Solitary Pulses Research Articles

Detecting the Presence of High Water-to-Cement Ratio in Concrete Surfaces Using Highly Nonlinear Solitary Waves

We describe a nondestructive evaluation (NDE) method based on the propagation of highly nonlinear solitary waves (HNSWs) to determine the excess of water on the surface of existing concrete structures. HNSWs are induced in a one-dimensional granular chain placed in contact with the concrete to be tested. The chain is part of a built-in transducer designed and assembled to exploit the dynamic interaction between the particles and the concrete. The hypothesis is that the interaction depends on the stiffness of the concrete and influences the time-of-flight of the solitary pulse reflected at the transducer/concrete interface. Two sets of experiments were conducted. In the first set, eighteen concrete cylinders with different water-to-cement (w/c) ratios were cast and tested in order to obtain baseline data to link the ratio to the time of flight. Then, sixteen short beams with fixed w/c ratio, but subject to water in excess at one surface, were cast. The novel NDE method was applied along with the conventional ultrasonic pulse velocity technique in order to determine advantages and limitations of the proposed approach. The results show that the time of flight detected the excess of water in the beams. In the future, the proposed method may be employed in the field to evaluate rapidly and reliably the condition of existing concrete structures and, in particular, concrete decks.

Appearance of an ensemble solitary pulse train in transient backward stimulated Raman scattering

A self-similarity approximation model for three-wave resonant interaction in transient backward stimulated Raman scattering (BSRS) was derived. Interestingly, as its asymptotic solution, the train of solitary backward Raman pulse train is possibly formed. This result can be considered as an increment of “single” soliton observed previously [A. Abdolvand et al., Phys. Rev. Lett 103, 183902 (2009)].

Spherical nonlinear ion-acoustic solitary waves in Titan’s atmosphere

Propagation of spherical nonlinear ion-acoustic solitary waves in positive and negative ion plasmas with superthermal electrons is investigated. The effects of perturbations of the azimuthal and zenith-angle as well as the radial coordinate on the solitary wave profile are reported. The existence domains and the characteristics of the spherical solitary pulses are examined. The solitary excitations are found to be strongly dependent on the plasma parameters; the mass ratio of the positive-to-negative ions, electrons superthermality, and the spherical geometry. The role of superthermal electrons in formation of the spherical nonlinear ion-acoustic solitary excitations for two ion mass groups in Titan’s upper atmosphere is investigated.

On the Kapitza instability and the generation of capillary waves

We revisit the classical problem of a liquid film falling along a vertical wall due to the action of gravity, i.e. the Kapitza paradigm (Kapitza,Zh. Eksp. Teor. Fiz., vol. 18, 1948, pp. 3–28). The free surface of such a flow is typically deformed into a train of solitary pulses that consists of large asymmetric wave humps preceded by small precursory ripples, designated as ‘capillary waves’. We set out to answer four fundamental questions. (i) By what mechanism do the precursory ripples form? (ii) How can they travel at the same celerity as the large-amplitude main humps? (iii) Why are they designated as ‘capillary waves’? (iv) What determines their wavelength and number and why do they attenuate in space? Asymptotic expansion as well as direct numerical simulations and calculations with a low-dimensional integral boundary-layer model have yielded the following conclusions. (i) Precursory ripples form due to an inertia-based mechanism at the foot of the leading front of the main humps, where the local free-surface curvature is large. (ii) The celerity of capillary waves is matched to that of the large humps due to the action of surface tension, which speeds up the former and slows down the latter. (iii) They are justly designated as ‘capillary waves’ because their wavelength is systematically shorter than the visco-capillary cutoff wavelength of the Kapitza instability. Due to a nonlinear effect, namely that their celerity decreases with decreasing amplitude, they nonetheless attain/maintain a finite amplitude because of being continuously compressed by the pursuing large humps. (iv) The number and degree of compression of capillary waves is governed by the amplitude of the main wave humps as well as the Kapitza number. Large-amplitude main humps travel fast and strongly compress the capillary waves in order for these to speed up sufficiently. Also, the more pronounced the first capillary wave becomes, the more (spatially attenuating) capillary waves are needed to allow a smooth transition to the back of the next main hump. These effects are amplified by decreasing the Kapitza number, whereby, at very small values, streamwise viscous diffusion increasingly attenuates the amplitude of the capillary waves.

