A stochastic multi-cluster model of freeway traffic

A stochastic approach based on the Master equation is proposed to describe the process of formation and growth of car clusters in traffic flow in analogy to usual aggregation phenomena such as the formation of liquid droplets in supersaturated vapour. By this method a coexistence of many clusters on a one-lane circular road has been investigated. Analytical equations have been derived for calculation of the stationary cluster distribution and related physical quantities of an infinitely large system of interacting cars. If the probability per time (or p) to decelerate a car without an obvious reason tends to zero in an infinitely large system, our multi-cluster model behaves essentially in the same way as a one-cluster model studied before. In particular, there are three different regimes of traffic flow (free jet of cars, coexisting phase of jams and isolated cars, highly viscous heavy traffic) and two phase transitions between them. At finite values of p the behaviour is qualitatively different, i.e., there is no sharp phase transition between the free jet of cars and the coexisting phase. Nevertheless, a jump-like phase transition between the coexisting phase and the highly viscous heavy traffic takes place both at and at a finite p. Monte-Carlo simulations have been performed for finite roads showing a time evolution of the system into the stationary state. In distinction to the one-cluster model, a remarkable increasing of the average flux has been detected at certain densities of cars due to finite-size effects. Received 17 September 1999     

Collapse transitions of a periodic hydrophilic hydrophobic chain

We study a single self avoiding hydrophilic hydrophobic polymer chain, through Monte-Carlo lattice simulations. The affinity of monomer i for water is characterized by a (scalar) charge , and the monomer-water interaction is short-ranged. Assuming incompressibility yields an effective short ranged interaction between monomer pairs (i,j), proportional to . In this article, we take (resp. ()) for hydrophilic (resp. hydrophobic) monomers and consider a chain with (i) an equal number of hydro-philic and -phobic monomers (ii) a periodic distribution of the along the chain, with periodicity 2p. The simulations are done for various chain lengths N, in d=2 (square lattice) and d=3 (cubic lattice). There is a critical value p _c (d,N) of the periodicity, which distinguishes between different low temperature structures. For p >p _c , the ground state corresponds to a macroscopic phase separation between a dense hydrophobic core and hydrophilic loops. For p <p _c (but not too small), one gets a microscopic (finite scale) phase separation, and the ground state corresponds to a chain or network of hydrophobic droplets, coated by hydrophilic monomers. We restrict our study to two extreme cases, and to illustrate the physics of the various phase transitions. A tentative variational approach is also presented. Received: 10 March 1998 / Received in final form: 25 June 1998 / Accepted: 1st July 1998     

Metastable states in two-lane traffic flow models with slow-to-start rule

Using computer simulations, we show that metastable states still occur in two-lane traffic models with slow to start rules. However, these metastable states no longer exist in systems where aggressive drivers (which do not look back before changing lanes) are present. Indeed, the presence of only one aggressive driver in the circuit, triggers the breakdown of the high flow states. In these systems, the steady state is unique and its relaxation dynamics should depend on the lane changing probability p_ch and the number of aggressive drivers present in the circuit. It is found also that the relaxation time τ diverges as the form of a power-law: τ∝p_ch ^-β, β=1. 89.40.+k     

Smoothening transition of a two-dimensional pressurized polymer ring

We revisit the problem of a two-dimensional polymer ring subject to an inflating pressure differential. The ring is modeled as a freely jointed closed chain of N monomers. Using a Flory argument, mean-field calculation and Monte Carlo simulations, we show that at a critical pressure, p_c ∼ N^-1, the ring undergoes a second-order phase transition from a crumpled, random-walk state, where its mean area scales as 〈A〉 ∼ N, to a smooth state with 〈A〉 ∼ N². The transition belongs to the mean-field universality class. At the critical point a new state of polymer statistics is found, in which 〈A〉 ∼ N^3/2. For p ≫ p_c we use a transfer-matrix calculation to derive exact expressions for the properties of the smooth state.     

Kernquadrupolwechselwirkung für Elektronenkonfigurationen vom Typ s p d und Anwendung auf das Lanthan I-Spektrum

The electrostatic and spin-orbit matrices are calculated for spd configurations in LS-coupling using the sp-parent system. Diagonalizing the energy matrices by an electronic computer approximative eigenvectors in intermediate coupling for states of the configuration 5d6s6p in the lanthanum I-spectrum were received. For the interpretation of several new hfs data obtained by levelcrossing – technique a compact formula for the quadrupole interaction in jj – coupling has been derived. In addition the complete quadrupole interaction matrices in LS-coupling for spd configurations are given including relativistic corrections. As an application the hfs interaction in the configuration 5d6s6p of the lanthanum I-spectrum was discussed.     

