Nonlinear and nonequilibrium dynamics in geomaterials

The transition from linear to nonlinear dynamical elasticity in rocks is of considerable interest in seismic wave propagation as well as in understanding the basic dynamical processes in consolidated granular materials. We have carried out a careful experimental investigation of this transition for Berea and Fontainebleau sandstones. Below a well-characterized strain, the materials behave linearly, transitioning beyond that point to a nonlinear behavior which can be accurately captured by a simple macroscopic dynamical model. At even higher strains, effects due to a driven nonequilibrium state, and relaxation from it, complicate the characterization of the nonlinear behavior.     

Nonlinear dynamics of surface dust vortex and dust zonal flow systems

We present analytical and simulation studies of highly resolved dust fluid flows involving nonlinearly coupled incompressible surface dust vortex modes (SDVMs) and dust zonal flows (DZFs) in nonuniform unmagnetized dusty plasmas. For this purpose, we use the hydrodynamic equations for the dust fluid and Boltzmann distributed electrons and ions and obtain a set of equations that exhibit nonlinear couplings between the SDVMs and DZFs. The nonlinear equations are then used to investigate the parametric excitation of DZFs by the Reynolds stresses of the SDVMs. Large scale SDVMs emerge through nonlinear interactions with DZFs, and they suppress the dust particle transport across the density gradient. In contrast, DZFs possess short scale vortices with a higher turbulent transport. The relevance of our investigation into the role of coherent structures in a nonuniform dusty plasma is discussed.     

Conservation laws for a vortex in a compressible nonequilibrium medium

The problem of conservation of magnitudes is considered for a vortex in a relaxing compressible medium. Heat release due to the relaxation of a nonequilibrium medium leads to the propagation of compression waves, which remove material. Traditional integrals of motion are inapplicable in this case. We pro-pose the concept of integral quantity, which is conserved with an arbitrary degree of accuracy despite the fact that waves cross the boundary of the integration domain. Based on this concept, a broad class of conservation laws is derived for axisymmetric disturbances of columnar vortices, including conservation of the circulation and total angular momentum of the vortex. For nonaxisymmetric disturbances, it is shown that the total angular momentum and properly defined energy integral are conserved. Numerical verification of the derived conservation laws is performed and the perspectives for using these conservation laws in numerical simulations are discussed.     

Nonlinear dynamics of a flexible mechanism with impact

The nonlinear dynamics of a slider-crank mechanism with a flexible rod is considered in this study. The flexible rod is modeled with lumped masses and periodically impacted by an external flexible sphere. The impact is modeled using a kinematic coefficient of restitution. Nonlinear dynamics tools are applied to analyze the simulated data captured from the connecting rod of the mechanism. The chaotic behavior of the system is analyzed. The stability of the motion is studied using the Lyapunov exponents. The dependence between the Lyapunov exponents and the corresponding angular velocity of the driver link of the mechanism is investigated.     

Nonlinear dynamics for magnetic systems with a single-spin potential with variable shapes

We discuss the influence of a zero-temperature environment on a coherent quantum system. First, we calculate the reduced density operator of the system in the framework of the well-known, exactly solvable model of an oscillator coupled to a bath of harmonic oscillators. Then, we propose the sketch of an Aharonov–Bohm-like interferometer showing, through interference measurements, the decrease of the coherence length of the system due to the interaction with the environment, even in the zero temperature limit.     

Nonlinear dynamics of domain walls with a vortex internal structure in magnetouniaxial films with planar anisotropy

