Solitons and kinks in a general car-following model

We study a car-following model of traffic flow which assumes only that a car's acceleration depends on its own speed, the headway ahead of it, and the rate of change of headway, with only minimal assumptions about the functional form of that dependence. The velocity of uniform steady flow is found implicitly from the acceleration function, and its linear stability criterion can be expressed simply in terms of it. Crucially, unlike in previously analyzed car-following models, the threshold of absolute stability does not generally coincide with an inflection point in the steady velocity function. The Burgers and KdV equations can be derived under the usual assumptions, but the mKdV equation arises only when absolute stability does coincide with an inflection point. Otherwise, the KdV equation applies near absolute stability, while near the inflection point one obtains the mKdV equation plus an extra, quadratic term. Corrections to the KdV equation "select" a single member of the one-parameter set of soliton solutions. In previous models this has always marked the threshold of a finite- amplitude instability of steady flow, but here it can alternatively be a stable, small-amplitude jam. That is, there can be a forward bifurcation from steady flow. The new, augmented mKdV equation which holds near an inflection point admits a continuous family of kink solutions, like the mKdV equation, and we derive the selection criterion arising from the corrections to this equation.Comment: 25 page

Physical inactivity is associated with chronic musculoskeletal complaints 11 years later: results from the Nord-Trøndelag Health Study

Background Physical inactivity is associated with several diseases, but studies evaluating the association between chronic musculoskeletal complaints (MSCs) and physical exercise have shown conflicting results. The aim of this large-scale prospective population-based study was to investigate the association between self-reported physical exercise at baseline and the prevalence of chronic musculoskeletal complaints (MSCs) 11 years later. Methods The results are based upon two consecutive public health studies conducted within the county of Nord-Trøndelag, Norway (The HUNT studies). A total of 39,520 (83%) out of 47,556 adults who participated in HUNT 1 and HUNT 2 responded to questions about physical exercise at baseline in 1984–86, and to questions about musculoskeletal complaints 11 years later (1995–97). Chronic MSCs was defined as MSCs ≥ 3 months during the past year, and chronic widespread MSCs such as pain ≥ 15 days during the last month from the axial region, above the waist, and below the waist. Associations were assessed using multiple logistic regression, estimating prevalence odds ratio (OR) with 95% confidence intervals (CIs). All the final analyses were adjusted for age, gender, body mass index, smoking and education level. Results At follow-up 20,223 (51%) reported chronic MSCs, and among these 2,318 (5.9%) reported chronic widespread MSCs. Individuals who exercised at baseline were less likely to report chronic MSCs 11 years later (OR 0.91, 95% CI 0.85–0.97) than inactive persons. Among individuals who exercised more than three times per week, chronic widespread MSCs were 28% less common (OR 0.72, 95% CI 0.59–0.88) compared to inactive individuals. Conclusion In this large-scale population-based study, physical exercise was associated with lower prevalence of chronic MSCs, in particular chronic widespread MSCs. Future studies should try to clarify whether chronic MSCs are a cause or a consequence of inactivity

Fisher zeros of the Q-state Potts model in the complex temperature plane for nonzero external magnetic field

The microcanonical transfer matrix is used to study the distribution of the Fisher zeros of the $Q>2$ Potts models in the complex temperature plane with nonzero external magnetic field $H_q$. Unlike the Ising model for $H_q\ne0$ which has only a non-physical critical point (the Fisher edge singularity), the $Q>2$ Potts models have physical critical points for $H_q<0$ as well as the Fisher edge singularities for $H_q>0$. For $H_q<0$ the cross-over of the Fisher zeros of the $Q$-state Potts model into those of the ($Q-1$)-state Potts model is discussed, and the critical line of the three-state Potts ferromagnet is determined. For $H_q>0$ we investigate the edge singularity for finite lattices and compare our results with high-field, low-temperature series expansion of Enting. For $3\le Q\le6$ we find that the specific heat, magnetization, susceptibility, and the density of zeros diverge at the Fisher edge singularity with exponents $\alpha_e$, $\beta_e$, and $\gamma_e$ which satisfy the scaling law $\alpha_e+2\beta_e+\gamma_e=2$.Comment: 24 pages, 7 figures, RevTeX, submitted to Physical Review

Generalized Force Model of Traffic Dynamics

Floating car data of car-following behavior in cities were compared to existing microsimulation models, after their parameters had been calibrated to the experimental data. With these parameter values, additional simulations have been carried out, e.g. of a moving car which approaches a stopped car. It turned out that, in order to manage such kinds of situations without producing accidents, improved traffic models are needed. Good results have been obtained with the proposed generalized force model.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.htm

Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. IV. Chromatic polynomial with cyclic boundary conditions

We study the chromatic polynomial P_G(q) for m \times n square- and triangular-lattice strips of widths 2\leq m \leq 8 with cyclic boundary conditions. This polynomial gives the zero-temperature limit of the partition function for the antiferromagnetic q-state Potts model defined on the lattice G. We show how to construct the transfer matrix in the Fortuin--Kasteleyn representation for such lattices and obtain the accumulation sets of chromatic zeros in the complex q-plane in the limit n\to\infty. We find that the different phases that appear in this model can be characterized by a topological parameter. We also compute the bulk and surface free energies and the central charge.Comment: 55 pages (LaTeX2e). Includes tex file, three sty files, and 22 Postscript figures. Also included are Mathematica files transfer4_sq.m and transfer4_tri.m. Journal versio

