Transition from homogeneous to inhomogeneous flows in a lattice-gas binary mixture of slender particles

We study the unidirectional flow of a binary mixture of biased-random walkers on a square lattice under a periodic boundary. The lattice-gas mixture consists of two types of slender particles (walkers) which have different biases (drift coefficients). When the density is higher than a critical value, a dynamical transition occurs from the homogeneous flow to the inhomogeneous flow and clogging appears. The inhomogeneous state returns to the homogeneous congested flow with further increasing density. The clogging does not appear in the unidirectional flow of the conventional lattice-gas binary mixture of single-site particles. The jamming (clogging) transition is clarified for various sizes of slender particles.     

Traffic flow of mobile objects through obstacles: Turning and translational objects

We study the unidirectional flow of mobile objects through obstacles on a square lattice. Two models are presented: one is the lattice gas model consisting of translational particles and the other is that of turning particles. Fundamental diagrams for the two models are presented. The traffic flow of translational particles is compared with that of turning particles. In the traffic flow of translational particles, the fundamental diagram shows a trapezoid shape in the random configuration of obstacles, while it shows a parabolic shape in the periodic configuration of obstacles. The traffic flow of turning particles with a back step shows a similar behavior to that of translational particles. In the traffic flow of turning particles without backward moves, the current becomes zero when the density is higher than a critical density. In the traffic flow of turning particles without a back step, the dynamical transition between free traffic and a perfectly jammed state occurs at the critical density, while dynamical transition does not occur in traffic flow of translational particles.     

Velocity enhancement of slow particles in lattice-gas binary mixture

We study the unidirectional flow of a binary mixture of biased-random walkers on square lattice under a periodic boundary. The lattice-gas mixture consists of two types of walkers which have different biases (drift coefficients). The characteristics of unidirectional flow are clarified numerically. The mean velocity of slow particles in the binary mixture is enhanced higher than that in lattice-gas consisting of only slow particles. The mean velocity of slow particles shows a maximal value at an intermediate density. The dependence of velocity enhancement on both drift coefficient and mixture fraction is shown. Velocity enhancement is intensified with decreasing fraction of slow particles. Also, when the bias is lower, the velocity enhancement is higher.     

Vicious random walkers in the limit of a large number of walkers

The vicious random walker problem on a line is studied in the limit of a large number of walkers. The multidimensional integral representing the probability that thep walkers will survive a timet (denotedP _t ^(p) ) is shown to be analogous to the partition function of a particular one-component Coulomb gas. By assuming the existence of the thermodynamic limit for the Coulomb gas, one can deduce asymptotic formulas forP _t ^(p) in the large-p, large-t limit. A straightforward analysis gives rigorous asymptotic formulas for the probability that after a timet the walkers are in their initial configuration (this event is termed a reunion). Consequently, asymptotic formulas for the conditional probability of a reunion, given that all walkers survive, are derived. Also, an asymptotic formula for the conditional probability density that any walker will arrive at a particular point in timet, given that allp walkers survive, is calculated in the limittp.     

The runaway effect in a Lorentz gas

The Lorentz gas of charged particles in a constant and uniform electric field is studied. The gas flows through the medium of immobile, randomly distributed scatterers. Particles with velocity v suffer collisions with frequency proportional to ¦v¦ ⁿ . Forn < 0 runaway of the gas is forced by the field: the mean velocity of the flow increases without bounds. By a simple physical argument an integral relation is established between the probability of collisionless motion and the velocity distribution. It is then shown that whenn < –1 a fraction of particles moves as if the scattering centers were absent. The detailed discussion of this uncollided runaway is presented. Some qualitative features of the velocity distribution are illustrated on rigorous solutions in one dimension.     

Effect of following strength on pedestrian counter flow

This paper proposes a modified lattice gas model to simulate pedestrian counter flow by considering the effect of following strength which can lead to appropriate responses to some complicated situations.Periodic and open boundary conditions are adopted respectively.The simulation results show that the presented model can reproduce some essential features of pedestrian counter flows,e.g.,the lane formation and segregation effect.The fundamental diagrams show that the complete jamming density is independent of the system size only when the width W and the length L are larger than some critical values respectively,and the larger asymmetrical conditions can better avoid the occurrence of deadlock phenomena.For the mixed pedestrian flow,it can be found that the jamming cluster is mainly caused by those walkers breaking the traffic rules,and the underlying mechanism is analysed.Furthermore,the comparison of simulation results and the experimental data is performed,it is shown that this modified model is reasonable and more realistic to simulate and analyse pedestrian counter flow.     

Subconscious Effect on Pedestrian Counter Flow

We propose an extended lattice gas model with different maximum velocities to simulate pedestrian counter flow by considering the subconscious behaviour of walkers. Four types of walkers including faster right walkers, slower right walkers, faster left walkers and slower left walkers are involved in the simulation. The simulation results show that our model can capture some essential features of pedestrian counter flows, such as the lane formation, segregation effect and phase separation at higher densities. We also find that the subconscious effect can reduce the occurrence of jam cluster evidently compared with the ease of un-subeonscious effect. At large maximum velocity, the critical density corresponding to the maximum flow rate of the fundamental diagram is in good agreement with the empirical results.     

