Pathwidth Research Articles

Wave-front tracking for the equations of non-isentropic gas dynamics

We study the model equations of polytropic gas dynamics, which constitute a system of three hyperbolic conservation laws. Global in time BV solutions were obtained by Liu (Indiana Univ Math J 26(1):147–177, 1977) provided that $$(\gamma - 1)$$ times the total variation of the initial data is sufficiently small; here $$\gamma $$ is the adiabatic coefficient. The aim of this paper is to give an alternative proof by exploiting the Dafermos–Bressan–Risebro wave-front tracking scheme. An original feature is the use of the path decomposition method to obtain pathwise estimates of the approximate solutions; these estimates show the decay properties of the solutions and play a crucial role in proving the stability of the wave-front tracking scheme.

Lévy processes conditioned on having a large height process

Dans ce travail, on considere des processus de Levy $(X_{t},t\geq0)$ ne derivant pas vers $+\infty$ et on s’interesse a leur conditionnement a atteindre des hauteurs arbitrairement grandes (au sens du processus des hauteurs associe a $X$) avant de toucher $0$. On obtient ainsi une nouvelle maniere de conditionner des processus de Levy a rester positifs. La loi (honnete) ${\mathbb{P}}_{x}^{\star}$ de ce processus conditionne (partant de $x>0$) est definie selon une $h$-transformee de Doob a l’aide d’une martingale. En ce qui concerne les processus de Levy ayant des trajectoires a variation infinie, cette martingale est $(\int\tilde{\rho}_{t}(\mathrm{d}z)\mathrm{e}^{\alpha z}+I_{t})\mathbf{1} _{\{t\leq T_{0}\}}$ pour un certain $\alpha$ et ou $(I_{t},t\geq0)$ est le processus infimum de $X$, ou $(\tilde{\rho}_{t},t\geq0)$ est le processus d’exploration defini dans [10] et ou $T_{0}$ est le temps d’atteinte de 0 par $X$. Sous ${\mathbb{P}}_{x}^{\star}$, on obtient egalement une decomposition de la trajectoire de $X$ en son minimum; ce qui permet de prouver la convergence de ${\mathbb{P}}_{x}^{\star}$ quand $x\to0$. Lorsque le processus $X$ est un processus de Poisson compose compense, la martingale est definie a partir des sauts du processus infimum futur de $X$. Les preuves sont plus simples dans ce cas puisque on peut voir $X$ comme le processus de contour d’un arbre de ramification (sous)critique. Dans ce cas, on enonce aussi une caracterisation alternative du processus conditionne dans l’esprit des decompositions spinales.

Assessment of motor imagery in cerebral palsy via mental chronometry: The case of walking

Recent studies show varying results on whether motor imagery capacity is compromised in individuals with cerebral palsy (CP). Motor imagery studies in children predominantly used the implicit hand laterality task. In this task participants judge the laterality of displayed hand stimuli. A more explicit way of studying motor imagery is mental chronometry. This paradigm is based on the comparison between the movement durations of actually performing a task and imagining the same task. The current study explored motor imagery capacity in CP by means of mental chronometry of a whole body task. Movement durations of 20 individuals with CP (mean age=13 years, SD=3.6) were recorded in two conditions: actual walking and imagined walking. Six unique trajectories were used that varied in difficulty via manipulation of walking distance and path width. We found no main effect of condition (actual walking versus imagining) on movement durations. Difficulty of the walking trajectory did affect movement durations. In general, this was expressed by an increase in movement durations with increasing difficulty of the task. No interaction between task difficulty and movement condition was found. Our results show that task difficulty has similar effects on movement durations for both actual walking and imagined walking. These results exemplify that the tested individuals were able to use motor imagery in an explicit task involving walking. Previous studies using the implicit hand laterality task showed varying results on motor imagery capacity in CP. We therefore conclude that motor imagery capacity is task dependent and that an explicit paradigm as the one used in this study may reveal the true motor imagery capacity. The implications of these findings for the use of motor imagery training are discussed.

