review, we discuss a broad range of problems involving nonlinear PT-symmetric photonic systems with an intensity-dependent refractive index. Nonlinearity in such PT symmetric systems provides a basis for many effects such as the formation of localized modes, nonlinearly-induced PT-symmetry breaking, and all-optical switching. Nonlinear PT-symmetric systems can serve as powerful building blocks for the development of novel photonic devices targeting an active light control.

physics.optics↗

arXiv2015

Interaction of discrete breathers with primary lattice defects in bcc Fe

The interaction of discrete breathers with the primary lattice defects in transition metals such as vacancy, dislocation, and surface is analyzed on the example of bcc iron employing atomistic simulations. Scattering of discrete breathers on the lattice defects induces localized atomic excitations, with intensity and relaxation time depending on the defect structure and breather kinetic energy. The dissipation of the intrinsic breather energy due to the scattering is computed and analyzed. It is concluded that the breather-to-defect energy transfer may stipulate the activation of the lattice defects causing unexpected athermal effects such as enhanced mass transfer or electroplasticity, already experimentally reported but so far not fully understood at the atomic-scale level.

cond-mat.mtrl-sci↗

arXiv2015

High energy density in multi-soliton collisions

Solitons are very effective in transporting energy over great distances and collisions between them can produce high energy density spots of relevance to phase transformations, energy localization and defect formation among others. It is then important to study how energy density accumulation scales in multi-soliton collisions. In this study, we demonstrate that the maximal energy density that can be achieved in collision of $N$ slowly moving kinks and antikinks in the integrable sine-Gordon field, remarkably, is proportional to $N^2$, while the total energy of the system is proportional to $N$. This maximal energy density can be achieved only if the difference between the number of colliding kinks and antikinks is minimal, i.e., is equal to 0 for even $N$ and 1 for odd $N$ and if the pattern involves an alternating array of kinks and anti-kinks. Interestingly, for odd (even) $N$ the maximal energy density appears in the form of potential (kinetic) energy, while kinetic (potential) energy is equal to zero. The results of the present study rely on the analysis of the exact multi-soliton solutions for $N=1,2,$ and 3 and on the numerical simulation results for $N=4,5,6,$ and 7. Based on these results one can speculate that the soliton collisions in the sine-Gordon field can, in principle, controllably produce very high energy density. This can have important consequences for many physical phenomena described by the Klein-Gordon equations.

nlin.PS↗

arXiv2015

Scroll configurations of carbon nanoribbons

Carbon nanoscroll is a unique topologically open configuration of graphene nanoribbon possessing outstanding properties and application perspectives due to its morphology. However molecular dynamics study of nanoscrolls with more than a few coils is limited by computational power. Here, we propose a simple model of the molecular chain moving in the plane, allowing to describe the folded and rolled packaging of long graphene nanoribbons. The model is used to describe a set of possible stationary states and the low-frequency oscillation modes of isolated single-layer nanoribbon scrolls as the function of the nanoribbon length. Possible conformational changes of scrolls due to thermal fluctuations are analyzed and their thermal stability is examined. Using the full-atomic model, frequency spectrum of thermal vibrations is calculated for the scroll and compared to that of the flat nanoribbon. It is shown that the density of phonon states of the scroll differs from the one of the flat nanoribbon only in the low (omega<100 cm-1) and high (omega>1450 cm-1) frequency ranges. Finally, the linear thermal expansion coefficient for the scroll outer radius is calculated from the long-term dynamics with the help of the developed planar chain model. The scrolls demonstrate anomalously high coefficient of thermal expansion and this property can find new applications.

cond-mat.mes-hall↗

arXiv2014

Kink scattering from a parity-time-symmetric defect in the $ϕ^4$ model

In this paper, we study the $ϕ^4$ kink scattering from a spatially localized $\mathcal{PT}$-symmetric defect and the effect of the kink's internal mode (IM) is discussed. It is demonstrated that if a kink hits the defect from the gain side, a noticeable IM is excited, while for the kink coming from the opposite direction the mode excitation is much weaker. This asymmetry is a principal finding of the present work. Similar to the case of the sine-Gordon kink studied earlier, it is found that the $ϕ^4$ kink approaching the defect from the gain side always passes through the defect, while in the opposite case it must have sufficiently large initial velocity, otherwise it is trapped by the loss region. It is found that for the kink with IM the critical velocity is smaller, meaning that the kink bearing IM can pass more easily through the loss region. This feature, namely the "increased transparency" of the defect as regards the motion of the kink in the presence of IM is the second key finding of the present work. A two degree of freedom collective variable model offered recently by one of the co-authors is shown to be capable of reproducing both principal findings of the present work. A simpler, analytically tractable single degree of freedom collective variable method is used to calculate analytically the kink phase shift and the kink critical velocity sufficient to pass through the defect. Comparison with the numerical results suggests that the collective variable method is able to predict these parameters with a high accuracy.