Уединенная волна в структуре заряженных микрочастиц

Уединенная волна в структуре заряженных микрочастиц

On the Reliability of a Solitary Wave Based Transducer to Determine the Characteristics of Some Materials.

In the study presented in this article we investigated the feasibility and the reliability of a transducer design for the nondestructive evaluation (NDE) of the stiffness of structural materials. The NDE method is based on the propagation of highly nonlinear solitary waves (HNSWs) along a one-dimensional chain of spherical particles that is in contact with the material to be assessed. The chain is part of a built-in system designed and assembled to excite and detect HNSWs, and to exploit the dynamic interaction between the particles and the material to be inspected. This interaction influences the time-of-flight and the amplitude of the solitary pulses reflected at the transducer/material interface. The results of this study show that certain features of the waves are dependent on the modulus of elasticity of the material and that the built-in system is reliable. In the future the proposed NDE method may provide a cost-effective tool for the rapid assessment of materials’ modulus.

Mechanisms for impulsive energy dissipation and small-scale effects in microgranular media.

We study impulse response in one-dimensional homogeneous microgranular chains on a linear elastic substrate. Microgranular interactions are analytically described by the Schwarz contact model which includes nonlinear compressive as well as snap-to and from-contact adhesive effects forming a hysteretic loop in the force deformation relationship. We observe complex transient dynamics, including disintegration of solitary pulses, local clustering, and low-to-high-frequency energy transfers resulting in enhanced energy dissipation. We study in detail the underlying dynamics of cluster formation in the impulsively loaded medium and relate enhanced energy dissipation to the rate of cluster formation. These unusual and interesting dynamical phenomena are shown to be robust over a range of physically feasible conditions and are solely scale effects since they are attributed to surface forces, which have no effect at the macroscale. We establish a universal relation between the reclustering rate and the effective damping in these systems. Our findings demonstrate that scale effects generating new nonlinear features can drastically affect the dynamics and acoustics of microgranular materials.

Induced dark solitary pulse in an anomalous dispersion cavity fiber laser.

We report on the formation of induced dark solitary pulses in a net anomalous dispersion cavity fiber laser. In a weak birefringence cavity fiber laser simultaneous laser oscillation along the two orthogonal polarization directions of the cavity could be achieved. Under suitable conditions bright cavity solitons could be formed along one polarization direction while CW emission occurs along the orthogonal polarization direction. In a previous paper we have shown that under incoherent polarization coupling a bright soliton always induces a broad dark pulse on the CW beam. In the paper we further show that under coherent polarization coupling a bright soliton could further induce either a weak bright or a dark solitary pulse on the bottom of the broad dark pulse. Numerical simulations have also well reproduced the experimental observations, and further show whether a weak dark or bright solitary pulse is induced is determined by the presence or absence of a phase jump in the induced pulse.