Foot Pressure Pattern and its Correlation With Knee Range of Motion Limitations for Individuals With Medial Knee Osteoarthritis

ObjectiveTo determine the foot pressure pattern of individuals with medial knee osteoarthritis (OA) and to analyze its relation with knee flexion/extension range of motion. DesignDescriptive. SettingRehabilitation center. ParticipantsIndividuals with unilateral, painful medial knee OA (n=50; mean age, 75y; OA group) were enrolled as subjects, and young, healthy persons (n=50; mean age, 28y; young group) and elderly persons (n=44; mean age, 74y; elderly group) without any pain, deformity, or apparent OA changes in either knee were enrolled as controls. InterventionWalking 10m at a comfortable speed. Main Outcome MeasuresPartial foot pressures as percentages of body weight (%PFP), anteroposterior length of the center of pressure (COP) path as a percentage of foot length (%Long), transverse width of the COP path as a percentage of foot width (%Trans), knee flexion/extension range of motion (in the OA group). ResultsThe %PFP values for the heel and hallux, %Long, and %Trans were all significantly lower in the OA group than in controls (P<.001, all). Within the OA group, a limited range of knee extension was significantly associated with a short %Long (P<.001) but not with %Trans. ConclusionsIndividuals with medial knee OA exhibited low pressure on the heel and hallux and short %Long of the COP path, and limitation of knee extension was associated with shortness of %Long. The shortness of %Long in the OA group likely resulted from insufficient knee extension during the heel-contact phase associated with low pressure on the heel. %Long is a useful parameter in gait analysis by using a foot pressure measurement system.

Modeling of selected electric properties of textile signal lines using neural networks

Research into new textile transmission lines is currently being conducted. Thanks to the flexibility of textile material used for their construction, these lines can become elements of a textronic system incorporated in modern smart garments to considerably enhance the comfort of its use. Textile transmission lines are required, however, to meet some specific requirements. A properly designed line should assure the minimum of signal losses and reflections. The normalized characteristic impedance of lines is assumed to be 50 ohms. This paper presents a new type of textile transmission lines. A method for measuring the line impedance is discussed. The construction of a measuring stand to be used for testing the electric properties of textile transmission lines is shown. Using artificial neural networks, a model for selected electric properties of textile transmission lines was obtained. The results of a sensibility analysis carried out based on the three-layer perceptron indicates a significant influence of selected model input quantities, such as the width of the inner conductive path, the distance between paths, path surface resistance, path thickness, and the number of warp and weft yarns occurring in a conductive path on the electric properties of textile transmission lines.

Decomposition of Graphs into Paths and Cycles

A decomposition of a graph is a collection of edge-disjoint subgraphs of such that every edge of belongs to exactly one . If each is a path or a cycle in , then is called a path decomposition of . If each is a path in , then is called an acyclic path decomposition of . The minimum cardinality of a path decomposition (acyclic path decomposition) of is called the path decomposition number (acyclic path decomposition number) of and is denoted by () (()). In this paper we initiate a study of the parameter and determine the value of for some standard graphs. Further, we obtain some bounds for and characterize graphs attaining the bounds. We also prove that the difference between the parameters and can be made arbitrarily large.

Traffic conflicts on bicycle paths: A systematic observation of behaviour from video

In The Netherlands, on bicycle paths, single-bicycle accidents, bicycle–bicycle and bicycle–moped accidents constitute a considerable share of all bicyclist injuries. Over three quarters of all hospitalised bicyclist victims in the Netherlands cannot be directly related to a crash with motorised traffic. As the usage of bicycle paths steadily increases, it is to be expected that safety on bicycle paths will become a major issue in the coming years in The Netherlands.A study was conducted into the behaviour of bicyclists and moped riders to improve traffic safety on bicycle paths. By behavioural observations with video, mutual conflicts and bicyclist behaviour on bicycle paths were recorded and analysed, among other things by means of the conflict observation method DOCTOR (Dutch Objective Conflict Technique for Operation and Research). The explorative phase of the study (phase 1), included two research locations, one in the city of Amsterdam and one in Eindhoven. The results gave guidance for a better understanding of the behaviour between different users of separate two-directional bicycle paths. An example includes the relationship between bicyclist–moped rider behaviour and the width of the bicycle path. For a condition with busy bicycle traffic in both directions the width of the bicycle path in Amsterdam (effectively 3.55m) is relatively narrow, whereas the bicycle path width in Eindhoven (>4.94m) appears to be sufficient to accommodate large flows of bicyclists. Because of a large flow of crossing pedestrians resulting in (severe) conflicts with bicyclists in Amsterdam, additional countermeasures to better control these interactions are needed.The DOCTOR conflict observation method from video appears to be applicable for conflicts between intersecting road users and for head-on conflicts on the bicycle path. Conflict situations between bicyclists in the same direction (constituting an important share of injury accidents on bicycle paths) require an additional and more general systematic observation of specific behaviour. Therefore, phase 2 of the project will focus in particular on interactions between bicycle path users in the same direction and underlying processes.

