Control of electron and electron-hole pair dynamics on nonlinear lattice bilayers by strong solitons.

We consider the dynamics of electrons and holes moving in two-dimensional lattice layers and bilayers. As an example, we study triangular lattices with units interacting via anharmonic Morse potentials and investigate the dynamics of excess electrons and electron-hole pairs according to the Schrödinger equation in the tight binding approximation. We show that when single-site lattice solitons or M-solitons are excited in one of the layers, those lattice deformations are capable of trapping excess electrons or electron-hole pairs, thus forming quasiparticle compounds moving approximately with the velocity of the solitons. We study the temporal and spatial nonlinear dynamical evolution of localized excitations on coupled triangular double layers. Furthermore, we find that the motion of electrons or electron-hole pairs on a bilayer is slaved by solitons. By case studies of the dynamics of charges bound to solitons, we demonstrate that the slaving effect may be exploited for controlling the motion of the electrons and holes in lattice layers, including also bosonic electron-hole-soliton compounds in lattice bilayers, which represent a novel form of quasiparticles.

About electron transfer over long distances with tunable sub/supersonic velocities.

Provided in this paper is a theory of long-range electron transfer with near sound (supersonic or subsonic) velocity along one-dimensional crystal lattices. The theory represents the development of an earlier work by introducing Marcus formulation. To illustrate its application to a realistic case, the theory is used to offer an explanation of two puzzling observations made by Donovan and Wilson in transient photoconduction experiments with non-dopable perfectly crystalline polydiacetylene crystals in the presence of an electric field: transport velocity value close to sound velocity being independent of field for four orders of magnitude of field (102 V/m-106 V/m) and, in the low field values, an ultra-high mobility greater than 20 m2/V s. We also study factors eventually leading to lowering of the transport velocity.

Discrete-breather-assisted charge transport along DNA-like molecular wires.

Mobile discrete breathers (MDBs) are here suggested as localized excitations underlying the trapping and transport of charged particles (electron or hole) along a DNA-like molecular wire with anchored ends such as attached to two electrodes. For illustration the Peyrard-Bishop-Dauxois-Holstein (PBDH) model is used. MDBs are excited by imposing appropriate disturbances to velocities or space positions of adjacent nucleotide pairs or lattice units of the wire. They can be directed either towards or away from the wire hence transverse to it. Numerical computer simulations show that a rather stable quasiparticle MDB + electron is possible when just a few of the nucleotide pairs near one of the fixed ends of the wire are excited. For the process to be effective, the charge, e.g., the electron, must be initially placed around the disturbed region of the molecule. Once the MDB + electron quasiparticle is formed it may be transported to quite a long distance up to ca. 60-70 nm in real space. Our findings show that such process does not demand intervention of an externally applied electric field and hence it may be considered as alternative to the polaron transport process.

Compounds of paired electrons and lattice solitons moving with supersonic velocity.

We study the time evolution of two correlated electrons of opposite spin in an anharmonic lattice chain. The electrons are described quantum mechanically by the Hubbard model while the lattice is treated classically. The lattice units are coupled via Morse-Toda potentials. Interaction between the lattice and the electrons arises due to the dependence of the electron transfer-matrix element on the distance between neighboring lattice units. Localized configurations comprising a paired electron and a pair of lattice deformation solitons are constructed such that an associated energy functional is minimized. We investigate long-lived, stable pairing features. It is demonstrated that traveling pairs of lattice solitons serve as carriers for the paired electrons realizing coherent transport of the two correlated electrons. We also observe dynamical narrowing of the states, that is, starting from an initial double-peak profile of the electron probability distribution, a single-peak profile is adopted going along with enhancement of localization of the paired electrons. Interestingly, a parameter regime is identified for which supersonic transport of paired electrons is achieved.

Electron capture and transport mediated by lattice solitons.