Landau damping of Gardner solitons in a dusty bi-ion plasma

The effects of linear Landau damping on the nonlinear propagation of dust-acoustic solitary waves (DASWs) are studied in a collisionless unmagnetized dusty plasma with two species of positive ions. The extremely massive, micron-seized, cold, and negatively charged dust particles are described by fluid equations, whereas the two species of positive ions, namely, the cold (heavy) and hot (light) ions are described by the kinetic Vlasov equations. Following Ott and Sudan [Phys. Fluids 12, 2388 (1969)], and by considering lower and higher-order perturbations, the evolution of DASWs with Landau damping is shown to be governed by Korteweg-de Vries (KdV), modified KdV (mKdV), or Gardner (KdV-mKdV)-like equations. The properties of the phase velocity and the Landau damping rate of DASWs are studied for different values of the ratios of the temperatures (σ) and the number densities (μ) of hot and cold ions as well as the cold to hot ion mass ratio m. The distinctive features of the decay rates of the amplitudes of the KdV, mKdV, and Gardner solitons with a small effect of Landau damping are also studied in different parameter regimes. It is found that the Gardner soliton points to lower wave amplitudes than the KdV and mKdV solitons. The results may be useful for understanding the localization of solitary pulses and associated wave damping (collisionless) in laboratory and space plasmas (e.g., the F-ring of Saturn), in which the number density of free electrons is much smaller than that of ions and the heavy, micron seized dust grains are highly charged.

Electrokinetic instability of liquid micro- and nanofilms with a mobile charge

The instability of ultra-thin films of an electrolyte bordering a dielectric gas in an external tangential electric field is scrutinized. The solid wall is assumed to be either a conducting or charged dielectric surface. The problem has a steady one-dimensional solution. The theoretical results for a plug-like velocity profile are successfully compared with available experimental data. The linear stability of the steady-state flow is investigated analytically and numerically. Asymptotic long-wave expansion has a triple-zero singularity for a dielectric wall and a quadruple-zero singularity for a conducting wall, and four (for a conducting wall) or three (for a charged dielectric wall) different eigenfunctions. For infinitely small wave numbers, these eigenfunctions have a clear physical meaning: perturbations of the film thickness, of the surface charge, of the bulk conductivity, and of the bulk charge. The numerical analysis provides an important result: the appearance of a strong short-wave instability. At increasing Debye numbers, the short-wave instability region becomes isolated and eventually disappears. For infinitely large Weber numbers, the long-wave instability disappears, while the short-wave instability persists. The linear stability analysis is complemented by a nonlinear direct numerical simulation. The perturbations evolve into coherent structures; for a relatively small external electric field, these are large-amplitude surface solitary pulses, while for a sufficiently strong electric field, these are short-wave inner coherent structures, which do not disturb the surface.

Solitary pulse-on-demand production by optical injection locking of passively Q-switched InGaN diode laser near lasing threshold

In this letter, we investigate the behavior of a Q-switched InGaN multi-section laser diode (MSLD) under optical injection from a continuous wave external cavity diode laser. We obtain solitary optical pulse generation when the slave MSLD is driven near free running threshold, and the peak output power is significantly enhanced with respect to free running configuration. When the slave laser is driven well above threshold, optical injection reduces the peak power. Using standard semiconductor laser rate equation model, we find that both power enhancement and suppression effects are the result of partial bleaching of the saturable absorber by externally injected photons.

Light bullets in coupled nonlinear Schrödinger equations with spatially modulated coefficients and Bessel trapping potential

We discuss three-dimensional (3D) light bullets (LBs) in a system of coupled nonlinear Schrödinger equations with spatially modulated diffraction and nonlinearity coefficients, under the action of a Bessel trapping potential. Exact spatiotemporal vector solitary waves, or LBs, are obtained using the method of separation of variables and the Hirota’s bilinear method. An inverse solution procedure is introduced, in which the desired localized solutions of equations are proposed first and then the corresponding diffraction and nonlinearity coefficients determined. New 3D wave packets are built with the help of spherical harmonics in the form of multipole, necklace, and toroidal solitary pulses. Numerical solution of the full system of equations indicates that an initial wave in the form of such 3D wave packets is longlived but slowly changing along the propagation direction.