흡입 유로 형상이 터보펌프의 성능 및 캐비테이션에 미치는 영향에 관한 실험적 연구

Super-cavitating vehicle which is operating under water speeds up to 100m/s. In this process super-cavitation around body reduces frictional resistance. This paper introduces experimental study on different width of suction path as there is a warhead in the torpedo. Hydraulic performances of turbopump at non-cavitating condition does not display a significant differences depending on different width of suction path. However, cavitation performance of each model shows obvious differences in the same condition of experience. In case of radial inlet, the value of critical NPSH(which indicates 3% head drop) increases about 20% in comparison of axial inlet.

Detonation Transition Around Cylindrical Reflector of Pulse Detonation Engine Initiator

To achieve reliable transmission of detonation waves to a pulse detonation engine combustor (detonation chamber), the authors propose a pulse detonation engine initiator that uses a cylindrical reflector downstream of a predetonator exit. The detonation wave propagates around the reflector to change the wave shape in three transition stages: from a planar detonation wave in the predetonator to an expanding cylindrical detonation wave, from the cylindrical wave to a planar toroidal detonation wave, and from the toroidal wave to a planar detonation wave in the detonation chamber. The cylindrical wave propagates along a cylindrical path between the reflector and front wall of the detonation chamber, and the toroidal wave propagates along an annular path between the reflector and sidewall of the detonation chamber. The purpose of this study was to examine the influence of the gap width of the annular path on the transition stages from cylindrical to toroidal and from toroidal to planar. A series of experiments that filled the entire test section with the driver gas mixture (stoichiometric hydrogen–oxygen mixture) showed that the expanding cylindrical detonation wave was sufficiently strong to survive the rarefaction waves from the corners of the reflector at all of the investigated annular gap widths (5, 10, 15, and 20 mm) and was transmitted to the planar toroidal wave successfully in all cases. When the strength of the cylindrical detonation wave was under a supercritical condition for diffraction at the reflector corner, the necessary filling distance for the driver gas was predicted well by the Whitham theory. A second series of experiments showed the influence of the annular gap width on the detonation transition from the planar toroidal detonation wave to the planar detonation wave. Two different types of detonation transitions termed “continuous transition” and “temporal quenching” were observed. The threshold value of for continuous transition is approximately four.

The arrival-time distribution: the extended probability approaches

We present a calculation of the arrival-time probability distribution based on the extended probability, as proposed by Hartle (2008 Phys. Rev.A 78 012108). We show that two cases of the arrival-time probability distribution can be used. First, we use the path decomposition expansion to discuss a fine-grained history, for which a particle has a first crossing x = 0 at time τ. The arrival-time probability, related to the probability current, is obtained. Second, we consider that the arrival-time distribution is modeled by the first photon emitted from a two-level atom (the basic atom–laser model). The partition dynamic of this system is discussed. Each history is in the form of a coarse-grained history. We confirm that the arrival-time probability distribution computed by this method agrees with that computed via the probability of no-photon detection. Crucially, the resulting arrival-time distributions can be obtained without the restriction of the consistency condition.

Software Design Principles of Intelligent Evacuation Indication System

Abstract This essay introduces the research significance of intelligent evacuation indication system, concluding the set conditions for intelligent evacuation indication system by analyzing and summarizing the safe evacuation principles, and by the particular example how dual fire exits and the width of evacuation path affects the arrangement of evacuation signs, which provides a theoretical support for software design of intelligent evacuation indication system.

