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Peter Wagner

Publications and source records attributed to Peter Wagner.

18 recordsLinked to original sources
arXiv2023

Physical models of traffic safety at crossings

Traffic safety at intersections is studied quantitatively using methods from Statistical Mechanics on the basis of simple microscopic traffic flow models. In order to determine a relationship between traffic flow and the number of crashes, the modelling focus is on the building block of any road network, namely the crossing of two streams. In this paper, it is shown that the number of crossing conflicts is proportional to the product of the two traffic flows from which a simple model is developed. This model substantiates known empirical findings. Since real crash data are obtained by an involved process from such building blocks, there is a difference between the theoretical and empirical results. This process is modelled here as well and narrows the gap between theory and observation.

cond-mat.stat-mech↗
arXiv2014

Macroscopic Elastic Properties of Textured ZrN--AlN Polycrystalline Aggregates: From Ab initio Calculations to Grain-Scale Interactions

Despite the fast development of computational materials modelling, theoretical description of macroscopic elastic properties of textured polycrystalline aggregates starting from basic principles remains a challenging task. In this communication we use a supercell-based approach to obtain the elastic properties of random solid solution cubic ZrAlN system as a function of the metallic sublattice composition and texture descriptors. The employed special quasi-random structures are optimised not only with respect to short range order parameters, but also to make the three cubic directions $[1\,0\,0]$, $[0\,1\,0]$, and $[0\,0\,1]$ as similar as possible. In this way, only a small spread of elastic constants tensor components is achieved and an optimum trade-off between modelling of chemical disorder and computational limits regarding the supercell size is achieved. The single crystal elastic constants are shown to vary smoothly with composition, yielding $x\approx0.4$-0.5 an alloy constitution with an almost isotropic response. Consequently, polycrystals with this composition are suggested to have Young's modulus independent on the actual microstructure. This is indeed confirmed by explicit calculations of polycrystal elastic properties, both within the isotropic aggregate limit, as well as with fibre textures with various orientations and sharpness. It turns out, that for low AlN mole fractions, the spread of the possible Young's moduli data caused by the texture variation can be larger than 100 GPa. Consequently, our discussion of Young's modulus data of cubic ZrAlN contains also the evaluation of the texture typical for thin films.

cond-mat.mtrl-sci↗
arXiv2013

Division problem for spatially periodic distributions

We give a sufficient condition for the surjectivity of partial differential operators with constant coefficients on a class of distributions on R^{n+1} (here we think of there being n space directions and one time direction), that are periodic in the spatial directions and tempered in the time direction.

math.AP↗
arXiv2007

Cosmology and Dark Matter at the LHC

We examine the question of whether neutralinos produced at the LHC can be shown to be the particles making up the astronomically observed dark matter. If the WIMP alllowed region lies in the SUGRA coannihilation region, then a strong signal for this would be the unexpected near degeneracy of the stau and neutralino i.e., a mass difference ΔM\simeq (5-15) GeV. For the mSUGRA model we show such a small mass difference can be measured at the LHC using the signal 3τ+jet+E_T^{\rm miss}. Two observables, opposite sign minus like sign pairs and the peak of the ττmass distribution allows the simultaneous determination of ΔM to 15% and the gluino mass M_{\tilde g} to be 6% at the benchmark point of M_{\tilde g}=850 GeV, A_0=0, μ>0 with 30 fb^{-1}. With 10 fb^{-1}, ΔM can be determined to 22% and one can probe the parameter space up to m_{1/2}=700 GeV with 100 fb^{-1}.

hep-ph↗
arXiv2006

How human drivers control their vehicle

The data presented here show that human drivers apply a discrete noisy control mechanism to drive their vehicle. A car-following model built on these observations, together with some physical limitations (crash-freeness, acceleration), led to non-Gaussian probability distributions in the speed difference and distance which are in good agreement with empirical data. All model parameters have a clear physical meaning and can be measured. Despite its apparent complexity, this model is simple to understand and might serve as a starting point to develop even quantitatively correct models.

physics.soc-ph↗
arXiv2005

A new approach to quantum backflow

We derive some rigorous results concerning the backflow operator introduced by Bracken and Melloy. We show that it is linear bounded, self adjoint, and not compact. Thus the question is underlined whether the backflow constant is an eigenvalue of the backflow operator. From the position representation of the backflow operator we obtain a more efficient method to determine the backflow constant. Finally, detailed position probability flow properties of a numerical approximation to the (perhaps improper) wave function of maximal backflow are displayed.

quant-ph↗
arXiv2004

Modelling traffic flow fluctuations

By analyzing empirical time headway distributions of traffic flow, a hypothesis about the underlying stochastic process can be drawn. The results found lead to the assumption that the headways $T_i$ of individual vehicles follow a linear stochastic process with multiplicative noise, $\dot T_i = α(m_T - T_i) + D T_iξ$. The resulting stationary distribution has a power-law tail, especially for densities where cars are interacting strongly. Analyzing additionally the headways for accelerating and decelerating cars, the slow-to-start effect proposed as a mechanism for traffic jam stability can be demonstrated explicitly. Finally, the standard deviation of the speed differences between following cars can be used to get a clear characterization of (at least) three different regimes of traffic flow that can be identified in the data. Using the empirical results to enhance a microscopic traffic flow model, it can be demonstrated that such a model describes the fluctuations of traffic flow quite satisfactorily.

