Perturbed soliton-like molecular excitations in a deformed DNA chain

We study the nonlinear dynamics of a deformed Deoxyribonucleic acid (DNA) molecular chain which is governed by a perturbed sine-Gordon equation coupled with a linear wave equation representing the lattice deformation. The DNA chain considered here is assumed to be deformed periodically which is the energetically favourable configuration, and the periodic deformation is due to the repulsive force between base pairs, stress in the helical backbones and due to the elastic strain force in both the strands. A multiple scale soliton perturbation analysis is carried out to solve the perturbed sine-Gordon equation and the resultant perturbed kink and antikink solitons represent open state configuration with small fluctuation. The perturbation due to periodic deformation of the lattice changes the velocity of the soliton. However, the width of the soliton remains unchanged.     

Capillary Adhesion of Microbeams： Finite Deformation Analysis

Capillary force may cause adhesion of devices at micro- and nano-scales. Considering the fact that large deformation is often involved in adhesion of microbeams, we analysed the capillary adhesion of two beams using finite deformation elasticity theory. The critical adhesion condition can be obtained from the present method as a function of the bending stiffness, Young＇s contact angle, the spacing of the two beams as well as the surface tensions of the solid and liquid phases. The solution for the capillary adhesion of a beam with a rigid substrate is also given. The results from the finite deformation analysis are compared with that of infinitesimal deformation method in order to show the necessity of accounting for the nonlinear effect associated with large deflection. The method adopted in this study can also be used to solve other adhesion problems associated with van der Waals force or electrostatic force.     

An exploration in acoustic radiation force experienced by cylindrical shells via resonance scattering theory

In nonlinear acoustic regime, a body insonified by a sound field is known to experience a steady force that is called the acoustic radiation force (RF). This force is a second-order quantity of the velocity potential function of the ambient medium. Exploiting the sufficiency of linear solution representation of potential function in RF formulation, and following the classical resonance scattering theorem (RST) which suggests the scattered field as a superposition of the resonant field and a background (non-resonant) component, we will show that the radiation force is a composition of three components: background part, resonant part and their interaction. Due to the nonlinearity effects, each part contains the contribution of pure partial waves in addition to their mutual interaction. The numerical results propose the residue component (i.e., subtraction of the background component from the RF) as a good indicator of the contribution of circumferential surface waves in RF. Defining the modal series of radiation force function and its components, it will be shown that within each partial wave, the resonance contribution can be synthesized as the Breit-Wigner form for adequately none-close resonant frequencies. The proposed formulation may be helpful essentially due to its inherent value as a canonical subject in physical acoustics. Furthermore, it may make a tunnel through the circumferential resonance reducing effects on radiation forces.     

Nanoscale deformation of a liquid surface

We study the interaction between a solid particle and a liquid interface. A semianalytical solution of the nonlinear equation that describes the interface deformation points out the existence of a bifurcation behavior for the apex deformation as a function of the distance. We show that the apex curvature obeys a simple power-law dependency on the deformation. Relationships between physical parameters disclose the threshold distance at which the particle can approach the liquid before capillarity provokes a "jump to contact." A prediction of the interface original position before deformation takes place, as well as the attraction force measured by an approaching probe, are produced. The results of our analysis agree with the force curves obtained from atomic force microscopy experiments over a liquid puddle.     

On the validity of Hertz contact law for granular material acoustics

We discuss the acoustical behavior of a 1D model of granular medium, which is a chain of identical spherical beads. In this geometry, we are able to test quantitatively alternative models to the Hertz theory of contact between elastic solids. We compare the predictions of the different models to experimental results that concern linear sound wave propagation in the chain submitted to a static force, and nonlinear solitary wave propagation in an unconstrained chain. We use elastic, elastic-plastic and brittle materials, the beads roughness extends on one order of magnitude, and we also use oxidized metallic beads. We demonstrate experimentally that at low static forces, for all types of beads, the linear acoustic waves propagate in the system as predicted by Hertz's theory. At larger forces, after onset of permanent plastic deformation at the contacts, the brass beads exhibit non Hertzian behavior, and hysteresis. Except in the case of brass beads, the nonlinear waves follow the predictions of Hertz theory. Revised: 28 May 1998 / Accepted: 27 July 1998     