The nonlinear and generally unsteady dynamics of domain walls with a vortex internal structure in a constant magnetic field H is investigated on the basis of the numerical solution of the Landau-Lifshitz equation for a 2D distribution of magnetization M in magnetic films with planar anisotropy taking into account exactly the main interaction, including the dipole-dipole interaction. It is shown that in addition to field H _c (bifurcation field) above which the motion of a wall becomes unsteady and its internal structure experiences global dynamic changes, there exists a field H₀ separating two steady motions of the wall with different structures. The data clarifying the physical origin of the nonlinear dynamic rearrangement of the wall structure are presented. New rearrangement mechanisms associated with the generation and attenuation of vortices as well as their tunneling through the central surface of the wall are established. The existence of subperiod oscillations of the wall velocity in a static field in addition to the oscillations associated with the precession of M around the easy magnetization axis is predicted. The period T of dynamic variations of the wall structure is studied, and an empirical formula is proposed for describing the singular behavior of the T(H) dependence near H=H _Hc with the critical index depending on the film parameters. The bifurcation process is studied, and a nonlinear dependence of the critical field H _c on the film thickness and the saturation magnetization is established. The possibility of direct experimental investigation of the dynamic rearrangement of the internal structure of the wall is indicated.     

Semiclassical mechanism for the quantum decay in open chaotic systems

We address the decay in open chaotic quantum systems and calculate semiclassical corrections to the classical exponential decay. We confirm random matrix predictions and, going beyond, calculate Ehrenfest time effects. To support our results we perform extensive numerical simulations. Within our approach we show that certain (previously unnoticed) pairs of interfering, correlated classical trajectories are of vital importance. They also provide the dynamical mechanism for related phenomena such as photoionization and photodissociation, for which we compute cross-section correlations. Moreover, these orbits allow us to establish a semiclassical version of the continuity equation.     

Compression and stretching of ring vortex in a bulk nonlinear medium

We explore the nonlinear gain coupled Schr?dinger system through the utilization of the variables separation method and ansatz technique. By employing these approaches, we generate hierarchies of explicit dissipative vector vortices(DVVs) that possess diverse vorticity values. Numerous fundamental characteristics of the DVVs are examined, encompassing amplitude profiles, energy fluxes, parameter effects, as well as linear and dynamic stability.     

Molecular dynamics investigation of plastic deformation mechanism in bulk nanotwinned copper with embedded cracks

The plastic deformation of bulk nanotwinned copper with embedded cracks under tension has been explored by using molecular dynamics simulations. Simulation results show that the cracks mainly act as dislocation sources during the plastic deformation and occasionally as sinks at later stage. The dislocation pile-up, accumulation and transformation at twin boundaries (TBs) control the plastic hardening and softening deformations. The TB dislocation pile-up zone is estimated to be 5.6–8 nm, which agrees well with previous experimental and simulation results. Furthermore, it is found that the flow stress vs. dislocation density at the hardening stage follows the Taylor-type relationship.     

Nonlinear dynamics of complex hysteretic systems: Oscillator in a magnetic field

Complex hysteresis is a well-known phenomenon in many branches of science. The most prominent examples come from materials with a complex microscopic structure such as magnetic materials, shape-memory alloys, or, porous materials. Their hysteretic behavior is characterized by the existence of multiple internal system states for a given external parameter and by a non-local memory. The input-output behavior of such systems is well studied and in a standard phenomenological approach described by the so-called Preisach operator. What is not well understood, are situations, where such a hysteretic system is dynamically coupled to its environment. Since the hysteretic sub-system provides a complicated form of nonlinearity, one expects non-trivial, possibly chaotic behavior of the combined dynamical system. We study such a combined dynamical system with hysteretic nonlinearity. In this original contribution a simple differential-operator equation with hysteretic damping, which describes a magnetic pendulum is considered. We find, for instance, a fractal dependence of the asymptotic behavior as function of the starting values. The sensitivity of the system to perturbations is investigated by several methods, such as the 0–1 test for chaos and sub-Lyapunov exponents. The power spectral density is also calculated and compared with analytical results for simple input-output scenarios.     

Spectral flow and vortex dynamics in a temperature gradient

In the mixed state of superconductors the spectral flow of fermion zero modes in the vortex core couples the motion of vortices to that of the normal fluid. This gives rise to a heat current perpendicular to the direction of vortex motion and therefore to longitudinal thermomagnetic effects like the thermopower and the Peltier effect. Analysis of vortex motion in a temperature gradient on this basis yields excellent agreement with experimental results.     