We study electron transport in a one-dimensional molecular lattice chain. The molecules are linked by Morse interaction potentials. The electronic degree of freedom, expressed in terms of a tight binding system, is coupled to the longitudinal displacements of the molecules from their equilibrium positions along the axis of the lattice. More specifically, the distance between two sites influences in an exponential fashion the corresponding electronic transfer matrix element. We demonstrate that when an electron is injected in the undistorted lattice it causes a local deformation such that a compression results leading to a lowering of the electron's energy below the lower edge of the band of linear states. This corresponds to self-localization of the electron due to a polaronlike effect. Then, if a traveling soliton lattice deformation is launched a distance apart from the electron's position, upon encountering the polaronlike state it captures the latter dragging it afterwards along its path. Strikingly, even when the electron is initially uniformly distributed over the lattice sites a traveling soliton lattice deformation gathers the electronic amplitudes during its traversing of the lattice. Eventually, the electron state is strongly localized and moves coherently in unison with the soliton lattice deformation. This shows that for the achievement of coherent electron transport we need not start with the polaronic effect.

Spreading of liquid drops over porous substrates.

The spreading of small liquid drops over thin and thick porous layers (dry or saturated with the same liquid) has been investigated in the case of both complete wetting (silicone oils of different viscosities) and partial wetting (aqueous SDS solutions of different concentrations). Nitrocellulose membranes of different porosity and different average pore size have been used as a model of thin porous layers, glass and metal filters have been used as a model of thick porous substrates. The first problem under investigation has been the spreading of small liquid drops over thin porous layers saturated with the same liquid. An evolution equation describing the drop spreading has been deduced, which showed that both an effective lubrication and the liquid exchange between the drop and the porous substrates are equally important. Spreading of silicone oils over different nitrocellulose microfiltration membranes was carried out. The experimental laws of the radius of spreading on time confirmed the theory predictions. The spreading of small liquid drops over thin dry porous layers has also been investigated from both theoretical and experimental points of view. The drop motion over a dry porous layer appears caused by the interplay of two processes: (a). the spreading of the drop over already saturated parts of the porous layer, which results in a growth of the drop base, and (b). the imbibition of the liquid from the drop into the porous substrate, which results in a shrinkage of the drop base and a growth of the wetted region inside the porous layer. As a result of these two competing processes the radius of the drop base goes through a maximum as time proceeds. A system of two differential equations has been derived to describe the time evolution of the radii of both the drop base and the wetted region inside the porous layer. This system includes two parameters, one accounts for the effective lubrication coefficient of the liquid over the wetted porous substrate, and the other is a combination of permeability and effective capillary pressure inside the porous layer. Two additional experiments were used for an independent determination of these two parameters. The system of differential equations does not include any fitting parameter after these two parameters were determined. Experiments were carried out on the spreading of silicone oil drops over various dry nitrocellulose microfiltration membranes (permeable in both normal and tangential directions). The time evolution of the radii of both the drop base and the wetted region inside the porous layer was monitored. In agreement with our theory all experimental data fell on two universal curves if appropriate scales were used with a plot of the dimensionless radii of the drop base and of the wetted region inside the porous layer using a dimensionless time scale. Theory predicts that (a). the dynamic contact angle dependence on the dimensionless time should be a universal function, (b). the dynamic contact angle should change rapidly over an initial short stage of spreading and should remain a constant value over the duration of the rest of the spreading process. The constancy of the contact angle on this stage has nothing to do with hysteresis of the contact angle: there is no hysteresis in our system. These predictions are in the good agreement with our experimental observations. In the case of spreading of liquid drops over thick porous substrates (complete wetting) the spreading process goes in two similar stages as in the case of thin porous substrates. In this case also both the drop base and the radii of the wetted area on the surface of the porous substrates were monitored. Spreading of oil drops (with a wide range of viscosities) on dry porous substrates having similar porosity and average pore size shows universal behavior as in the case of thin porous substrates. However, the spreading behavior on porous substrates having different average pore sizes deviates from the universal behavior. Yet, even in this case the dynamic contact angle remains constant over the duration of the second stage of spreading as in the case of spreading on thin porous substrates. Finally, experimental observations of the spreading of aqueous SDS solution over nitrocellulose membranes were carried out (case of partial wetting). The time evolution of the radii of both the drop base and the wetted area inside the porous substrate was monitored. The total duration of the spreading process was subdivided into three stages: in the first stage the drop base growths until a maximum value is reached. The contact angle rapidly decreases during this stage; in the second stage the radius of the drop base remains constant and the contact angle decreases linearly with time; finally in the third stage the drop base shrinks while the contact angle remains constant. The wetted area inside the porous substrate expands during the whole spreading process. Appropriate scales were used to have a plot of the dimensionless radii of the drop base, of the wetted area inside the porous substrate, and the dynamic contact angle vs. the dimensionless time. Our experimental data show: the overall time of the spreading of drops of SDS solutions over dry thin porous substrates decreases with the increase of surfactant concentration; the difference between advancing and hydrodynamic receding contact angles decreases with the surfactant concentration increase; the constancy of the contact angle during the third stage of spreading has nothing to do with the hysteresis of contact angle, but determined by the hydrodynamics. Using independent spreading experiments of the same drops on a non-porous nitrocellulose substrate we have shown that the static receding contact angle is equal to zero, which supports our conclusion on the hydrodynamic nature of the hydrodynamic receding contact angle on porous substrates.