Nonlinear propagation of neutrinos in a strongly magnetized medium

The nonlinear propagation of an intense neutrino flux in an electron-positron plasma with equilibrium density and magnetic field inhomogeneities is considered. It is found that the neutrinos are nonlinearly coupled with electrostatic and electromagnetic disturbances due to weak Fermi interaction and ponderomotive forces. The process is governed by a Klein-Gordon equation for the neutrino flux and a wave equation for the plasma oscillations in the presence of the ponderomotive force of the neutrinos. This pair of equations is then used to derive a nonlinear dispersion relation which exhibits that nonthermal electrostatic and electromagnetic fluctuations are created on account of the energy density of the neutrinos. The relevance of our investigation to the anomalous absorption of neutrinos in a nonuniform magnetized medium is pointed out.     

Nonlinear capillary vibrations of a charged drop placed in a dielectric medium: Single-mode initial deformation of the drop shape

The nonlinear vibrations of the equilibrium spherical shape of a charged drop placed in a perfect incompressible dielectric medium are asymptotically calculated in the second-order approximation in single-mode initial deformation of the drop surface. The drop is assumed to be a perfect incompressible liquid. It is shown that the nonlinear vibration amplitudes, as well as the energy distribution between nonlinearly excited modes, depend significantly on the parameter ρ, where ρ is the ratio of the environmental density to that of the drop. It is also demonstrated that an increase in ρ raises the amplitude of the highest of the vibration modes excited due to second-order nonlinear interaction. In the second order of smallness, the amplitude of the zeroth mode is independent of the density ratio. As ρ grows, the effect of the self-charge of the drop, the interfacial tension, and the permittivity of the environment on the nonlinear oscillations increases.     

Hysteresis in response of nonlinear bistable interface to continuously varying acoustic loading

In many experimental situations it is an equation of the forced relaxator and not of the forced oscillator that describes a variation in the acoustic field of the interface width (i.e. of a characteristic distance between the surfaces composing the interface). The developed theory predicts that some types of the nonlinear relaxators (depending on the structure of the nonlinear interaction force between the surfaces) exhibit hysteresis in their response to continuous acoustic loading of first increasing and then decreasing amplitude. Nonlinear (unharmonic) variation of the interface width starts at threshold amplitude of the incident sinusoidal acoustic wave, which is higher than threshold amplitude for returning to sinusoidal motion. This dynamic hysteresis (and accompanying it bistability) are possible, in particular, if the dependence of the effective interaction force on the interface width admits two quasi-equilibrium positions of the interface (bistable interface) or if the force itself is hysteretic (hysteretic interface). These theoretical predictions are relevant to some recent experimental observations on the interaction of powerful ultrasonic fields with cracks.     

Generation of pulses upon nonresonant acousto-electromagnetic interaction

New mechanisms of generation of acoustic and electromagnetic soliton-like pulses in an optoelastic medium upon nonlinear nonresonant interaction of the polarization components of an electromagnetic field with acoustic oscillations in the medium are considered. It is shown that the acousto-electromagnetic interaction in such a system may lead to the formation of coherent soliton excitations in a thin crystal plate. It is found that a modulation instability occurs in an extended medium, which is caused by the spatial effects and leads to the generation of transverse sound waves. The evolution of a light field in a one-dimensional extended periodic optoelastic medium is also considered. It is shown that acoustic and electromagnetic solitons can be generated due to the mixing of direct and backward optical waves and their nonresonant interaction with a sound wave.     