Close to Close Packing

For various lattice gas models with nearest neighbor exclusion (and, in one case, second-nearest neighbor exclusion as well), we obtain lower bounds on m, the average number of particles on the nonexcluded lattice sites closest to a given particle. They are all of the form m/m _cp 1–const·(N _cp /N–1), where N is the number of occupied sites, m _cp is the value of m at close packing, and N _cp is the value of N at close packing. An analogous result exists for hard disks in the plane.     

Solid-phase synthesis in Ni-Mg and Ni-Mg-C systems upon ball milling of powder mixtures

It is shown by X-ray diffraction analysis and differential scanning calorimetry that phase formation in mechanochemical synthesis (MS) of two-component mixtures in the Ni-Mg system occurs through amorphization. The final product of the MS of Ni₇₅Mg₂₅ mixture is the nonequilibrium nanocrystalline Ni-7.5 at % Mg solid solution with a lattice constant a = 0.3602 nm (a _Ni = 0.3526 nm). Milling of a mixture with a higher magnesium content (Ni_66.7Mg_33.3) yields a two-phase mixture composed of an amorphous phase and Ni(Mg) solid solution. MS of three-component mixtures in the Ni-Mg-C system, regardless of the form of the initial components (Ni₆₀Mg₂₅C₂₀ mixtures of elementary components or a mixture of Ni₂Mg intermetallic compound, Ni powder, and graphite), yields double cubic carbide of antiperovskite type, Ni₃MgC_0.75 (E2₁ structure type), with a lattice constant of 0.3782 nm. It is shown that the initial milling stage for a mixture of this elementary components in the presence of graphite is characterized by the distortion of Mg particles with the formation of texture in the (002) basic plane.     

Volatile jam and flow fluctuation in counter flow of slender particles

We study the counter flow of slender particles on square lattice under periodic boundaries. Two types of particles going to the right and to the left are taken into account, where the size of right particles is larger than that of left particles. The counter flow of slender particles with different sizes is compared with that of slender particles with the same size. The jamming transition occurs at a critical density. Near the transition point, the volatile jam appears with a period, disappears in time, is formed again, and the process occurs repeatedly. The flow fluctuates highly by forming the volatile jam. The volatile jam moves slowly to the left direction, while the jam is stationary when the size of right particles equals that of left particles.     

Lateral Migration and Orientation of Elliptical Particles in Poiseuille Flows

The simulations of elliptical particles in a pressure driven flow are performed using a lattice Boltzmann (LB) method. Effects of multi-particle interaction on the lateral migration and orientation of both neutrally and non-neutrally buoyant particles are investigated. Low and itermediate solid concentrations in terms of area fraction f _a =13, 25, and 40% are included in these simulations.     

Coaxial turbulent jet flames: Scaling relations for measured stoichiometric mixing lengths

Previous studies have quantified the fuel–air mixing processes within jet flames having a central fuel jet surrounded by an oxidizer coflow, where the mixing primarily occurs in the far field. The present work instead quantifies mixing within coaxial jet flames having a central jet of oxygen and a surrounding finite thickness coflow of hydrogen. These flames are relatively short and the primary mixing occurs in the near field. The stoichiometric mixing length (L_S) was measured, which is the distance along the centerline at which the stoichiometric condition occurs. Values of L_S were measured for a wide range of velocity ratios for both reacting and nonreacting cases using Planar Laser Induced Fluorescence (PLIF). Acetone PLIF was utilized for nonreacting cases, while OH PLIF was used for reacting. In nonreacting cases the use of a nondimensional momentum flux ratio collapses the nonreacting coaxial jet values of L_S to a single curve, which confirms previous theory. It also was found that the reacting and nonreacting coaxial jet data collapses approximately to a single curve, if one uses both the nondimensional momentum flux ratio and an effective outer flow gas density which is predicted by the analysis of Tacina and Dahm.     

The symmetric heavy-light ansatz

The symmetric heavy-light ansatz is a method for finding the ground state of any dilute unpolarized system of attractive two-component fermions. Operationally it can be viewed as a generalization of the Kohn-Sham equations in density functional theory applied to N -body density correlations. While the original Hamiltonian has an exact Z₂ symmetry, the heavy-light ansatz breaks this symmetry by skewing the mass ratio of the two components. In the limit where one component is infinitely heavy, the many-body problem can be solved in terms of single-particle orbitals. The original Z₂ symmetry is recovered by enforcing Z₂ symmetry as a constraint on N -body density correlations for the two components. For the 1D, 2D, and 3D attractive Hubbard models the method is in very good agreement with exact Lanczos calculations for few-body systems at arbitrary coupling. For the 3D attractive Hubbard model there is very good agreement with lattice Monte Carlo results for many-body systems in the limit of infinite scattering length.     