Properties of surface wave trains excited by mass transfer through a liquid surface.

In annular containers, various traveling periodic surface wave trains are generated in liquid layers during the absorption process of a miscible surface-active substance out of the vapor phase. Single and counter-rotating wave trains are observed. We here report on waves found to be dispersion-free associated to mostly longitudinal, dilational surface-tension-gradient-driven motions. We report on interactions of the wave crests and on modulations that lead to wave-number changes of the wave trains. The wave interactions show behavior typically known for solitons.

Falling films and the Marangoni effect.

The instability of a falling liquid film of an aqueous surfactant solution along a vertical slope with surfactant adsorption-desorption at its open surface originating surface stresses (Marangoni effect) is investigated. The diffusion of surfactant to the film surface from the bulk and desorption of surfactant to the gas phase are taken into account. The Navier-Stokes and Fick equations are reduced to a system of simpler hence, analytically and numerically, more tractable nonlinear evolution equations albeit with nine dimensionless parameters. The linear stability analysis yields a dispersion equation that is numerically solved and eigenvalues are obtained for various values of significant dimensionless parameters. A very rich picture of instabilities appears. In addition to the earlier known (Kapitza) hydrodynamic mode there are up to four new (Marangoni-driven) diffusion modes. Two modes travel with the liquid velocity on the film surface and the other two travel on their own downstream and upstream, respectively. One diffusion mode could be identified, in the reference frame moving with the liquid on the film surface, as a monotonic instability mode hence leading to a patterned film surface. All other modes are oscillatory ones. Resonance of modes is also predicted for suitable combinations of the parameters of the problem. The mode observed depends upon the surface stress (in terms of a dimensionless Marangoni number), the particular choice of the adsorption-desorption kinetics, and the surface tension state equation at the open surface of the film.

Film rupture in the diffuse interface model coupled to hydrodynamics.

The process of dewetting of a thin liquid film is usually described using a long-wave approximation yielding a single evolution equation for the film thickness. This equation incorporates an additional pressure term-the disjoining pressure-accounting for the molecular forces. Recently a disjoining pressure was derived coupling hydrodynamics to the diffuse interface model [L. M. Pismen and Y. Pomeau, Phys. Rev. E 62, 2480 (2000)]. Using the resulting evolution equation as a generic example for the evolution of unstable thin films, we examine the thickness ranges for linear instability and metastability for flat films, the families of stationary periodic and localized solutions, and their linear stability. The results are compared to simulations of the nonlinear time evolution. From this we conclude that, within the linearly unstable thickness range, there exists a well defined subrange where finite perturbations are crucial for the time evolution and the resulting structures. In the remainder of the linearly unstable thickness range the resulting structures are controlled by the fastest flat film mode assumed up to now for the entire linearly unstable thickness range. Finally, the implications for other forms of disjoining pressure in dewetting and for spinodal decomposition are discussed.