The influence of 3-photon absorption and pulse interactions on discrete X-waves in normally dispersive waveguide arrays

In this paper, we investigate the influences of 3-photon absorption on discrete X-waves in nonlinear normally dispersive waveguide arrays. It is found that 3-photon absorption can cause the decrease of the total power, which results in the appearances of the discrete diffraction for an intermediate input peak-power and the discrete X-wave for a higher input peak-power. Also, the interaction between pulses for different waveguide excitation are studied in detail. The results show that for the in-phase waveguide excitation of neighboring channels, the bound states can be formed by choosing properly the initial peak-power; for the in-phase waveguide excitation of distant channels, however, the bound states can not be formed. For the out-of-phase multiple waveguide excitation, due to interplay the repulsive force and nonlinearity, the interaction of two pulses can form the X-like wave or the double X-like wave as long as choosing the proper input peak-power.     

A numerical study of contact force in competitive evacuation

Crowd force by the pushing or crushing of people has resulted in a number of accidents in recent decades. The aftermath investigations have shown that the physical interaction of a highly competitive crowd could produce dangerous pressure up to 4500 N/m, which leads to compressive asphyxia or even death. In this paper, a numerical model based on discrete element method(DEM) as referenced from granular flow was proposed to model the evacuation process of a group of highly competitive people, in which the movement of people follows Newton's second law and the body deformation due to compression follows Hertz contact model. The study shows that the clogs occur periodically and flow rate fluctuates greatly if all people strive to pass through a narrow exit at high enough desired velocity. Two types of contact forces acting on people are studied. The first one, i.e., vector contact force, accounts for the movement of the people following Newton's second law. The second one, i.e., scale contact force, accounts for the physical deformation of the human body following the contact law. Simulation shows that the forces chain in crowd flow is turbulent and fragile. A few narrow zones with intense forces are observed in the force field, which is similar to the strain localization observed in granular flow. The force acting on a person could be as high as 4500 N due to force localization, which may be the root cause of compressive asphyxia of people in many crowd incidents.     

On the interaction between a charged drop and an external acoustic field

An interaction between capillary oscillations of a charged drop and an external acoustic field is investigated under conditions in which nonlinear components of the acoustic pressure on the drop surface may be neglected. It is shown that equations describing the temporal evolution of modes of the capillary waves in this case may be either the Mathieu-Hill equations or ordinary inhomogeneous equations of the second order describing forced oscillations. In both cases, the drop instability (of a parametric or resonance type) may result in its disintegration due to deformation caused by the acoustic field at its own drop charge, subcritical in the sense of the Rayleigh criterion.     

Tripartite entanglement dynamics for an atom interacting with nonlinear couplers

In this communication we introduce a new model which represents the interaction between an atom and two fields injected simultaneously within a cavity including the nonlinear couplers. By using the canonical transformation the model can be regarded as a generalization of several well-known models. We calculate and discuss entanglement between the tripartite system of one atom and the two cavity modes. For a short interaction time, similarities between the behavior based on our solution compared with the other simulation based on a numerical linear algebra solution of the original Hamiltonian with truncated Fock bases for each mode, is shown. For a specific value of the Kerr-like medium defined in this letter, we find that the entanglement, as measured by concurrence, may terminate abruptly in a finite time.     

Fourier synthesization of optical pulses and “polar” light

It is shown that the direct Fourier synthesization of light beams allows one to create polarity-asymmetric waves, which are able, in the process of nonlinear interaction with a medium, to break its inversion symmetry. As a result, these “polar” waves may show the effect of optical rectification in nonlinear centrosymmetric media by generating light-induced dc electric polarization. At the same time, waves of this type, due to their unusual symmetry properties, can be used for detecting the direction and sign of a dc electric field applied to the medium. The prospects of application of polar waves to data recording and processing are discussed.     

Self-localized nonlinear surface magnetic polaritons in a ferromagnetic medium

The properties of electromagnetic waves propagating in a semibounded, nonlinear, ferromagnetic medium are investigated. It is shown that under certain conditions the interaction between the spin and electromagnetic waves results in the localization of volume polaritons near the surface. Self-localization of surface polaritons due to the nonlinear properties of the medium occurs thereby. The nonlinear Schrödinger equation for nonlinear surface and volume polaritons is derived, and the conditions under which solitons of these waves exist are determined. The wave intensity required to observe the predicted effects is estimated.     

