Stationary shapes of deformable particles moving at low Reynolds numbers

We introduce an iterative solution scheme in order to calculate stationary shapes of deformable elastic capsules which are steadily moving through a viscous fluid at low Reynolds numbers. The iterative solution scheme couples hydrodynamic boundary integral methods and elastic shape equations to find the stationary axisymmetric shape and the velocity of an elastic capsule moving in a viscous fluid governed by the Stokes equation. We use this approach to systematically study dynamical shape transitions of capsules with Hookean stretching and bending energies and spherical resting shape sedimenting under the influence of gravity or centrifugal forces. We find three types of possible axisymmetric stationary shapes for sedimenting capsules with fixed volume: a pseudospherical state, a pear-shaped state, and buckled shapes. Capsule shapes are controlled by two dimensionless parameters, the Föppl-von-Kármán number characterizing the elastic properties and a Bond number characterizing the driving force. For increasing gravitational force the spherical shape transforms into a pear shape. For very large bending rigidity (very small Föppl-von-Kármán number) this transition is discontinuous with shape hysteresis. The corresponding transition line terminates, however, in a critical point, such that the discontinuous transition is not present at typical Föppl-von-Kármán numbers of synthetic capsules. In an additional bifurcation, buckled shapes occur upon increasing the gravitational force.     

准静态颗粒介质的弹性势能弛豫分析

颗粒体系是典型的多体相互作用体系, 具有多重的能量亚稳态. 对于准静态颗粒体系, 引入构型颗粒温度T_c描述弹性势能涨落. 本文认为平衡的体系具有一定的构型颗粒温度T_a, 其量值反映了其结构特征. 当外界扰动激发的构型颗粒温度超出T_a时, 产生不可逆过程. 通过对应力松弛过程的分析, 发现(T_c-T_a)激发了弹性弛豫, 且(T_c-T_a)越大则松弛过程中应力变化越大, 最终构型颗粒温度T_c→T_a时,宏观应力松弛结束,体系达到新的能量亚稳态.     

Towards a Landau–Ginzburg-Type Theory for Granular Fluids

In this paper we show how, under certain restrictions, the hydrodynamic equations for the freely evolving granular fluid fit within the framework of the time dependent Landau–Ginzburg (LG) models for critical and unstable fluids. The granular fluid, which is usually modeled as a fluid of inelastic hard spheres (IHS), exhibits two instabilities: the spontaneous formation of vortices and of high density clusters. We suppress the clustering instability by imposing constraints on the system sizes, in order to illustrate how LG-equations can be derived for the order parameter, being the rate of deformation or shear rate tensor, which controls the formation of vortex patterns. From the shape of the energy functional we obtain the stationary patterns in the flow field. Quantitative predictions of this theory for the stationary states agree well with molecular dynamics simulations of a fluid of inelastic hard disks.     

Acoustic streaming in a rotating fluid

Acoustic streaming theory is derived that is applicable to a fluid that is slow moving in a reference frame that rotates with a constant angular velocity omega. A simplified streaming equation is obtained for the special case in which the acoustic angular frequency omega is large relative to omega, and the change in fluid density due to rotation alone is negligible. For this special case it is shown that the "driving force" for the acoustic streaming is independent of omega. Thus, if no acoustic streaming is present in a fluid system that is stationary, then no steady-state acoustic streaming is predicted for a similar system that rotates with constant angular velocity. For a system in which acoustic streaming is present, the flow behavior depends on the relative magnitudes of the Coriolis forces and the viscous forces. If the Ekman number is large (that is, the viscous force dominates) then the predicted flow is identical to that which would exist in a stationary system. If, on the other hand, the Ekman number is small then the Coriolis force dominates and the component of flow in the direction of the axis of rotation can be much smaller in the rotating system than in a similar system at rest.     

Convective Cahn-Hilliard models: from coarsening to roughening

In this paper we demonstrate that convective Cahn-Hilliard models, describing phase separation of driven systems (e.g., faceting of growing thermodynamically unstable crystal surfaces), exhibit, with the increase of the driving force, a transition from the usual coarsening regime to a chaotic behavior without coarsening via a pattern-forming state characterized by the formation of various stationary and traveling periodic structures as well as structures with localized oscillations. Relation of this phenomenon to a kinetic roughening of thermodynamically unstable surfaces is discussed.     

Phase Transition and Critical Phenomenon Occurring in Granular Matter

We investigate the granular flow states in a channel with bottleneck by molecular dynamics simulations.Our study is restricted only on a selected key area rather than on the whole system to focus on the flow properties of a single granular state.A random force field is introduced to control the granular temperature.It is also pointed out that the flow rate in the granular flow can be correlated with the pressure,which leads us to carry out a comprehensive study similar to the classical study for general liquid-gas phase transition.Our results show that the dilute flow state and the dense flow state of the granules are similar to the gas state and the liquid state of general substances,respectively,and the properties of phase transition and critical phenomenon are also similar to those occurring in general substances.     