Dissipative Toda-Rayleigh lattice and its oscillatory modes.

A detailed theoretical and experimental analysis of the possible oscillatory regimes of the dissipative Toda-Rayleigh lattice system is provided. It is shown that the system has (N-1) oscillatory modes with different space-time scales and two rotatory modes. Using its analog electronic circuit implementation we also show with a simple and robust method how switching between modes occurs.

Mode transitions and wave propagation in a driven-dissipative Toda-Rayleigh ring.

A circular lattice (ring) of N electronic elements with Toda-type exponential interactions and Rayleigh-type dissipation is used to illustrate wave formation, propagation, and switching between wave modes. A methodology is provided to help controlling modes, thus allowing it to realize any of (N-1) different wave modes (including soliton-type modes) and the switching between them by means of a single control parameter.

Sliding drops in the diffuse interface model coupled to hydrodynamics.

Using a film thickness evolution equation derived recently combining long-wave approximation and diffuse interface theory [L. M. Pismen and Y. Pomeau, Phys. Rev. E 62, 2480 (2000)] we study one-dimensional surface profiles for a thin film on an inclined plane. We discuss stationary flat film and periodic solutions including their linear stability. Flat sliding drops are identified as universal profiles, whose main properties do not depend on mean film thickness. The flat drops are analyzed in detail, especially how their velocity, advancing and receding dynamic contact angles and plateau thicknesses depend on the inclination of the plane. A study of nonuniversal drops shows the existence of a dynamical wetting transition with hysteresis between droplike solutions and a flat film with small amplitude nonlinear waves.

Synchronization, re-entry, and failure of spiral waves in a two-layer discrete excitable system.

A three-dimensional structure composed of two coupled discrete excitable lattices is considered. Each lattice (layer) is a discrete excitable subsystem and using a local model of excitation transfer and failure we have estimated the sufficient conditions for it to exhibit spiral waves. Then we show how interlayer synchronization of all motions is possible. Various effects of spiral wave synchronization, re-entry and failure are also investigated.

Capillary imbibition of surfactant solutions in porous media and thin capillaries: partial wetting case.

The capillary imbibition of aqueous surfactant solutions into dry porous substrates is investigated from both theoretical and experimental points of view in the case of partial wetting. Cylindrical capillaries are used as a model of porous media to study the problem. It is shown that if the mean pore size is below a critical value, then the permeability of the porous medium is not influenced by the presence of surfactants whatever the value of the concentration: the imbibition front moves exactly in the same way as in the case of the imbibition of pure water. The critical radius is determined by the adsorption of the surfactant molecules onto the inner surface of the pores. If the mean pore size is larger than the critical value, then the permeability increases with increasing surfactant concentration. These theoretical conclusions are in agreement with the experimental observations.

Spreading of liquid drops over saturated porous layers.

Spreading of small liquid drops over thin porous layers saturated with the same liquid is investigated from both theoretical and experimental points of view. A theory is presented that shows that spreading is governed by the same power law as in the case of spreading over a dry solid substrate. The Brinkman's equations are used to model the liquid flow inside the porous substrate. An equation of the drop spreading is deduced, which shows that both an effective lubrication and the liquid exchange between the drop and the porous substrates are equally important. The presence of these two phenomena removes the well-known singularity at the moving three-phase contact line. Matching of the drop profile in the vicinity of the three-phase contact line with the main spherical part of the drop gives the possibility to calculate the pre-exponential factor in the spreading law via permeability and effective viscosity of the liquid in the porous layer. Unfortunately, the latter dependency turns out to be very weak. Spreading of silicone oils over different microfiltration membranes is carried out. Radii of spreading on time experimental dependencies confirm the theory predictions. Experimentally found coefficients agree with theoretical estimations.