Electromechanical properties of biomembranes and nerves

Lipid membranes are insulators and capacitors, which can be charged by an external electric field. This phenomenon plays an important role in the field of electrophysiology, for instance when describing nerve pulse conduction. Membranes are also made of polar molecules meaning that they contain molecules with permanent electrical dipole moments. Therefore, the properties of membranes are subject to changes in trans-membrane voltage. Vice versa, mechanical forces on membranes lead to changes in the membrane potential. Associated effects are flexoelectricity, piezoelectricity, and electrostriction.Lipid membranes can melt from an ordered to a disordered state. Due to the change of membrane dimensions associated with lipid membrane melting, electrical properties are linked to the melting transition. Melting of the membrane can induce changes in trans-membrane potential, and application of voltage can lead to a shift of the melting transition. Further, close to transitions membranes are very susceptible to piezoelectric phenomena.We discuss these phenomena in relation with the occurrence of lipid ion channels. Close to melting transitions, lipid membranes display step-wise ion conduction events, which are indistinguishable from protein ion channels. These channels display a voltage-dependent open probability. One finds asymmetric current-voltage relations of the pure membrane very similar to those found for various protein channels. This asymmetry falsely has been considered a criterion to distinguish lipid channels from protein channels. However, we show that the asymmetry can arise from the electromechanical properties of the lipid membrane itself.Finally, we discuss electromechanical behavior in connection with the electromechanical theory of nerve pulse transduction. It has been found experimentally that nerve pulses are related to changes in nerve thickness. Thus, during the nerve pulse a solitary mechanical pulse travels along the nerve. Due to electromechanical coupling it is unavoidable that this pulse generates a trans-membrane voltage. In the past, we have proposed that this electromechanical pulse is the origin of the action potential in nerves.

Multiscale tunability of solitary wave dynamics in tensegrity metamaterials

A class of strongly nonlinear metamaterials based on tensegrity concepts is proposed, and the solitary wave dynamics under impact loading is investigated. Such systems can be tuned into elastic hardening or elastic softening regimes by adjusting local and global prestress. In the softening regime these metamaterials are able to transform initially compression pulse into a solitary rarefaction wave followed by oscillatory tail with progressively decreasing amplitude. Interaction of a compression solitary pulse with an interface between elastically hardening and softening materials having correspondingly low-high acoustic impedances demonstrates anomalous behavior: a train of reflected compression solitary waves in the low impedance material; and a transmitted solitary rarefaction wave with oscillatory tail in high impedance material. The interaction of a rarefaction solitary wave with an interface between elastically softening and elastically hardening materials with high-low impedances also demonstrates anomalous behavior: a reflected solitary rarefaction wave with oscillatory tail in the high impedance branch; and a delayed train of transmitted compression solitary pulses in the low impedance branch. These anomalous impact transformation properties may allow for the design of ultimate impact mitigation devices without relying on energy dissipation.

Nonlinear mixed solitary—Shear waves and pulse equi-partition in a granular network

We study primary pulse transmission in a two-dimensional granular network composed of two ordered chains that are nonlinearly coupled through Hertzian interactions. Impulsive excitation is applied to one of the chains (designated as ‘excited chain’), and the resulting transmitted primary pulses in both chains are considered, especially in the non-directly excited chain (the ‘absorbing chain’). A new type of mixed nonlinear solitary pulses–shear waves is predicted for this system, leading to primary pulse equi-partition between chains. An analytical reduced model for primary pulse transmission is derived to study the strongly nonlinear acoustics in the small-amplitude approximation. The model is re-scalable with energy and parameter-free, and is asymptotically solved by extending the one-dimensional nonlinear mapping technique of Starosvetsky (2012). The resulting nonlinear maps governing the amplitudes of the mixed-type waves accurately capture the primary pulse propagation in this system and predict the first occurrence of energy equipartition in the network. To confirm, in part, the theoretical results we experimentally test a series of two-dimensional granular networks, and prove the occurrence of strong energy exchanges leading to eventual pulse equi-partition between the excited and absorbing chains, provided that the number of beads is sufficiently large.