cond-mat.other↗
arXiv2004

Prospects of Searches for Neutral, Long-Lived Particles which Decay to Photons using Timing at CDF

We present the prospects of searches for neutral, long-lived particles which decay to photons using their time of arrival measured with a newly installed timing system on the electromagnetic calorimeter (EMTiming) of the Collider Detector at Fermilab (CDF). A Monte Carlo simulation shows that EMTiming can provide separation between decay photons from particles with both a long lifetime and a low boost, and prompt photons from Standard Model backgrounds. Using a gauge mediated supersymmetry breaking (GMSB) $\tildeχ_{1}^{0}\toγ\tilde{G}$ model we estimate a quasi-model-independent sensitivity using only direct neutralino pair production, and also estimate the expected 95% confidence level exclusion regions for all superpartner production as a function of the neutralino mass and lifetime. We find that a combination of single photon and diphoton analyses should allow the Tevatron in run II to easily extend the exclusion regions from LEP II at high neutralino masses and lifetimes, and cover much, if not all, of the theoretically favored $m_{\tilde{G}}$ < 1 keV/c^2 parameter space for neutralino masses less than 150 GeV/c^2.

hep-ph↗
arXiv2003

Empirical basis for car-following theory development

By analyzing data from a car-following experiment, it is shown that drivers control their car by a simple scheme. The acceleration $a(t)$ is held approximately constant for a certain time interval, followed by a jump to a new acceleration. These jumps seem to include a deterministic and a random component; the time $T$ between subsequent jumps is random, too. This leads to a dynamic, that never reaches a fixed-point ($a(t) \to 0$ and velocity difference to the car in front $Δv \to 0$) of the car-following dynamics. The existence of such a fixed-point is predicted by most of the existing car-following theories. Nevertheless, the phase-space distribution is clustered strongly at $Δv=0$. Here, the probability distribution in $Δv$ is (for small and medium distances $Δx$ between the cars) described by $p(Δv) \propto \exp(-|Δv|/Δv_0)$ indicating a dynamic that attracts cars to the region with small speed differences. The corresponding distances $Δx$ between the cars vary strongly. This variation might be a possible reason for the much-discussed widely scattered states found in highway traffic.

cond-mat.stat-mech↗
arXiv2003

Towards the fundamentals of car following theory

The problem of a car following a lead car driven with constant velocity is considered. To derive the governing equations for the following car dynamics a cost functional that ranks the outcomes of different driving strategies is constructed, which applies to fairly general properties of the driver behavior. Assuming the driver behavior to be rational, the existence of the Nash equilibrium is proved. Rational driving is defined by supposing that a driver corrects continuously the car motion to follow the optimal path minimizing the cost functional. The corresponding car-following dynamics is described quite generally by a boundary value problem based on the obtained extremal equations. Linearization of these equations around the stationary state results in a generalization of the widely used optimal velocity model. Moreover, it is shown that there are conditions (the ``dense traffic'' limit) under which the rational car dynamics comprises two stages, fast and slow. During the fast stage a driver eliminates the velocity difference between the cars, the subsequent slow stage optimizes the headway. In the ``dense traffic'' limit an effective Hamiltonian description is constructed. This allows a more detailed nonlinear analysis. Finally, the differences between rational and bounded rational driver behavior are discussed. The latter, in particular, justifies some basic assumptions used recently by the authors to construct a car-following model lying beyond the frameworks of rationality.

cond-mat.soft↗
arXiv2003

Noised induced phase transition in an oscillatory system with dynamical traps

A new type of noised induced phase transitions is proposed. It occurs in noisy systems with dynamical traps. Dynamical traps are regions in the phase space where the regular forces are depressed substantially. By way of an example, a simple oscillatory system {x,v} with additive white noise is considered and its dynamics is analyzed numerically. The dynamical trap region is assumed to be located near the x-axis where the velocity v of the system becomes sufficiently low. The meaning of this assumption is discussed. The observed phase transition is caused by the asymmetry in the residence time distribution in the vicinity of zero value velocity. This asymmetry is due to a cooperative effect of the random Langevin force in the trap region and the regular force not changing the direction of action when crossing the trap region.

cond-mat.soft↗
arXiv2003

Effects of anticipatory driving in a traffic flow model

Anticipation in traffic means that drivers estimate their leaders' velocities for future timesteps. In the article a specific stochastic car--following model with non--unique flow--density relation is investigated with respect to anticipatory driving. It is realized by next--nearest--neighbour interaction which leads to large flows and short temporal headways. The underlying mechanism that causes these effects is explained by the headways of the cars which organize in an alternating structure with a short headway following a long one, thereby producing a strong anti-correlation in the gaps or in the headways of subsequent cars. For the investigated model the corresponding time headway distributions display the short headways observed in reality. Even though these effects are discussed for a specific model, the mechanism described is in general present in any traffic flow models that work with anticipation.