Stability and bifurcations of a stationary state for an impact oscillator

The motion of a vibroimpacting one-degree-of-freedom model is analyzed. This model is motivated by the behavior of a shearing granular material, in which a transitional phenomenon is observed as the concentration of the grains decreases. This transition changes the motion of a granular assembly from an orderly shearing between two blocks sandwiching a single layer of grains to a chaotic shear flow of the whole granular mass. The model consists of a mass-spring-dashpot assembly that bounces between two rigid walls. The walls are prescribed to move harmonically in opposite phases. For low wall frequencies or small amplitudes, the motion of the mass is damped out, and it approaches a stationary state with zero velocity and displacement. In this paper, the stability of such a state and the transition into chaos are analyzed. It is shown that the state is always changed into a saddle point after a bifurcation. For some parameter combinations, horseshoe-like structures can be observed in the Poincare sections. Analyzing the stable and unstable manifolds of the saddle point, transversal homoclinic points are found to exist for some of these parameter combinations. (c) 1994 American Institute of Physics.     

Shear stress fluctuations in the granular liquid and solid phases

We report on experimentally observed shear stress fluctuations in both granular solid and fluid states, showing that they are non-Gaussian at low shear rates, reflecting the predominance of correlated structures (force chains) in the solidlike phase, which also exhibit finite rigidity to shear. Peaks in the rigidity and the stress distribution's skewness indicate that a change to the force-bearing mechanism occurs at the transition to fluid behavior, which, it is shown, can be predicted from the behavior of the stress at lower shear rates. In the fluid state stress is Gaussian distributed, suggesting that the central limit theorem holds. The fiber bundle model with random load sharing effectively reproduces the stress distribution at the yield point and also exhibits the exponential stress distribution anticipated from extant work on stress propagation in granular materials.     

Force fluctuations in a vertically pushed granular column

We present series of experiments on the resistance force encountered by a bottom piston pushing a vertical granular column confined in a two-dimensional cell. We show that, due to the presence of friction at the boundaries and between the grains, the signal shows many complex features. At slow driving velocities, we observe a transition to a stick-slip dynamic instability. Depending on the granular material used, the elementary stick-slip events may either be well characterized or largely distributed. We present a statistical study on the waiting time between events and the distribution of energy release as a function of the spring stiffness and the driving velocity. Received 5 August 1998 and Received in final form 22 October 1998     

A DFT investigation into the structure and energetics for nonadiabatic proton transfer in the benzophenone/N,N‐dimethylaniline contact radical ion pair

For the past 60 years, the standard model for the interpretation of the mechanism for proton transfer has been based upon transition‐state theory, which posits that the transition state is found in the proton transfer coordinate involving the breaking and making of bonds. However, the observed dynamics of proton transfer within the triplet contact radical ion pair, derived from a variety of substituted benzophenones complexed with N,N‐dimethylaniline, cannot be accounted for within the standard model for proton transfer. Instead, the kinetic behavior is in accord with nonadiabatic proton transfer theory that has the transition state in the solvent coordinate. Evidence for the importance of the solvent coordinate comes from the existence of an inverted region; as the driving force for reaction increases, the rate of proton transfer decreases. This kinetic behavior is not found in the standard model. The present paper employs density function theory to examine the question as to whether the inverted region can be attributed to the transition state being in the solvent coordinate or whether the inverted region is an artifact produced by changes in the structure of the triplet contact radical ion pair with the placement of substituents upon the p,p′ positions of benzophenone. It is concluded that the inverted region is not an artifact of substituent effects upon structure. These results support the conclusion that the transition state for proton transfer resides in the solvent coordinate and challenges the validity of the standard model for interpreting the mechanism of proton transfer. Copyright © 2014 John Wiley & Sons, Ltd.     

Oscillatory patterns in a rotating aqueous suspension

Suspensions of granular material in glycerin-water mixtures agitated in horizontally aligned rotating tubes show a whole variety of patterns. The stationary pattern of a homogeneous distribution and a chain of rings have been investigated before. Here we report on two types of oscillatory states in the same system. For a certain range of the rotation frequency and sufficiently high viscosity traveling waves propagate with constant velocity back and forth along the tube in an almost homogeneous distribution of sedimenting particles. The transition from a stationary to the traveling-wave state is found to be an imperfect supercritical bifurcation. The dependence of the wave length and speed on the tube's rotation frequency and the dynamic viscosity of the fluid are determined. Experiments with low viscosities show no traveling waves but low-frequency oscillations, when the previously known chain of rings undergoes a secondary instability.     

Random systems,turbulence and disordering fields

The statistical theory of random processes is cast into a Lagrangian form. The formalism requires the existence of an arbitrarily weak random stirring force, playing the role of a disordering field. In scale invariant systems the coupling strength of the weak stirring force can be scaled out and it disappears from the theory. The formalism is applied to the turbulent flow of an incompressible fluid; in particular, we derive the Feynman rules by means of which the distribution of fluctuations around an average flow can be determined. The formalism is further illustrated on the example of a stationary fluid flow between parallel planes: an approximate formula for the correlation function of vorticities is obtained, which is expected to be valid at large Reynolds numbers.     