Propagation of cylindrical acoustic waves in dusty plasma with positive dust

The hydrodynamic equations of positive and negative dust, Boltzmann electron and ion density distribution, and Poisson equation are used along with the reductive perturbation method to derive a cylindrical Kadomtsev-Petviashvili (CKP) equation. G′/G expansion method is used to obtain a new class of solutions. At certain condition, the solutions degenerate to solitary wave solutions. The effects of the physical parameters on the characteristics of solitary pulses are examined. The results give elucidation of the properties of dust acoustic solitary pulses in multicomponent space plasmas, particularly in interstellar dust clouds in a galactic disk and astrophysical plasma systems.

Evidence for two-dimensional solitary sound waves in a lipid controlled interface and its implications for biological signalling.

Biological membranes by virtue of their elastic properties should be capable of propagating localized perturbations analogous to sound waves. However, the existence and the possible role of such waves in communication in biology remain unexplored. Here, we report the first observations of two-dimensional solitary elastic pulses in lipid interfaces, excited mechanically and detected by FRET. We demonstrate that the nonlinearity near a maximum in the susceptibility of the lipid monolayer results in solitary pulses that also have a threshold for excitation. These experiments clearly demonstrate that the state of the interface regulates the propagation of pulses both qualitatively and quantitatively. Finally, we elaborate on the striking similarity of the observed phenomenon to nerve pulse propagation and a thermodynamic basis of cell signalling in general.

Three-dimensional coherent structures of electrokinetic instability.

A direct numerical simulation of the three-dimensional elektrokinetic instability near a charge-selective surface (electric membrane, electrode, or system of micro- or nanochannels) has been carried out and analyzed. A special finite-difference method has been used for the space discretization along with a semi-implicit 31/3-step Runge-Kutta scheme for the integration in time. The calculations employ parallel computing. Three characteristic patterns, which correspond to the overlimiting currents, are observed: (a) two-dimensional electroconvective rolls, (b) three-dimensional regular hexagonal structures, and (c) three-dimensional structures of spatiotemporal chaos, which are a combination of unsteady hexagons, quadrangles, and triangles. The transition from (b) to (c) is accompanied by the generation of interacting two-dimensional solitary pulses.

Propagation and collision of soliton rings in quantum semiconductor plasmas

Abstract The intrinsic localization of electrostatic wave energies in quantum semiconductor plasmas can be described by solitary pulses. The collision properties of these pulses are investigated. In the present study, the fundamental model includes the quantum term, degenerate pressure of the plasma species, and the electron/hole exchange–correlation effects. In cylindrical geometry, using the extended Poincare–Lighthill–Kuo (PLK) method, the Korteweg–de Vries (KdV) equations and the analytical phase shifts after the collision of two soliton rings are derived. Typical values for GaSb and GaN semiconductors are used to estimate the basic features of soliton rings. It is found that the pulses of GaSb semiconductor carry more energies than the pulses of GaN semiconductor. In addition, the degenerate pressure terms of electrons and holes have strong impact on the phase shift. The present theory may be useful to analyze the collision of localized coherent electrostatic waves in quantum semiconductor plasmas.

Propagation of Solitary Pulses in Optical Fibers with Both Self-Steepening and Quintic Nonlinear Effects

Pulse dynamics and stability in optical fibers in the presence of both self-steepening and quintic nonlinear effects are analyzed. Propagating profiles of the quintic derivative nonlinear Schrödinger model are isolated via two invariants of motion. The resulting canonical equation admits exact periodic propagating patterns in terms of the Jacobi elliptic functions, and solitary pulses are recovered in the long wave limit, i.e. degenerate cases of periodic profiles where each pulse is widely separated from the adjacent ones. Two families of such exact wave profiles are identified. The first one has a precise constraint concerning the magnitude of self-steepening and quintic nonlinear effects, while the second one permits more freedom. The reduction to the well established temporal soliton in an optical fiber waveguide in the absence of self-steepening and quintic nonlinearity is demonstrated explicitly. Numerical simulations are performed to identify regimes of parameter values where robust propagation patterns exist.