Dynamics of semi-flexible tethered sheets

The dynamics of a semi-flexible sheet or tethered membrane in a solvent is studied using the method of stochastic rotation dynamics. Hydrodynamic interactions between different parts of the sheet are naturally included in this method. We confirm the scaling law for the radius of gyration versus sheet size predicted for a self-avoiding tethered membrane. The mean-square displacement shows both sub-diffusive and diffusive behavior similar to linear polymers. In the intermediate scattering function the sub-diffusive behavior appears as stretched exponential which we reproduce in our simulations. Thereby, we confirm an early prediction between the roughness and the sub-diffusion exponent derived from Zimm dynamics (E. Frey, D.R. Nelson, J. Phys. I 1, 1715 (1991)). Finally, we show that the diffusion coefficient of the square sheet is inversely proportional to the edge length of the sheet again in good agreement with theoretical predictions.     

Simulating the dynamics of flexible bodies and vortex sheets

We present a numerical method for the dynamics of a flexible body in an inviscid flow with a free vortex sheet. The formulation is implicit with respect to body variables and explicit with respect to the free vortex sheet. We apply the method to a flexible foil driven periodically in a steady stream. We give numerical evidence that the method is stable and accurate for a relatively small computational cost. A continuous form of the vortex sheet regularization permits continuity of the flow across the body’s trailing edge. Nonlinear behavior arises gradually with respect to driving amplitude, and is attributed to the rolling-up of the vortex sheet. Flow quantities move across the body in traveling waves, and show large gradients at the body edges. We find that in the small-amplitude regime, the phase difference between heaving and pitching which maximizes trailing edge deflection also maximizes power output; the phase difference which minimizes trailing edge deflection maximizes efficiency.     

Microscopic description of aging dynamics: fluctuation-dissipation relations,effective temperature,and heterogeneities

We consider the dynamics of a diluted mean-field spin glass model in the aging regime. The model presents a particularly rich heterogeneous behavior. In order to catch this behavior, we perform a spin-by-spin analysis for a given disorder realization. We confirm the connection between statics and dynamics at the level of single degrees of freedom. Moreover, working with single-site quantities, we can introduce a new response-vs-correlation plot, which clearly shows how heterogeneous degrees of freedom undergo coherent structural rearrangements. We discuss the general scenario which emerges from our work and (possibly) applies to more realistic glassy models. Interestingly enough, some features of this scenario can be understood recurring to thermometric considerations.     

Dynamic criticality in glass-forming liquids

We propose that the dynamics of supercooled liquids and the formation of glasses can be understood from the existence of a zero-temperature dynamical critical point. To support our proposal, we derive a dynamic field theory for a generic kinetically constrained model, which we expect to describe the dynamics of a supercooled liquid. We study this field theory using the renormalization group (RG). Its long time behavior is dominated by a zero-temperature critical point, which for d>2 belongs to the directed percolation universality class. Molecular dynamics simulations seem to confirm the existence of dynamic scaling behavior consistent with the RG predictions.     

Stochastic Event-Driven Molecular Dynamics

A novel Stochastic Event-Driven Molecular Dynamics (SEDMD) algorithm is developed for the simulation of polymer chains suspended in a solvent. SEDMD combines event-driven molecular dynamics (EDMD) with the Direct Simulation Monte Carlo (DSMC) method. The polymers are represented as chains of hard-spheres tethered by square wells and interact with the solvent particles with hard-core potentials. The algorithm uses EDMD for the simulation of the polymer chain and the interactions between the chain beads and the surrounding solvent particles. The interactions between the solvent particles themselves are not treated deterministically as in EDMD, rather, the momentum and energy exchange in the solvent is determined stochastically using DSMC. The coupling between the solvent and the solute is consistently represented at the particle level retaining hydrodynamic interactions and thermodynamic fluctuations. However, unlike full MD simulations of both the solvent and the solute, in SEDMD the spatial structure of the solvent is ignored. The SEDMD algorithm is described in detail and applied to the study of the dynamics of a polymer chain tethered to a hard-wall subjected to uniform shear. SEDMD closely reproduces results obtained using traditional EDMD simulations with two orders of magnitude greater efficiency. Results question the existence of periodic (cycling) motion of the polymer chain.     

Conformational fluctuations of a tethered polymer in uniform flow

The decay of correlations in the conformational fluctuations of a tethered polymer subjected to a uniform flow is analyzed in terms of relaxation times and associated normal modes. These quantities are calculated numerically from Brownian dynamics simulations of several bead spring polymer models. In this way, the influence of different effects like a finite extensibility of the springs and excluded-volume as well as hydrodynamic interactions between the beads on the decay of fluctuations is identified. Moreover, by comparison of the simulation results to analytically tractable blob models with corresponding assumptions, the capability of the tensile-blob picture to predict relaxation times and modes is assessed. For excluded-volume and hydrodynamic interactions a crossover to Rouse-like behavior occurs when the flow velocity and hence the polymer deformation exceeds a certain value. For finitely extensible springs, in contrast, the relaxation times decrease monotonically with increasing polymer deformation. This latter behavior differs from assumptions often used in rheological modeling by dumbbells and is not captured by the blob model.Received: 4 April 2003, Published online: 12 August 2003PACS: 83.80.Rs Polymer solutions - 83.10.Mj Molecular dynamics, Brownian dynamics - 36.20.Ey Conformation (statistics and dynamics) - 47.50. + d Non-Newtonian fluid flows     