nlin.PS↗

arXiv2014

Interaction of sine-Gordon kinks and breathers with a $\mathcal{PT}$-symmetric defect

The scattering of kinks and low-frequency breathers of the nonlinear sine-Gordon (SG) equation on a spatially localized $\mathcal{PT}$-symmetric perturbation (defect) with a balanced gain and loss is investigated numerically. It is demonstrated that if a kink passes the defect, it always restores its initial momentum and energy and the only effect of the interaction with the defect is a phase shift of the kink. A kink approaching the defect from the gain side always passes, while in the opposite case it must have sufficiently large initial momentum to pass through the defect instead of being trapped in the loss region. The kink phase shift and critical velocity are calculated with the use of the collective variable method. Kink-kink (kink-antikink) collisions at the defect are also briefly considered, showing how their pairwise repulsive (respectively, attractive) interaction can modify the collisional outcome of a single kink within the pair with the defect. For the breather, the result of its interaction with the defect strongly depends on the breather parameters (velocity, frequency and initial phase) and on the defect parameters. The breather can gain some energy from the defect and as a result potentially even split into a kink-antikink pair or it can lose a part of its energy. Interestingly, the breather translational mode is very weakly affected by the dissipative perturbation, so that a breather penetrates more easily through the defect when it comes from the lossy side, than a kink. In all studied soliton-defect interactions the energy loss to radiation of small-amplitude extended waves is negligible.

nlin.PS↗

arXiv2012

Breathers in PT-symmetric optical couplers

We show that the parity-time (PT) symmetric coupled optical waveguides with gain and loss support localised oscillatory structures similar to the breathers of the classical $ϕ^4$ model. The power carried by the PT-breather oscillates periodically, switching back and forth between the waveguides, so that the gain and loss are compensated on the average. The breathers are found to coexist with solitons and be prevalent in the products of the soliton collisions. We demonstrate that the evolution of the small-amplitude breather's envelope is governed by a system of two coupled nonlinear Schrödinger equations, and employ this Hamiltonian system to show that the small-amplitude PT-breathers are stable.

nlin.PS↗

arXiv2012

Generalized continuum models for analysis of one-dimensional shear deformations in a structural interface with micro-rotations

Generalized continuum models for describing one-dimensional shear deformations of a Cosserat lattice are considered and their application to describing of structural effects essential for interfaces are discussed. The two-field long-wavelength micropolar model and its gradient and four-field generalizations are obtained and compared to the single-field conventional and gradient micropolar models. The single-field models can be applied to the analysis of long-wavelength deformations, but it does not describe short-wavelength waves and boundary effects. It is demonstrated that the two-field models describe both long-wavelength and short-wavelength harmonic waves and localized deformations and may be used in order to find stop band edges and to study the filtering properties of the interface. The two-field models make it possible to describe not only exponential but also short-wavelength boundary effects and evaluate degree of its spatial localization. The four-field model improves the two-field model in the description of the waves with wavenumbers in the middle part of the first Brillouin zone and may be useful to specify stop band edges in the case when minima/maxima of the dispersion curves belong to this region. The reported results are especially important for modeling of structural interfaces in the case when the length of localization is comparable with the interface thickness.

cond-mat.mtrl-sci↗

arXiv2012

Wave scattering on a domain wall in a chain of PT-symmetric couplers

We study wave propagation in linear arrays composed of pairs of conjugate waveguides with balanced gain and loss, i.e. arrays of the PT-symmetric couplers, where the linear spectrum is known to feature high-frequency and low-frequency branches. We introduce a domain wall by switching the gain and loss in a half of the array, and analyze the scattering of linear waves on this defect. The analysis reveals two major effects: amplification of both reflected and transmitted waves, and excitation of the reflected and transmitted low-frequency and high-frequency waves by the incident high-frequency and low-frequency waves, respectively.

physics.optics↗