Order parameter quantum fluctuations in a two-dimensional system of mesoscopic Josephson junctions

The boson lattice Hubbard model is used to study the role of quantum fluctuations of the phase and local density of the superfluid component in establishing a global superconducting state for a system of mesoscopic Josephson junctions or grains. The quantum Monte Carlo method is used to calculate the density of the superfluid component and fluctuations in the number of particles at sites of the two-dimensional lattice for various average site occupation numbers n ₀ (i.e., number of Cooper pairs per grain). For a system of strongly interacting bosons, the phase boundary of the ordered superconducting state lies above the corresponding boundary for its quasiclassical limit—the quantum XY-model—and approaches the latter as n ₀ increases. When the boson interaction is weak in the boson Hubbard model (i.e., the quantum fluctuations of the phase are small), the relative fluctuations of the order parameter modulus are significant when n ₀<10, while quantum fluctuations in the phase are significant when n ₀<8; this determines the region of mesoscopic behavior of the system. Comparison of the results of numerical modeling with theoretical calculations show that mean-field theory yields a qualitatively correct estimate of the difference between the phase diagrams of the quantum XY-model and the Hubbard model. For a quantitative estimate of this difference the free energy and thermodynamic averages of the Hubbard model are expanded in powers of 1/n ₀ using the method of functional integration. Zh. éksp. Teor. Fiz. 113, 261–277 (January 1998)     

Lower bounds on the cluster size distribution

We rigorously prove that the probabilityP _n that the origin of ad-dimensional lattice belongs to a cluster of exactlyn sites satisfiesP _n > exp(–n ^(d–1)/d ) whenever percolation occurs. This holds for the usual (noninteracting) percolation models for any concentrationp > p _c , as well as for the equilibrium states of lattice spin systems with quite general interactions. Such a lower bound applies also if no percolation occurs, but if it appears in some other phase of the system.     

Features of the Percolation Scheme of Vibrational Spectrum Reconstruction in the Ga1 – xAl x P Alloy

Specific features of the properties of Ga–P lattice vibrations have been investigated using the percolation model of a mixed Ga_{1 – x}Al _x P crystal (alloy) with zero lattice mismatch between binary components of the alloy. In contrast to other two-mode alloy systems, in Ga_{1 – x}Al _x P a percolation splitting of δ ~ 13 cm^–1 is observed for the low-frequency mode of GaP-like vibrations. An additional GaP mode (one of the percolation doublet components) split from the fundamental mode is observed for the GaP-rich alloy, which coincides in frequency with the gap corresponding to the zero density of one-phonon states of the GaP crystal. The vibrational spectrum of impurity Al in the GaP crystal has been calculated using the theory of crystal lattice dynamics. Upon substitution of lighter Al for the Ga atom, the calculated spectrum includes, along with the local mode, a singularity near the gap with the zero density of phonon states of the GaP crystal, which coincides with the mode observed experimentally at a frequency of 378 cm^–1 in the Ga_{1 – x}Al _x P (x < 0.4) alloy.

     

Multiple trapping of random walkers on periodic lattices

Formulas are obtained for the mean absorption time of a set ofk independent random walkers on periodic space lattices containingq traps. We consider both discrete (here we assume simultaneous stepping) and continuous-time random walks, and find that the mean lifetime of the set of walkers can be obtained, via a convolution-type recursion formula, from the generating function for one walker on the perfect lattice. An analytical solution is given for symmetric walks with nearest neighbor transitions onN-site rings containing one trap (orq equally spaced traps), for both discrete and exponential distribution of stepping times. It is shown that, asN , the lifetime of the walkers is of the form Ta_kN², whereT is the average time between steps. Values ofa _k, 2 Sk 6, are provided.     

Dynamical phase transition in two-dimensional fully frustrated Josephson junction arrays with resistively shunted junction dynamics

The dynamical phase transitions in two-dimensional fully frustrated Josephson junction arrays at zero temperature are investigated numerically with the resistively shunted junction model through the fluctuating twist boundary condition. The model is subjected to a driving current with nonzero orthogonal components i _x , i _y parallel to both axes of the square lattice. We find a roughly lattice size independent phase diagram with three dynamical phases: a pinned vortex lattice phase, a moving vortex lattice phase and a moving plastic phase. The phase diagram shows a direct transition from the pinned vortex to the moving vortex phase and the separation of the pinned vortex and the moving plastic phases. The time-dependent voltages v _x and v _y are periodic in the moving vortex lattice phase. But they are aperiodic in the moving plastic phase, resulting in non-monotonic characteristics and hysteresis in the current-voltage curves. It is found that the characteristic frequency is twice the time-averaged voltage in the moving vortex phase and around the time-averaged voltage in the plastic flow regime.Received: 29 May 2003, Published online: 2 October 2003PACS: 64.60.Ht Dynamic critical phenomena - 74.25.Sv Critical currents - 74.25.Fy Transport properties