Spreading of non-Newtonian liquids over solid substrates.

The spreading of drops of a non-Newtonian liquid (Ostwald-de Waele liquid) over horizontal solid substrates is theoretically investigated in the case of complete wetting and small dynamic contact angles. Both gravitational and capillary regimes of spreading are considered. The evolution equation deduced for the shape of the spreading drops has self-similar solutions, which allows obtaining spreading laws for both gravitational and capillary regimes of spreading. In the gravitational regime case of spreading the profile of the spreading drop is provided.

Spreading of aqueous SDS solutions over nitrocellulose membranes.

Experimental investigations were carried out on the spreading of small drops of aqueous SDS solutions over dry thin porous substrates (nitrocellulose membranes) in the case of partial wetting. The time evolution was monitored of the radii of both the drop base and the wetted area inside the porous substrate. The total duration of the spreading process was subdivided into three stages: the first stage: the drop base expands until the maximum value of the drop base is reached, the contact angle rapidly decreases during this stage; the second stage: the radius of the drop base remains constant and the contact angle decreases linearly with time; the third stage: the drop base shrinks and the contact angle remains constant. The wetted area inside the porous substrate expends during the whole spreading process. Appropriate scales were used with a plot of the dimensionless radii of the drop base, of the wetted area inside the porous substrate and the dynamic contact angle on the dimensionless time. Our experimental data show: the overall time of the spreading of drops of SDS solution over dry thin porous substrates decreases with the increase of surfactant concentration; the difference between advancing and hydrodynamic receding contact angles decreases with the surfactant concentration increase; the constancy of the contact angle during the third stage of spreading has nothing to do with the hysteresis of contact angle, but determined by the hydrodynamic reasons. It is shown using independent spreading experiments of the same drops on nonporous nitrocellulose substrate that the static receding contact angle is equal to zero, which supports our conclusion on the hydrodynamic nature of the hydrodynamic receding contact angle on porous substrates.

Surface forces and wetting phenomena.

Conditions for thermodynamic equilibrium of liquid drops on solid substrates are presented. It is shown that if surface force (disjoining/conjoining Derjaguin pressure) action in a vicinity of the three-phase contact line is taken into account the condition of thermodynamic equilibrium is duly satisfied. Then the thermodynamic expressions for equilibrium contact angles of drops on solid substrates and menisci in thin capillaries are expressed in terms of the corresponding Derjaguin isotherm. It is shown that equilibrium contact angles of drops vary significantly depending on the vapour pressure in the ambient atmosphere, while there is a single, unique equilibrium contact angle in thin capillaries. It is also shown that the static advancing contact angle of a drop depends on its volume, in agreement with experimental data. In the case of menisci in capillaries, the expression for the receding contact angle is deduced, with results that are also in agreement with known experimental data.

Bifurcation analysis and existence of periodic solutions in a simple neural network with delays.

Results are provided here about the stability and bifurcation of periodic solutions for a (neural) network with n elements where delays between adjacent units and external inputs are included. The particular cases n = 2 and n = 3 are discussed in details, to explicitly illustrate the role of the delays in the corresponding bifurcation sets and the stability properties, like a Hopf bifurcation, a pitchfork bifurcation, and a Bogdanov-Takens bifurcation.

On the back-firing instability.

The onset of the back-firing instability is studied in a one-dimensional spatially extended and dissipative system, where propagating localized solutions become unstable. It corresponds to the emission in the tail of a solitary wave of a new wave propagating in the opposite direction. The transition is illustrated, in geometrical terms, using a model normal form equation. (c) 2004 American Institute of Physics.