A mechanism for generation of strong energy fluctuations in one-dimensional systems

A mechanism for the generation of strong energy fluctuations in a chain of harmonically and anharmonically coupled atoms in a state of thermodynamic equilibrium has been investigated by a molecular dynamics method. Energy fluctuations multiply exceeding the mean value were localized in a group of three to five atoms with lifetime on the order of an atomic vibrational period. They arise as a consequence of collisions of density waves propagating along the chain. A collision of waves of the same density sign leads to a fluctuation of the potential energy, while for differing signs a fluctuation in the kinetic energy occurs. In particular, collision of dilitatin waves leads to thermal breaking of the chain. The energy concentration at the moment of collision is 30% greater in a harmonic chain than in an anharmonic one.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 47–52, May, 1991.     

Rheological evidence for a dynamical crossover in polymer melts via nonequilibrium molecular dynamics

A certain "critical" molecular weight controls rheological properties of the multibead finitely extensible nonlinear elastic (FENE) chain model polymer melt. The rheological crossover manifests itself in a change of power law behavior for the viscous properties at a critical number of beads per chain N(c) = 100+/-10. This finding confirms a newly proposed relationship between dimensionless critical weight, characteristic length, and flexibility which we obtain as a side result. Results further suggest that the entanglement molecular weight N(e) for the flexible FENE chain model could be comparable in size or even larger than its critical molecular weight N(c).     

水中自然超空泡机理及减阻效应的非平衡分子动力学研究

应用非平衡分子动力学方法,对水中超空泡流形成机理及减阻效应进行了模拟研究.计算得到了流体密度分布、局部空化数分布、阻力系数及含气百分比等流场细节数据,结果显示空化数判据在分子层面仍然成立,局部低空化数区域与超空泡形成区域在空间上分离;超空泡形成和稳定主要受物体运动速度影响;空化器构型对空泡内含气率有较大影响;从云雾空化状态过渡到超空泡,物体表面摩擦力可以减小50%—90%.与数值模拟结果的对比表明非平衡分子动力学模拟适用于研究微观超空泡机理,能够经济有效地探讨超高速流体运动的一些自然规律. 关键词： 非平衡分子动力学 超空泡 高速流体 摩擦系数     

Nonlinear dynamics extraction for time-delay systems using modular neural networks synchronization and prediction

It is shown that the nonlinear dynamics of chaotic time-delay systems can be reconstructed using a new type of neural network with two modules: one for nonfeedback part with input data delayed by the embedding time, and a second one for the feedback part with input data delayed by the feedback time. The method is applied to both simulated and experimental data from an electronic analog circuit of the Mackey–Glass system. Better results are obtained for the modular than for feedforward neural networks for the same number of parameters. It is found that the complexity of the neural network model required to reconstruct nonlinear dynamics does not increase with the delay time. Synchronization between the data and the model with diffusive coupling is also achieved. We have also shown by iterating the model from the present point that the dynamics can be predicted with a forecast horizon larger than the feedback delay time.     

Surface-driven instability and enhanced relaxation in the dynamics of a nonequilibrium interface

We determine the stability of a nonequilibrium interface between two coexisting solid phases in the presence of a weak external field. Starting at the coarsegrained (Cahn-Hilliard) level, we use the method of matched asymptotics to derive the macroscopic interfacial dynamics. We then show that the external field leads to an instability due to flux along the interface, in contrast with the more common Mullins-Sekerka type instability, which involves fluxes normal to the interface. We also find that the external field produces an important modification of the Gibbs-Thomson relation. With these results, we perform the linear stability analysis for an approximately flat interface. If the field is tangent to the interface, the modification of the Gibbs-Thomson relation is important and the interface is stabilized. If the field is normal to the interface, the surface flux is important, and the effect can be stabilizing or destabilizing, but the orientational dependence is opposite what would be obtained if the Mullins-Sekerka instability dominates. Numerical simulations are performed to study the effect of the surface current and are in agreement with our analytical results.