Fuzzy Controller for Automatic Steering in Heavy Vehicle Semi-Trailers

Trucks with semi-trailers are widely used for transportation of goods due their low operation cost, but inherent to these vehicles are some problems such as a poor maneuverability. To minimize the effects of this disadvantage, among other solutions, the incorporation of steerable axles in the semitrailers has been proposed. This paper presents a steering equation, and a fuzzy-logic controller for a semi-trailer automatic forced-steering system to minimize the off-tracking and the total swept path width, resulting in an improvement of vehicle's maneuverability at low speeds. To accomplish this, the suggested control algorithm considers the articulation angle and parameters such as vehicle speed and direction. The system was tested on an instrumented experimental semi-trailer during various predetermined test maneuvers.

A Card Stack Model to Elucidate Key Challenges in the Development of Future Generation Supercomputers

This paper intends to elucidate challenges in some aspects of the hardware design of future generation computers. We use a system model, a stack of integrated circuit cards cooled by a dielectric coolant (FC77). A set of equations is developed to describe the relationships between the system throughput, the volume, the power consumption, and those concerning the details of internal organization such as signal and power line dimensions and coolant path width. The calculated values of throughput, volume, and power are projected on a state point in a graph of the figures-of-merit pair, the computational density, and the computational efficiency. By manipulating the empirical parameters imbedded in the model, the state point is steered to follow the evolutionary line that runs through the points corresponding to the existing supercomputers of several generations. Then, calculation is extended on state points for future prospective computers with target system throughputs. The results point to the needs for research and development effort on thermal management and materials development. As for thermal management of exa- and zeta-scale computers, we need to refocus heat transfer research. Coolant channels will have very large length-to-width ratios (several thousand), while the heat flux on the channel surface is quite low. Micro-fluidics to guarantee stable coolant flow in such long micro-channels will be of primary importance in place of the means to deal with high heat flux. We also need to develop novel materials for signal transmission lines and cooling, particularly in the development of zeta-scale computers.

The visual control of bicycle steering: The effects of speed and path width

Although cycling is a widespread form of transportation, little is known about the visual behaviour of bicycle users. This study examined whether the visual behaviour of cyclists can be explained by the two-level model of steering described for car driving, and how it is influenced by cycling speed and lane width. In addition, this study investigated whether travel fixations, described during walking, can also be found during a cycling task. Twelve adult participants were asked to cycle three 15m long cycling lanes of 10, 25 and 40cm wide at three different self-selected speeds (i.e., slow, preferred and fast). Participants’ gaze behaviour was recorded at 50Hz using a head mounted eye tracker and the resulting scene video with overlay gaze cursor was analysed frame by frame. Four types of fixations were distinguished: (1) travel fixations, (2) fixations inside the cycling lane (path), (3) fixations to the final metre of the lane (goal), and (4) fixations outside of the cycling lane (external). Participants were found to mainly watch the path (41%) and goal (40%) region while very few travel fixations were made (<5%). Instead of travel fixations, an OptoKinetic Nystagmus was revealed when looking at the near path. Large variability between subjects in fixation location suggests that different strategies were used. Wider lanes resulted in a shift of gaze towards the end of the lane and to external regions, whereas higher cycling speeds resulted in a more distant gaze behaviour and more travel fixations. To conclude, the two-level model of steering as described for car driving is not fully in line with our findings during cycling, but the assumption that both the near and the far region is necessary for efficient steering seems valid. A new model for visual behaviour during goal directed locomotion is presented.