cond-mat.stat-mech↗
arXiv2002

A Bounded Rational Driver Model

This paper introduces a car following model where the driving scheme takes into account the deficiencies of human decision making in a general way. Aditionally, it improves certain shortcomings of most of the models currently in use: it is stochastic but has a continuous acceleration. This is achieved at the cost of formulating the model in terms of the time derivative of the acceleration, making it non-Newtonian.

cond-mat.soft↗
arXiv2002

Boundary-induced phase transitions in a space-continuous traffic model with non-unique flow-density relation

The Krauss-model is a stochastic model for traffic flow which is continuous in space. For periodic boundary conditions it is well understood and known to display a non-unique flow-density relation (fundamental diagram) for certain densities. In many applications, however, the behaviour under open boundary conditions plays a crucial role.In contrast to all models investigated so far, the high flow states of the Krauss-model are not metastable, but also stable. Nevertheless we find that the current in open systems obeys an extremal principle introduced for the case of simpler discrete models. The phase diagram of the open system will be completely determined by the fundamental diagram of the periodic system through this principle. In order to allow the investigation of the whole state space of the Krauss-model, appropriate strategies for the injection of cars into the system are needed.Two methods solving this problem are discussed and the boundary-induced phase transitions for both methods are studied.We also suggest a supplementary rule for the extremal principle to account for cases where not all the possible bulk states are generated by the chosen boundary conditions.

cond-mat.stat-mech↗
arXiv2002

Long-lived states in synchronized traffic flow. Empirical prompt and dynamical trap model

The present paper proposes a novel interpretation of the widely scattered states (called synchronized traffic) stimulated by Kerner's hypotheses about the existence of a multitude of metastable states in the fundamental diagram. Using single vehicle data collected at the German highway A1, temporal velocity patterns have been analyzed to show a collection of certain fragments with approximately constant velocities and sharp jumps between them. The particular velocity values in these fragments vary in a wide range. In contrast, the flow rate is more or less constant because its fluctuations are mainly due to the discreteness of traffic flow. Subsequently, we develop a model for synchronized traffic that can explain these characteristics. Following previous work (I.A.Lubashevsky, R.Mahnke, Phys. Rev. E v. 62, p. 6082, 2000) the vehicle flow is specified by car density, mean velocity, and additional order parameters $h$ and $a$ that are due to the many-particle effects of the vehicle interaction. The parameter $h$ describes the multilane correlations in the vehicle motion. Together with the car density it determines directly the mean velocity. The parameter $a$, in contrast, controls the evolution of $h$ only. The model assumes that $a$ fluctuates randomly around the value corresponding to the car configuration optimal for lane changing. When it deviates from this value the lane change is depressed for all cars forming a local cluster. Since exactly the overtaking manoeuvres of these cars cause the order parameter $a$ to vary, the evolution of the car arrangement becomes frozen for a certain time. In other words, the evolution equations form certain dynamical traps responsible for the long-time correlations in the synchronized mode.

cond-mat.soft↗
arXiv2001

Breakdown and recovery in traffic flow models

Most car-following models show a transition from laminar to ``congested'' flow and vice versa. Deterministic models often have a density range where a disturbance needs a sufficiently large critical amplitude to move the flow from the laminar into the congested phase. In stochastic models, it may be assumed that the size of this amplitude gets translated into a waiting time, i.e.\ until fluctuations sufficiently add up to trigger the transition. A recently introduced model of traffic flow however does not show this behavior: in the density regime where the jam solution co-exists with the high-flow state, the intrinsic stochasticity of the model is not sufficient to cause a transition into the jammed regime, at least not within relevant time scales. In addition, models can be differentiated by the stability of the outflow interface. We demonstrate that this additional criterion is not related to the stability of the flow. The combination of these criteria makes it possible to characterize commonalities and differences between many existing models for traffic in a new way.

cond-mat.stat-mech↗
arXiv1997

Two-lane traffic rules for cellular automata: A systematic approach

Microscopic modeling of multi-lane traffic is usually done by applying heuristic lane changing rules, and often with unsatisfying results. Recently, a cellular automaton model for two-lane traffic was able to overcome some of these problems and to produce a correct density inversion at densities somewhat below the maximum flow density. In this paper, we summarize different approaches to lane changing and their results, and propose a general scheme, according to which realistic lane changing rules can be developed. We test this scheme by applying it to several different lane changing rules, which, in spite of their differences, generate similar and realistic results. We thus conclude that, for producing realistic results, the logical structure of the lane changing rules, as proposed here, is at least as important as the microscopic details of the rules.

cond-mat.stat-mech↗