Formation of Hot Images in Laser Beams through a Self-defocusing Kerr Medium Slab

A nonlinear hot image is usually thought as of a special case of self-focusing, and thus occurs when a laser beam propagates through a slab of self-focusing medium. Here we show theoretically that a hot image may also be formed by a thin slab of self-defocusing medium. The physical origin for this hot image formation is akin to the in-line volume-phase holographic imaging due to the intensity-dependent refractive-index modulation of the self- defocusing medium. NumericM simulations confirm the theoretical prediction and further identify the dependence of the hot image on the beam power, the modulation depth of obscuration and the thickness of self-defocusing medium. The analysis presented here brings new insight into the physics of hot image formation in the high power laser system.     

Generation of acoustic solitons by a single-mode electromagnetic field

Mechanisms of acoustic pulse generation by a single-mode electromagnetic field propagating in a photoelastic material are analyzed. The anisotropy induced by acoustic excitations in an isotropic medium leads to nonlinear coupling between the polarization components of a single-mode electromagnetic field. For different conditions, it is shown that the acoustic-electromagnetic wave interaction due to mixing of the polarization components of light and acoustic waves can give rise to soliton-like coherent acoustic excitations in a thin crystal plate. When spatial dispersion is ignored, the governing system of equations for unidirectional acoustic solitons can be reduced to an integrable model. It is shown that qualitatively different scenarios of formation of acoustic solitons are possible, depending on the directions of deformation and field polarization.     

Numerical simulations of stable cavitation bubble generation and primary Bjerknes forces in a three-dimensional nonlinear phased array focused ultrasound field

We present a model developed for studying the generation of stable cavitation bubbles and their motion in a three-dimensional volume of liquid with axial symmetry under the effect of finite-amplitude phased array focused ultrasound. The density of bubbles per unit volume is determined by a nonlinear law which is a threshold-dependent function of the negative acoustic pressure reached in the liquid, in which nuclei are initially distributed. The nonlinear mutual interaction of ultrasound and bubble oscillations is modeled by a nonlinear coupled differential system formed by the wave and a Rayleigh-Plesset equations, for which both the pressure and the bubble oscillation variables are unknown. The system, which accounts for nonlinearity, dispersion, and attenuation due to the bubbles, is solved by numerical approximations. The nonlinear acoustic pressure field is then used to evaluate the primary Bjerknes force field and to predict the subsequent motion of bubbles. In order to illustrate the procedure, a medium-high and a low ultrasonic frequency configurations are assumed. Simulation results show where bubbles are generated, the nonlinear effects they have on ultrasound, and where they are relocated. Despite many physical restrictions and thanks to its particularities (two nonlinear coupled fields, bubble generation, bubble motion), the numerical model used in this work gives results that show qualitative coherence with data observed experimentally in the framework of stable cavitation and suggest their usefulness in some application contexts.     

Effects on squeezing and sub-poissonian of light in fourth harmonic generation up to first-order Hamiltonian interaction

The effects on squeezing and sub-poissonian of light in fourth harmonic generation (FHG) are investigated based on the fully quantum mechanically up to the first order Hamiltonian interaction in gt, where g is the coupling constant between the modes per second and t is the interaction time between the waves during the process in a nonlinear medium. FHG is a process in which an incident laser beam of the fundamental frequency ω interacts with a nonlinear medium to produce the harmonic frequency at 4ω. The coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators are established. The occurrence of amplitude squeezing effects in both the quadratures of the radiation field in the fundamental mode is investigated and found to be dependent on the selective phase values of the field amplitude. The photon statistics of the pump mode in this process have also been investigated and found to be sub-poissonian in nature. It is found that there is no possibility to produce squeezed light in the harmonic mode up to first-order interaction in gt. Further, we have found the case up to second-order Hamiltonian interaction in gt that the normal squeezing in the harmonic mode is directly depends upon the fourth-order squeezing of the initial pump field. This gives a method of converting higher-order (fourth-order) squeezing into normal squeezing in the harmonic mode and vice versa.