Selective preparation of ground state wave-packets: a theoretical analysis of femtosecond pump-dump-probe experiments on the potassium dimer

We present simulations on pump-dump-probe experiments performed on the potassium dimer. The interaction of two time-delayed laser pulses prepares vibrational wave packets in the electronic ground state. The quantum calculations reveal to what extent it is possible to prepare a ground state superposition of states with high versus low vibrational quantum numbers by changing the pump-dump delay time. It is shown that transient signals may exhibit interference effects which are due to characteristics of ground state wave-packets composed of two components showing different vibrational dynamics. In this way the signals are able to yield information about vibrational overtone motion. Received 27 September 2000 and Received in final form 21 November 2000     

Coupled aggregation and sedimentation processes: Three-dimensional off-lattice simulations

Coupled aggregation and sedimentation processes were studied by means of three-dimensional computer simulations. For this purpose, a large prism with no periodic boundary conditions for the sedimentation direction was considered. Furthermore, three equally sized and mutually excluded regions were defined inside the prism, a top, a middle and a bottom region. This allows to study the time evolution of the cluster size distribution and the cluster structure separately for each region. The mass distribution profile and the center-of-mass position were also accessed as a function of time. For the bottom region, the effects of the sediment formation on the kinetics of growth and on the cluster structure were clearly observed. The obtained results not only agree with the experimental data obtained by Allain et al. (C. Allain, M. Cloitre, M. Wafra, Phys. Rev. Lett. 74, 1478 (1995)) and with the simulations made by Gonzalez (A.E. Gonzalez, Phys. Rev. Lett. 86, 1243 (2001)), but also allow to gain further insight into the details. Received 7 November 2001     

Stochastic theory of nonlinear rate processes with multiple stationary states. II. Relaxation time from a metastable state

We have developed a methodology for obtaining a Fokker-Planck equation for nonlinear systems with multiple stationary states that yields the correct system size dependence, i.e., exponential growth with system size of the relaxation time from a metastable state. We show that this relaxation time depends strongly on the barrier heightU(x) between the metastable and stable states of the system. For a Fokker-Planck (FP) equation to yield the correct result for the relaxation time from a metastable state, it is therefore essential that the free energy functionU(x) of the FP equation not only correctly locate the extrema of U(x), but also have the correct magnitudeU at these extrema. This is accomplished by so choosing the coefficients of the FP equation that its stationary solution is identical to that of the master equation that defines the nonlinear system.This work was supported in part by the National Science Foundation under Grant CHE 75-20624.     

Stationary cell size distributions and mean protein chain length distributions of Archaea,Bacteria and Eukaryotes described with an increment model in terms of irreversible thermodynamics

In terms of an increment model irreversible thermodynamics allows to formulate general relations of stationary cell size distributions observed in growing colonies. The treatment is based on the following key postulates: i) The growth dynamics covers a broad spectrum of fast and slow processes. ii) Slow processes are considered to install structural patterns that operate in short periods as temporary stationary states of reference in the sense of irreversible thermodynamics. iii) Distortion during growth is balanced out via the many fast processes until an optimized stationary state is achieved. The relation deduced identifies the numerous different stationary patterns as equivalents, predicting that they should fall on one master curve. Stationary cell size distributions of different cell types, like Hyperphilic archaea, E. coli (Prokaryotes) and S. cerevisiae (Eukaryotes), altogether taken from the literature, are in fact consistently described. As demanded by the model they agree together with the same master curve. Considering the “protein factories” as subsystems of cells the mean protein chain length distributions deduced from completely sequenced genomes should be optimized. In fact, the mean course can be described with analogous relations as used above. Moreover, the master curve fits well to the patterns of different species of Archaea, Bacteria and Eukaryotes. General consequences are discussed.     

