Reversing the Brazil-nut effect: competition between percolation and condensation

We report on experiments on vertically shaken binary granular mixtures, which separate into their components due to the external excitation. This well-known phenomenon, where large particles rise to the top of the mixture, is called the Brazil-nut effect. Recent theoretical findings predict also a reverse Brazil-nut effect, where large particles sink to the bottom of the container. We choose spherical beads of various diameters and materials in order to observe the transition from Brazil-nut effect to its reverse form. The direction of demixing depends sensitively on the external excitation, so that it is possible to switch between both effects for a given mass density ratio.     

巴西果效应分离过程的计算颗粒力学模拟研究

采用离散单元模型对巴西果问题进行了模拟研究,采用本数学模型可以准确地预测出垂直机械振动导致的不同大小颗粒的分离现象.分析了影响振动床内颗粒分层的因素,讨论了振动频率、振动幅度等参数对分层的影响,发现振动频率和振动幅度会对分离效果造成较大的影响.当振动频率或振动幅度较小时,颗粒整体分离效果都较差,但分离的稳定性较好,当振动频率或振动幅度较大时,整体分离效果仍然较差,同时分离的稳定性也较差,振动分离过程中存在一个频率和振幅适中的最优操作点. 关键词： 分层 振动 模式形成 离散单元方法     

Three-dimensional site percolation problem and effective-medium theory: A computer study

A site percolation approach to classical transport in disordered two-phase materials is presented. A Monte Carlo computer experiment gives the bulk conductivity of a 30 x 30 x 30 site simple cubic resistor network consisting of two kinds of unit resistor with different conductance. A modified effective-medium theory predicts very accurately the bulk conductivity of the network. This theory is found to agree well with available data for the thermal conductivity of real two-phase materials: glass particle-silicon rubber; glass fiber-plastics; air-saturated porous sandstone; and air-saturated fire brick.     

Duality relations in the nonlinear percolation problem: Theory and numerical simulation

The problem of a nonlinear current flow in a heterophase medium formed by a random mixture of linear and nonlinear phases is investigated. The duality relation is derived for the critical indices describing the effective response of a heterogeneous system. The critical index is calculated at the percolation threshold (for equal concentrations of the phases). The nonlinear percolation problem is simulated numerically for degrees k = 3, 5, and 7 of the nonlinear phase. The existence of a duality relation for critical indices is established in a range of phase concentrations.     

Convergence of mean-field approximations in site percolation and application of CAM tod=1 further-neighbors percolation problem

We study the mean-field approximation in the site-percolation problem. Using the analog of the Simon-Lieb inequality, we show that the mean-field critical probability is convergent to the exact value when the size of clusters tends to infinity. Applying this approximation to the one-dimensional further-neighbor percolation problem and calculating some critical coefficients, we prove that the asymptotic scaling relations predicted by the coherent-anomaly method are satisfied.     

On the gauge Potts model and the plaquette percolation problem

It is shown that the ar 1, 0 limit of the Potts gauge model describes plaquette percolation as the analogous limit of the spin model describes bond percolation. These results further strengthen the connection between gauge theories and random surfaces. Moreover, further generalizations to other types of gauge theories are presented.     

Anisotropic percolation and the d-dimensional surface roughening problem

We review recent numerical simulations of several models of interface growth in d-dimensional media with quenched disorder. These models belong to the universality class of anisotropic diode-resistor percolation networks. The values of the roughness exponent δ=0.63±0.01 (d=1+1) and δ=0.48±0.02 (d=2+1) are in good agreement with our recent experiments. The values of δ in higher dimensions (δ=0.38±0.03 in d=4 and δ=0.27±0.05 in d=5) do not support a recent theoretical conjecture.     