Prediction of Permeability In Quartz-Rich Sandstones: Examples from the Norwegian Continental Shelf and the Fontainebleau Sandstone

Abstract Correctly predicting sandstone permeability from variables such as porosity, composition, and texture is one of the major problems of petroleum geology and hydrology. Using data sets comprising composition, texture, porosity, and permeability for sandstone samples from the Norwegian continental shelf and the Fontainebleau Sandstone, we have tested several previously suggested methods for permeability prediction, and also suggest a new method for sandstones containing significant volumes of clay. Our results indicate that permeability is successfully predicted from porosity and mean grain size by the Kozeny equation for most sandstones with clay contents less than 3% when porosities exceed 6–14%, with the lowest threshold values of porosity tending to occur in the sandstones containing least clay. The Kozeny equation also seems to enable calculation of the probable maximum possible permeabilities for sandstones with given porosities and grain sizes. For clay contents above 3%, the Kozeny equation typically overpredicts permeability. Including a percolation threshold in the Kozeny equation, using estimated macroporosity rather than total porosity, or applying a form of the equation where internal surface area is used as input instead of grain size does not provide generally acceptable permeability estimates. However, a modified Kozeny equation which includes a parameter reflecting the type of pore system often provides useful permeability estimates even for clay-rich samples. This parameter can often be regarded as a constant for a specific formation or sandstone unit when porosity variations are not excessive. Mercury-injection data suggest that its value is controlled by the width and connectivity of the dominant flow paths through the system, which in turn are probably determined by factors such as volume and distribution of clay.

Soft X-Ray Single-Photon Detection With Superconducting Tantalum Nitride and Niobium Nanowires

We have fabricated ultrafast dark count-free soft X-ray single-photon detectors (X-SNSPDs) from TaN with various conduction path widths, and we compare their properties with corresponding data from a Nb X-SNSPD. The TaN X-SNSPDs offer an improved detector performance regarding device detection efficiency, latching, and pulse amplitudes. Wide conduction paths allow for a certain energy-resolving capability in contrast to narrow TaN conduction paths. However, wide paths also limit the detection efficiency at low temperatures, which can be explained within a hot-spot model.

Treewidth, pathwidth and cospan decompositions with applications to graph-accepting tree automata

We will revisit the categorical notion of cospan decompositions of graphs and compare it to the well-known notions of path decomposition and tree decomposition from graph theory. More specifically, we will define several types of cospan decompositions with appropriate width measures and show that these width measures coincide with pathwidth and treewidth. Such graph decompositions of small width are used to efficiently decide graph properties, for instance via graph automata. Hence we will give an application by defining graph-accepting tree automata, thus integrating previous work by Courcelle into the setting of cospan decompositions. Furthermore we will show that regardless of whether we consider path or tree decompositions, we arrive at the same notion of recognizability.

TIME‐CHANGED ORNSTEIN–UHLENBECK PROCESSES AND THEIR APPLICATIONS IN COMMODITY DERIVATIVE MODELS

This paper studies subordinate Ornstein–Uhlenbeck (OU) processes, i.e., OU diffusions time changed by Lévy subordinators. We construct their sample path decomposition, show that they possess mean‐reverting jumps, study their equivalent measure transformations, and the spectral representation of their transition semigroups in terms of Hermite expansions. As an application, we propose a new class of commodity models with mean‐reverting jumps based on subordinate OU processes. Further time changing by the integral of a Cox–Ingersoll–Ross process plus a deterministic function of time, we induce stochastic volatility and time inhomogeneity, such as seasonality, in the models. We obtain analytical solutions for commodity futures options in terms of Hermite expansions. The models are consistent with the initial futures curve, exhibit Samuelson's maturity effect, and are flexible enough to capture a variety of implied volatility smile patterns observed in commodities futures options.

Brownian meanders, importance sampling and unbiased simulation of diffusion extremes

Computing expected values of functions involving extreme values of diffusion processes can find many applications in financial engineering. Conventional discretization simulation schemes often converge slowly. We propose a Wiener-measure-decomposition based approach to construct unbiased Monte Carlo estimators. Combined with the importance sampling technique and the Williams path decomposition of Brownian motion, this approach transforms simulating extreme values of a general diffusion process to simulating two Brownian meanders. Numerical experiments show this estimator performs efficiently for diffusions with and without boundaries.

Global existence of solutions by path decomposition for a model of multiphase flow

We consider a strictly hyperbolic system of three conservation laws, in one space dimension. The system is a simple model for a fluid flow undergoing liquid-vapor phase transitions. We prove, by a front-tracking algorithm, that weak solutions exist for all times under a condition on the (large) variation of the initial data. An original issue is the control of interactions by means of decompositions of shock waves into paths.