Numerical investigation of the tangential stress effects on a fluid flow structure in a partially open cavity

Mathematical and numerical modeling of fluid flows in the domains with free boundaries under co-current gas flow is widely investigated nowadays. A stationary problem of fluid motion in a rectangular cavity with a non-deformed free boundary is studied in a two-dimensional statement. The tangential stresses created on the free boundary by an adjoint gas flow are considered to be a driving force for a fluid motion. The influence of the cavity geometry (cavity aspect ratio) and of the free boundary (length of the open part of the boundary) on the velocity field is investigated numerically. The simulations are carried out for different values of the gas Reynolds numbers. The characteristic values for the flow parameters as well as geometrical characteristics described in this paper are motivated by the main features of the CIMEX-1 experiments prepared for the International Space Station. The paper presents examples of the fluid flow structure in the open cavities and conclusions.     

On granular surface flow equations

Conservation equations are written for surface flows (either fluid or granular). The particularity of granular surface flows is then pointed out, namely that the depth of the flowing layer is not a priori fixed, leading to open equations. It is shown how some hypothesis on the flowing layer allows to close the system of equations. A possible hypothesis, similar to that made for a fluid layer, but inspired from granular flow experiments, is presented. The force acting on the flowing layer is discussed. Averaging over the flowing depth, as in shallow water theory, then allows to transform these conservation laws into equations for the evolution of the profile of a granular pile. Apart from their interest for building models, these conservation laws can be used to measure experimentally the effective forces acting on a flowing layer. Received 25 July 1998 and Received in final form 14 January 1999     

环形耦合Duffing振子间的同步突变

以环形耦合Duffing振子系统为研究对象,分析了耦合振子间的同步演化过程.发现在弱耦合条件下,如果所有振子受到同一周期策动力的驱动,那么系统在经历倍周期分岔、混沌态、大尺度周期态的相变时,各振子的运动轨迹之间将出现由同步到不同步再到同步的两次突变现象.利用其中任何一次同步突变现象可以实现系统相变的快速判别,并由此补充了利用倍周期分岔与混沌态的这一相变对微弱周期信号进行检测的方法. 关键词： Duffing振子 同步突变 相变 微弱信号检测     

离散颗粒层被横向推移过程中的力学行为研究

研究发现,颗粒物质层被匀速推移挤压过程中,所需推移力先以线性规律增加,在某一确定点后,则会以指数规律增加.而颗粒物质是由众多离散颗粒组成的软凝聚态物质,其宏观上反映的是离散颗粒的个体性质和凝聚态物质的集体效应.颗粒与颗粒之间以及颗粒与边界之间的细观尺度接触力链的构成以及演变规律将会直接影响各种宏观受力情况,其摩擦力与挤压力便是力链的主要构成形式.围绕着定量描述细观力链特征,从而揭示力的变化规律这一目标,采用计算机模拟的方法,依照球形颗粒Hertz法向接触理论和Mindlin-Deresiewicz切向接触理论,对重力作用下不同数目的三维等径球体颗粒层的推移情况进行了离散元仿真模拟,量化分析了推移力变化规律、各摩擦力变化规律以及力链分布规律,发现摩擦力与挤压力在颗粒堆积的不同阶段对力链的构成起到了不同的主次作用,使得力链发生强弱演变,从而发现了推移颗粒物质层时推移力的变化规律及原因.这些结果有利于从力链角度揭示颗粒内部和颗粒与各边界之间的受力情况.     

Jamming as a critical phenomenon: a field theory of zero-temperature grain packings

A field theory of frictionless grain packings in two dimensions is shown to exhibit a zero-temperature critical point at a nonzero value of the packing fraction. The zero-temperature constraint of force balance plays a crucial role in determining the nature of the transition. Two order parameters, , the deviation of the average number of contacts from the isostatic value, and , the average magnitude of the force per contact, characterize the transition from the jammed (high packing fraction) to the unjammed (low packing fraction state). The critical point has a mixed character with the order parameters showing a jump discontinuity but with fluctuations of the contact force diverging. At the critical point, the distribution of phi shows the characteristic plateau observed in static granular piles. The theory makes falsifiable predictions about the spatial fluctuations of the contact forces.     

Crack propagation as a free boundary problem

A sharp interface model of crack propagation as a phase transition process is discussed. We develop a multipole expansion technique to solve this free boundary problem numerically. We obtain steady state solutions with a self-consistently selected propagation velocity and shape of the crack, provided that elastodynamic effects are taken into account. Also, we find a saturation of the steady state crack velocity below the Rayleigh speed, tip blunting with increasing driving force, and a tip splitting instability above a critical driving force.     

Insulator-metal transition in biased finite polyyne systems

A method for the study of the electronic transport in strongly coupled electron-phonon systems is formalized and applied to a model of polyyne chains biased through metallic Au leads. We derive a stationary non equilibrium polaronic theory in the general framework of a variational formulation. The numerical procedure we propose can be readily applied if the electron-phonon interaction in the device hamiltonian can be approximated as an effective single particle electron hamiltonian. Using this approach, we predict that finite polyyne chains should manifest an insulator-metal transition driven by the non-equilibrium charging which inhibits the Peierls instability characterizing the equilibrium state.