Variation of cluster properties in lattice percolation problem: A prototype of phase transition

Properties of clusters appearing in the site percolation problem on square and cubic lattices are expressed in a way that emphasizes the thermodynamic analogy. It is shown that the analog of the specific heat exhibits expected critical behaviour as a function of the analog of the temperature. The results support the notion that the partition of the specific heat of Ising systems (Borstnik and Lukman, Phys. Rev. E 60, 2595 (1999)) into the structural and populational component is a meaningful one. Another cluster property which is taken under the scrutiny is the fractal dimensionality of clusters which also indicates the presence of phase transition. Received 31 August 1999 and Received in final form 14 February 2000     

Selective sublattice dilution in ordered magnetic compounds: A new kind of percolation problem

A magnetic binary system is considered whereA-atoms andB-atoms occupy different sublattices but it is an exchangeJ _AB which is responsible for magnetic ordering. Diluting such a system with nonmagnetic atoms it is natural to treat situations where the dilution probability is different for both sublattices. In particular the extreme cases, where either only theA-sublattice or only theB-sublattice is diluted, is discussed for a variety of lattice structures atT=0. It is shown that in some cases the problem can be reduced to ordinary site- or bond percolation problems, while in other cases a new kind of percolation problem arises. Particular attention is paid to the case of spinel structures, and a discussion of recent experiments on the mixed systemyMg₂TiO₄–(1–y)MgFe₂O₄ is given. It is shown that additional frustration effects due to competing interactions are necessary to explain the breakdown of magnetic order upon dilution in that material. Critical exponents for this new kind of percolation problem are also estimated by Monte-Carlo methods and it is suggested that it belongs to the same universality class as usual percolation. As a check of the numerical procedures we redetermine the percolation concentrations of both sublattices of the spinel structure, and find that some of the earlier work on this problem is rather inaccurate.     

Interplay between fermion condensation and density-wave instability

It is shown that the phase transition of density-wave origin in homogeneous liquids is preceded by fermion condensation. Thus fermion condensation may be observed in low-density electron liquids, neutron stars, and liquid He³. Three-dimensional (3D) and two-dimensional (2D) liquids are considered. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 3, 242–247 (10 February 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Competition of Brazil nut effect,buoyancy, and inelasticity induced segregation in a granular mixture

It has been recently reported that a granular mixture in which grains differ in their restitution coefficients presents segregation: the more inelastic particles sink to the bottom. When other segregation mechanisms as buoyancy and the Brazil nut effect are present, the inelasticity induced segregation can compete with them. First, a detailed analysis, based on numerical simulations of two dimensional systems, of the competition between buoyancy and the inelasticity induced segregation is presented, finding that there is a transition line in the parameter space that determines which mechanism is dominant. In the case of neutrally buoyant particles having different sizes the inelasticity induced segregation can compete with the Brazil nut effect (BNE). Reverse Brazil nut effect (RBNE) could be obtained at large inelasticities of the intruder. At intermediate values, BNE and RBNE coexist and large inelastic particles are found both near the bottom and at the top of the system.     

Intruder trajectory tracking in a three-dimensional vibration-driven granular system: Unveiling the mechanism of the Brazil nut effect

We employ a Hall-effect magnetic sensor array to accurately track the trajectory of a single magnetic sphere, referred to as the “intruder,” within a three-dimensional vibro-fluidized granular bed to unravel the underlying physical mechanism governing the motion of the intruder. Within the acceleration range of 3.5 g ≥ Γ ≥ 1.5 g, we find that, regardless of the intruder’s initial position, it consistently reaches the same equilibrium depth when the vibration acceleration(Γ) and frequency(ω) are ...     

The finite element duct eigenvalue problem: An improved formulation with Hermitian elements and no-flow condensation

Hermitian elements are used in a finite element solution for the eigenvalue problem in lined ducts with flow. These elements give significantly greater accuracy for reduced dimensionality when compared with Lagrangian elements. Spurious mode generation associated with the Lagrangian formulation is eliminated. A dramatic improvement in the ratio of the number of reliable eigenvalues to the total number of computed eigenvalues is effected by the use of a condensation scheme based on the no-flow eigenvectors. Results are presented for two dimensional and axisymmetric ducts. In the axisymmetric case good resolution is obtained even for high order, high frequency modes by the use of continuously graded meshes.     

Growth Cone Pathfinding: a competition between deterministic and stochastic events

Background  

Growth cone migratory patterns show evidence of both deterministic and stochastic search modes.     

Connection between the thermodynamical and the percolation models of nuclear fragmentation

The connection is investigated between the percolation approach to nuclear fragmentation and the statistical multifragmentation model based on thermodynamical equilibrium concepts. The relation between the percolation parameter and the average excitation energy per nucleon of the fragmentating system has been investigated.