Effect of noise on coupled chaotic systems

Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by identical noise, show synchronization phenomena where chaotic trajectories exponentially converge towards a single noisy trajectory, independent of the initial conditions. In a random neural network, with infinite range coupling, chaos is suppressed due to noise and the system evolves towards a fixed point. Spatiotemporal stochastic resonance phenomenon has been observed in a square array of coupled threshold devices where a temporal characteristic of the system resonates at a given noise strength. In a chaotically evolving coupled map lattice with logistic map as local dynamics and driven by identical noise at each site, we report that the number of structures (a structure is a group of neighbouring lattice sites for whom values of the variable follow certain predefined pattern) follow a power-law decay with the length of the structure. An interesting phenomenon, which we call stochastic coherence, is also reported in which the abundance and lifetimes of these structures show characteristic peaks at some intermediate noise strength.Comment: 21 page LaTeX file for text, 5 Postscript files for figure

Traffic Equations and Granular Convection

We investigate both numerically and analytically the convective instability of granular materials by two dimensional traffic equations. In the absence of vibrations the traffic equations assume two distinctive classes of fixed bed solutions with either a spatially uniform or nonuniform density profile. The former one exists only when the function V(\rho) that monitors the relaxation of grains assumes a cut off at the closed packed density, \rho_c, with V(\rho_c)=0, while the latter one exists for any form of V. Since there is little difference between the uniform and nonuniform solution deep inside the bed, the convective instability of the bulk may be studied by focusing on the stability of the uniform solution. In the presence of vibrations, we find that the uniform solution bifurcates into a bouncing solution, which then undergoes a supercritical bifurcation to the convective instability. We determine the onset of convection as a function of control parameters and confirm this picture by solving the traffic equations numerically, which reveals bouncing solutions, two convective rolls, and four convective rolls. Further, convective patterns change as the aspect ratio changes: in a vertically long container, the rolls move toward the surface, and in a horizontally long container, the rolls move toward the walls. We compare these results with those reported previously with a different continuum model by Hayakawa, Yue and Hong[Phys. Rev. Lett. 75,2328, 1995]. Finally, we also present a derivation of the traffic equations from Enskoq equation.Comment: 34 pages, 10 figure

Spanning forests and the q-state Potts model in the limit q \to 0

We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating polynomial of spanning forests; physically, it provides information about the Potts-model phase diagram in the neighborhood of (q,v) = (0,0). We have studied this model on the square and triangular lattices, using a transfer-matrix approach at both real and complex values of w. For both lattices, we have computed the symbolic transfer matrices for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves of partition-function zeros in the complex w-plane. For real w, we find two distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp. w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w > w_0 we find a non-critical disordered phase, while for w < w_0 our results are compatible with a massless Berker-Kadanoff phase with conformal charge c = -2 and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w = w_0 we find a "first-order critical point": the first derivative of the free energy is discontinuous at w_0, while the correlation length diverges as w \downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0 seems to be the same for both lattices and it differs from that of the Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1, the leading thermal scaling dimension is x_{T,1} = 0, and the critical exponents are \nu = 1/d = 1/2 and \alpha = 1.Comment: 131 pages (LaTeX2e). Includes tex file, three sty files, and 65 Postscript figures. Also included are Mathematica files forests_sq_2-9P.m and forests_tri_2-9P.m. Final journal versio

Adiposity and Age Explain Most of the Association between Physical Activity and Fitness in Physically Active Men

BACKGROUND: To determine if there is an association between physical activity assessed by the short version of the International Physical Activity Questionnaire (IPAQ) and cardiorespiratory and muscular fitness. METHODOLOGY/PRINCIPAL FINDINGS: One hundred and eighty-two young males (age range: 20-55 years) completed the short form of the IPAQ to assess physical activity. Body composition (dual-energy X-Ray absorptiometry), muscular fitness (static and dynamic muscle force and power, vertical jump height, running speed [30 m sprint], anaerobic capacity [300 m running test]) and cardiorespiratory fitness (estimated VO(2)max: 20 m shuttle run test) were also determined in all subjects. Activity-related energy expenditure of moderate and vigorous intensity (EEPA(moderate) and EEPA(vigorous), respectively) was inversely associated with indices of adiposity (r = -0.21 to -0.37, P<0.05). Cardiorespiratory fitness (VO(2)max) was positively associated with LogEEPA(moderate) (r = 0.26, P<0.05) and LogEEPA(vigorous) (r = 0.27). However, no association between VO(2)max with LogEEPA(moderate), LogEPPA(vigorous) and LogEEPA(total) was observed after adjusting for the percentage of body fat. Multiple stepwise regression analysis to predict VO(2)max from LogEEPA(walking), LogEEPA(moderate), LogEEPA(vigorous), LogEEPA(total), age and percentage of body fat (%fat) showed that the %fat alone explained 62% of the variance in VO(2)max and that the age added another 10%, while the other variables did not add predictive value to the model [VO(2)max  = 129.6-(25.1× Log %fat) - (34.0× Log age); SEE: 4.3 ml.kg(-1). min(-1); R(2) = 0.72 (P<0.05)]. No positive association between muscular fitness-related variables and physical activity was observed, even after adjusting for body fat or body fat and age. CONCLUSIONS/SIGNIFICANCE: Adiposity and age are the strongest predictors of VO(2)max in healthy men. The energy expended in moderate and vigorous physical activities is inversely associated with adiposity. Muscular fitness does not appear to be associated with physical activity as assessed by the IPAQ