Magnetic reconstructions at the surface of the B2 FeV alloy

We present an ab initio study of the magnetic surface reconstructions of the B2 FeV alloy using a self-consistent tight-binding linearized muffin tin orbital method developed in the atomic spheres approximation. For (001) and (111), the surface reconstruction stabilizes configurations unstable in the bulk alloy. When Fe is at the (001) surface, a c(2×2) in-plane antiferromagnetic order is found to be the ground state with magnetic moments of -2.32 and 2.27. A p(1×1) ↓ ferromagnetic order is displayed in case of V toplayer with a magnetic moment of -1.83. At the (111) surface, we obtain for Fe toplayer two solutions p(1×1)↑ and p(2×1). The configuration p(1×1)↑ is found to be the ground state with a magnetic moment per atom of 2.34. For V toplayer, only the p(1×1) ↓ solution is obtained with a moment of -0.84. In all cases, the Fe-V coupling is always antiparallel like in the bulk. Our results are discussed and compared to experiments. Received 11 August 2000 and Received in final form 8 June 2001     

Disorder driven roughening transitions of elastic manifolds and periodic elastic media

The simultaneous effect of both disorder and crystal-lattice pinning on the equilibrium behavior of oriented elastic objects is studied using scaling arguments and a functional renormalization group technique. Our analysis applies to elastic manifolds, e.g., interfaces, as well as to periodic elastic media, e.g., charge-density waves or flux-line lattices. The competition between both pinning mechanisms leads to a continuous, disorder driven roughening transition between a flat state where the mean relative displacement saturates on large scales and a rough state with diverging relative displacement. The transition can be approached by changing the impurity concentration or, indirectly, by tuning the temperature since the pinning strengths of the random and crystal potential have in general a different temperature dependence. For D dimensional elastic manifolds interacting with either random-field or random-bond disorder a transition exists for 2<D<4, and the critical exponents are obtained to lowest order in . At the transition, the manifolds show a superuniversal logarithmic roughness. Dipolar interactions render lattice effects relevant also in the physical case of D=2. For periodic elastic media, a roughening transition exists only if the ratio p of the periodicities of the medium and the crystal lattice exceeds the critical value . For p<p _c the medium is always flat. Critical exponents are calculated in a double expansion in and and fulfill the scaling relations of random field models. Received 28 August 1998     

Swelling of two-dimensional polymer rings by trapped particles

The mean area of a two-dimensional Gaussian ring of N monomers is known to diverge when the ring is subject to a critical pressure differential, p _c ∼ N ^-1. In a recent publication (Eur. Phys. J. E 19, 461 (2006)) we have shown that for an inextensible freely jointed ring this divergence turns into a second-order transition from a crumpled state, where the mean area scales as 〈A〉 ∼ N, to a smooth state with 〈A〉 ∼ N ². In the current work we extend these two models to the case where the swelling of the ring is caused by trapped ideal-gas particles. The Gaussian model is solved exactly, and the freely jointed one is treated using a Flory argument, mean-field theory, and Monte Carlo simulations. For a fixed number Q of trapped particles the criticality disappears in both models through an unusual mechanism, arising from the absence of an area constraint. In the Gaussian case the ring swells to such a mean area, 〈A〉 ∼ NQ, that the pressure exerted by the particles is at p _c for any Q. In the freely jointed model the mean area is such that the particle pressure is always higher than p _c, and 〈A〉 consequently follows a single scaling law, 〈A〉 ∼ N ² f (Q/N), for any Q. By contrast, when the particles are in contact with a reservoir of fixed chemical potential, the criticality is retained. Thus, the two ensembles are manifestly inequivalent in these systems. An erratum to this article is available at .     

Three-dimensional array structures associated with Richtmyer-Meshkov and Rayleigh-Taylor instability

A boundary separating adjacent gas or liquid media is frequently unstable. Richtmyer-Meshkov and Rayleigh-Taylor instability cause the growth of intricate structures on such boundaries. All the lattice symmetries [rectangular (pmm2), square (p4mm), hexagonal (p6mm), and triangular (p3m1) lattices] which are of interest in connection with the instability of the surface of a fluid are studied for the first time. They are obtained from initial disturbances consisting of one (planar case, two-dimensional flow), two (rectangular cells), or three (hexagons and triangles) harmonic waves. It is shown that the dynamic system undergoes a transition during development from an initial, weakly disturbed state to a limiting or asymptotic stationary state (stationary point). The stability of these points (stationary states) is investigated. It is shown that the stationary states are stable toward large-scale disturbances both in the case of Richtmyer-Meshkov instability and in the case of Rayleigh-Taylor instability. It is discovered that the symmetry increases as the system evolves in certain cases. In one example the initial Richtmyer-Meshkov or Rayleigh-Taylor disturbance is a sum of two waves perpendicular to one another with equal wave numbers, but unequal amplitudes: a ₁(t=0)≠a ₂(t=0). Then, during evolution, the flow has p2 symmetry (rotation relative to the vertical axis by 180°), which goes over to p4 symmetry (rotation by 90°) at t→∞, since the amplitudes equalize in the stationary state: a ₁(t=∞)=a ₂(t=∞). It is shown that the hexagonal and triangular arrays are complementary. Upon time inversion (t→−t), “rephasing” occurs, and the bubbles of a hexagonal array transform into jets of a triangular array and vice versa. Zh. éksp. Teor. Fiz. 116, 908–939 (September 1999)     