Vibration analysis of defected and pristine triangular single-layer graphene nanosheets

This paper investigates the vibration behavior of pristine and defected triangular graphene sheets; which has recently attracted the attention of researchers and compare these two types in natural frequencies and sensitivity. Here, the molecular dynamics method has been employed to establish a virtual laboratory for this purpose. After measuring the different parameters obtained by the molecular dynamics approach, these data have been analyzed by using the frequency domain decomposition (FDD) method, and the dominant frequencies and mode shapes of the system have been extracted. By analyzing the vibration behaviors of pristine triangular graphene sheets in four cases (right angle of 45-90-45 configuration, right angle of 60-90-30 configuration, equilateral triangle and isosceles triangle), it has been demonstrated that the natural frequencies of these sheets are higher than the natural frequency of a square sheet, with the same number of atoms, by a minimum of 7.6% and maximum of 26.6%. Therefore, for increasing the resonance range of sensors based on 2D materials, non-rectangular structures, and especially the triangular structure, can be considered as viable candidates. Although the pristine and defective equilateral triangular sheets have the highest values of resonance, the sensitivity of defective (45,90,45) triangular sheet is more than other configurations and then, defective (45,90,45) sheet is the worst choice for sensor applications.     

The kinetics of carbon nanostructure 2D–3D transformation

The gas-phase process of formation of carbon nanostructures in an arc discharge plasma is considered. Most attention is paid to one of the key stages of the formation of these nanostructures, the transformation of plane structures into three-dimensional. The rolling up of a plane graphite sheet into a nanostructure similar to fullerene or a nanotube was simulated by the molecular dynamics method. The simulation data were described by a mechanism based on the generation of defects on the surface of the sheet. A set of elementary system structural transformations was determined, and the kinetic scheme describing the behavior of defects constructed. The lowest temperature of the observation of rolling up in practice was estimated.     

Hysteresis and bistability in a realistic cell model for calcium oscillations and action potential firing

Many cells reveal oscillatory behavior. Some cells reveal action-potential firing resulting from Hodgkin-Huxley (HH) type dynamics of ion channels in the cell membrane. Another type of oscillation relates to periodic inositol triphospate (IP3)-mediated calcium transients in the cytosol. In this study we present a bifurcation analysis of a cell with an excitable membrane and an IP3-mediated intracellular calcium oscillator. With IP3 concentration as a control parameter the model reveals a complex, rich spectrum of both stable and unstable solutions with hysteresis corresponding to experimental data. Our results reveal the emergence of complex behavior due to interactions between subcomponents with a relatively simple dynamical behavior.     

Analytic solution for magnetohydrodynamic boundary layer flow of Casson fluid over a stretching/shrinking sheet with wall mass transfer

In this analysis,the magnetohydrodynamic boundary layer flow of Casson fluid over a permeable stretching/shrinking sheet in the presence of wall mass transfer is studied.Using similarity transformations,the governing equations are converted to an ordinary differential equation and then solved analytically.The introduction of a magnetic field changes the behavior of the entire flow dynamics in the shrinking sheet case and also has a major impact in the stretching sheet case.The similarity solution is always unique in the stretching case,and in the shrinking case the solution shows dual nature for certain values of the parameters.For stronger magnetic field,the similarity solution for the shrinking sheet case becomes unique.     

Crumpling of a stiff tethered membrane

A first-principles numerical model for crumpling of a stiff tethered membrane is introduced. This model displays wrinkles, ridge formation, ridge collapse, and initiation of stiffness divergence. The amplitude and wavelength of the wrinkles and the scaling exponent of the stiffness divergence are consistent with both theory and experiment. Close to the stiffness divergence further buckling is hindered by the nonzero thickness of the membrane, and its elastic behavior becomes similar to that of dry granular media. No change in the distribution of contact forces can be observed at the crossover, implying that the network of ridges is then simultaneously a granular force-chain network.     

Resin dynamics contributes to the NMR line broadening of organic molecules grafted onto a polystyrene resin

Despite the use of high resolution magic angle spinning NMR, the NMR linewidth of anchored molecules on the commonly used Merrifield solid phase resins remains larger than that of the corresponding molecules in solution. We investigate the different mechanisms that might be at the origin of this line broadening. Experimentally, we use the CPMG method to determine the (15)N relaxation times of a tethered tripeptide and show that the slow resin dynamics significantly contributes to the transverse relaxation.     

Brownian dynamics in Fourier space: membrane simulations over long length and time scales

A simulation algorithm for elastic membrane sheets is presented. Overdamped stochastic dynamics including hydrodynamic coupling to surrounding solvent and arbitrary external forces are generated by employing Fourier modes of the sheet as the primary dynamic variables. Simulations over the micron length scale and second time scale are easily achieved. The dynamics of a lipid bilayer attached to an underlying network of cytoskeletal filaments is used to estimate the diffusion constant of membrane-bound proteins on the surface of the red blood cell.     

Collapse and stability of necklace beams in Kerr media

We investigate the spatial dynamics of optical necklace beams in Kerr media. For powers corresponding to less than the critical power for self-focusing per bead, we experimentally confirm the confinement of these necklace beams as proposed in [Phys. Rev. Lett. 81, 4851 (1998)10.1103/PhysRevLett.81.4851]. At higher powers, we observe a transition from collective necklace behavior to one in which the beads of the necklace collapse independently. We observe that, below the transition power, the perturbed necklace still behaves in a collective manner with coupling between individual beads but that, at higher powers, it undergoes a similar transition to a decoupled state of the necklace.     

A novel atomic force microscope operating in liquid with open probe unit and optimized laser tracking system

A novel atomic force microscope （AFM） for large samples to be measured in liquid is developed. An innovative laser beam tracking system is proposed to eliminate the tracking and feedback errors. The open probe design of the AFM makes the operation in liquid convenient and easy. A standard 1200-lines/mm grating and a sheet of filter paper axe imaged respectively in air and liquid to confirm its performance. The corrosion behavior of aluminum surface in 1-mol/L NaOH solution is further investigated by the AFM. Experimental results show that the system can realize wide range （20 × 20 （μm）） scanning for large samples both in air and liquid, while keeping nanometer order resolution in liquid by eliminating the tracking and feedback error.     

Grid-based photogrammetry system for large scale sheet metal strain measurement

This paper presents a new approach to fast strain measurement with high accuracy for large scale sheet metal based on the surface circular grid and digital close range photogrammetry. A multi-block measuring method of discretization is implemented to archive large scale measurement. The sheet metal is separated into several blocks for respective calculating and joined together by common reference points. A surface circular searching method is presented for fast and robust 3D grid generation. A flexible bundle adjustment method is proposed for large amount 3D grid nodes reconstruction, which employs the conception of sampling points and is proved to be efficient. Furthermore, a multi-stage grid registration method is introduced to improve the accuracy of strain field by correcting the true deformation gradient tensor. A novel system is developed and performances well in actual large scale sheet metal strain measurement. Two accuracy tests confirm that the system strain measurement error is less than 0.2%.     

Numerical bifurcation analysis of two coupled FitzHugh-Nagumo oscillators

The behavior of neurons can be modeled by the FitzHugh-Nagumo oscillator model, consisting of two nonlinear differential equations, which simulates the behavior of nerve impulse conduction through the neuronal membrane. In this work, we numerically study the dynamical behavior of two coupled FitzHugh-Nagumo oscillators. We consider unidirectional and bidirectional couplings, for which Lyapunov and isoperiodic diagrams were constructed calculating the Lyapunov exponents and the number of the local maxima of a variable in one period interval of the time-series, respectively. By numerical continuation method the bifurcation curves are also obtained for both couplings. The dynamics of the networks here investigated are presented in terms of the variation between the coupling strength of the oscillators and other parameters of the system. For the network of two oscillators unidirectionally coupled, the results show the existence of Arnold tongues, self-organized sequentially in a branch of a Stern-Brocot tree and by the bifurcation curves it became evident the connection between these Arnold tongues with other periodic structures in Lyapunov diagrams. That system also presents multistability shown in the planes of the basin of attractions.     

Impact of higher-order effects on dissipative soliton in metamaterials

We study the influence of higher-order effects such as third order dispersion (TOD), fourth order dispersion (FOD), quintic nonlinearity (QN), self steepening (SS) and second order nonlinear dispersion (SOND) on the dynamics of dissipative soliton (DS) in metamaterials. Considering each higher-order effect as a perturbation to the system and following Lagrangian variational method, we demonstrate stable dynamics of DS as a result of the interplay between different higher-order effects. We also perform numerical analysis to confirm the analytical results.     

载能氢原子与石墨(001)面碰撞过程中的能量传递行为的分子动力学研究

本文采用分子动力学方法研究了单一载能氢原子与石墨碰撞时氢原子被石墨反射、 吸附和石墨被氢原子穿透的发生系数以及碰撞中的能量传递机理. 研究发现: 与单层石墨相比, 多层石墨之间的长程相互作用增加了氢原子发生反射的能量范围, 尤其当入射能量大于20.0 eV时, 对反射过程的影响很明显; 当氢原子的入射能量大于25.0 eV时, 有一定的概率穿透四层石墨; 当氢原子入射能量高于28.0 eV时, 载能氢原子的能量传递给第二层石墨烯的比传递给第一层石墨烯的多. 这些结果对理解聚变反应中, 碳基材料的化学腐蚀及氚滞留有重要意义.