An universal relation between fractal and Euclidean (topological) dimensions of random systems

It is shown that a dimension-invariant form for fractal dimension D of random systems (where d is Euclidean dimension of the embedding space) is in good agreement with results of numerical simulations performed by different authors for critical (p=p _c ) and subcritical (p<p _c ) percolation, for lattice animals, and for different aggregation processes. Received: 9 July 1998 / Revised and Accepted: 12 July 1998     

Determination of the Parameter Ratio H0 2/K of Closed Thermal Diffusion Columns for Polynary Isotopic Mixtures

For the experimental determination of the H₀ ²/K ratio of the constants for prototype thermal diffusion columns from initial state mole fraction measurements there was a lack of sufficiently exact simple evaluation methods for polynary isotopic mixtures.

The investigation of mole fraction changes at closed ends obtained by numerical integration of the corresponding system of second order partial differential equations resulted in a concept of approximation which allows to utilize approximative analytical solutions originally developed for binary isotopic mixtures.

In the approximation the initial mole fractions are indirectly represented by the mean mass number of the initial mixture.

Thus, the measured mole fraction changes can be attributed to the difference between the actual mass number of the components and the mean mass number of the enclosed mixture. By simple regression analysis a partial derivative can be obtained which can be attributed to the approximative analytical solutions for binary mixtures.     

Schloegl’s Second Model for Autocatalysis on a Cubic Lattice: Mean-Field-Type Discrete Reaction-Diffusion Equation Analysis

Schloegl’s second model for autocatalysis on a hypercubic lattice of dimension d≥2 involves: (i) spontaneous annihilation of particles at lattice sites with rate p; and (ii) autocatalytic creation of particles at vacant sites at a rate proportional to the number of diagonal pairs of particles on neighboring sites. Kinetic Monte Carlo simulations for a d=3 cubic lattice reveal a discontinuous transition from a populated state to a vacuum state as p increases above p=p _e . However, stationary points, p=p _eq (≤p _e ), for planar interfaces separating these states depend on interface orientation. Our focus is on analysis of interface dynamics via discrete reaction-diffusion equations (dRDE’s) obtained from mean-field type approximations to the exact master equations for spatially inhomogeneous states. These dRDE can display propagation failure absent due to fluctuations in the stochastic model. However, accounting for this anomaly, dRDE analysis elucidates exact behavior with quantitative accuracy for higher-level approximations.     

Thermalization of gluons at RHIC: Dependence on initial conditions

We investigate how thermalization of gluons depends on the initial conditions assumed in ultrarelativistic heavy-ion collisions at RHIC. The study is based on simulations employing the pQCD inspired parton cascade solving the Boltzmann equation for gluons. We consider independently produced minijets with p _T > p ₀ = 1.3-2.0GeV and a color glass condensate as possible initial conditions for the freed gluons. It turns out that full kinetic equilibrium is achieved slightly sooner in denser systems and its timescale tends to saturate. Compared with the kinetic equilibration we find a stronger dependence of chemical equilibration on the initial conditions.     

Successive defects asymmetric simple exclusion processes with particles of arbitrary size

This paper uses various mean-field approaches and the Monte Carlo simulation to calculate asymmetric simple exclusion processes with particles of arbitrary size in the successive defects system. In this system, the hopping probability p (p<1) and the size d of particles are not constant. Through theoretical calculation and computer simulation, it obtains the exact theoretical results and finds that the theoretical results are in agreement with the computer simulation. These results are helpful in analysing the effect of traffic with different hopping probabilities p and sizes d of particle.     

Tuning of the open‐circuit voltage by wide band‐gap absorber and doped layers in thin film silicon solar cells

We present an experimental study combined with computer simulations on the effects of wide band‐gap absorber and window layers on the open‐circuit voltage (V_oc) in single junction thin film silicon solar cells. The quantity ΔE_p, taking as the difference between the band gap and the activation energy in ?p? layer, is treated as a measure of the p‐layer properties and shows a linear relation with V_oc over a range of 100 mV with a positive slope of around 430 mV/eV. Two limiting mechanisms of V_oc are identified: the built‐in potential at lower ΔE_p and the band gap of the absorber layer at higher ΔE_p. The results of the experimental findings are confirmed by computer simulations. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)