Mean Relative Speed Research Articles

Microscopic derivation of the collision properties of molecules in two systems at thermal equilibrium

The mean relative speed and relative speed distribution function of molecules play important roles in kinetics and related topics. College textbooks frequently present a simplified derivation of these quantities that, while yielding the correct result, are not well justified. This paper presents a detailed physical picture of collision-related processes based on the microscopic kinetic theory. Formulas for the mean relative speed and mean collision rate along with the relative speed distribution function and the distribution function of relative speed of the paired particles in collisions (collision possible distribution function) are derived for molecules from two different systems that are each at thermal equilibrium.

Assessing the impacts of heavy vehicles on traffic characteristics of highways under mixed traffic platooning conditions

The study aims to investigate the impact of heavy vehicles (HVs) on traffic characteristics under platoon conditions on Indian highways. Traffic volume, speed, and time headway data were gathered from different highway sections using infra-red sensors. The mean relative speed criteria were used as an indicator of variability to estimate the critical time headway. The threshold value of a critical time headway of 4 sec was determined to represent vehicles into non-platoon followers and platoon followers. The speed-flow-density model curves were developed for two different traffic regimes, one without platoons and the other with platoons created by the HVs. The results show that under platoon conditions, the speed at capacity, density at capacity, and traffic capacity reduced by 11.2%, 12.5%, and 22.3%, respectively, compared to non-platoon conditions. Additionally, the average travel time and travel delay increased by 18.1 s/km and 12.7 s/km, respectively. The study’s findings emphasize the importance of considering platoon dynamics under the influence of HVs to better understand their impact on traffic characteristics.

Impacts of predator-induced behavioural plasticity on the temperature dependence of predator-prey activity and population dynamics.

Predation is a key ecological interaction affecting populations and communities. Climate warming can modify this interaction both directly by the kinetic effects of temperature on biological rates and indirectly through integrated behavioural and physiological responses of the predators and prey. Temperature dependence of predation rates can further be altered by predator-induced plasticity of prey locomotor activity, but empirical data about this effect are lacking. We propose a general framework to understand the influence of predator-induced developmental plasticity on behavioural thermal reaction norms in prey and their consequences for predator-prey dynamics. Using a mesocosm experiment with dragonfly larvae (predator) and newt larvae (prey), we tested if the predator-induced plasticity alters the elevation or the slope of the thermal reaction norms for locomotor activity metrics in prey. We also estimated the joint predator-prey thermal response in mean locomotor speed, which determines prey encounter rate, and modelled the effect of both phenomena on predator-prey population dynamics. Thermal reaction norms for locomotor activity in prey were affected by predation risk cues but with minor influence on the joint predator-prey behavioural response. We found that predation risk cues significantly decreased the intercept of thermal reaction norm for total activity rate (i.e. all body movements) but not the other locomotor activity metrics in the prey, and that prey locomotor activity rate and locomotor speed increased with prey density. Temperature had opposite effects on the mean relative speed of predator and prey as individual speed increased with temperature in predators but decreased in prey. This led to a negligible effect of body temperature on predicted prey encounter rates and predator-prey dynamics. The behavioural component of predator-prey interaction varied much more between individuals than with temperature and the presence of predation risk cues in our system. We conclude that within-population variation in locomotor activity can buffer the influence of body temperature and predation risk cues on predator-prey interactions, and further research should focus on the magnitude and sources of behavioural variation in interacting species to predict the impact of climate change on predator-prey interactions and food web dynamics.

Relative movement on the articular surfaces of the tibiotalar and subtalar joints during walking.

ObjectivesThe objective of this study was to quantify the relative movement between the articular surfaces in the tibiotalar and subtalar joints during normal walking in asymptomatic individuals.Methods3D movement data of the ankle joint complex were acquired from 18 subjects using a biplanar fluoroscopic system and 3D-to-2D registration of bone models obtained from CT images. Surface relative velocity vectors (SRVVs) of the articular surfaces of the tibiotalar and subtalar joints were calculated. The relative movement of the articulating surfaces was quantified as the mean relative speed (RS) and synchronization index (SIENT) of the SRVVs.ResultsSIENT and mean RS data showed that the tibiotalar joint exhibited translational movement throughout the stance, with a mean SIENT of 0.54 (sd 0.21). The mean RS of the tibiotalar joint during the 0% to 20% post heel-strike phase was 36.0 mm/s (sd 14.2), which was higher than for the rest of the stance period. The subtalar joint had a mean SIENT value of 0.43 (sd 0.21) during the stance phase and exhibited a greater degree of rotational movement than the tibiotalar joint. The mean relative speeds of the subtalar joint in early (0% to 10%) and late (80% to 90%) stance were 23.9 mm/s (sd 11.3) and 25.1 mm/s (sd 9.5), respectively, which were significantly higher than the mean RS during mid-stance (10% to 80%).ConclusionThe tibiotalar and subtalar joints exhibited significant translational and rotational movement in the initial stance, whereas only the subtalar joint exhibited significant rotational movement during the late stance. The relative movement on the articular surfaces provided deeper insight into the interactions between articular surfaces, which are unobtainable using the joint coordinate system.Cite this article: C-B. Phan, D-P. Nguyen, K. M. Lee, S. Koo. Relative movement on the articular surfaces of the tibiotalar and subtalar joints during walking. Bone Joint Res 2018;7:501–507. DOI: 10.1302/2046-3758.78.BJR-2018-0014.R1.

Exceptional running and turning performance in a mite.

The Southern California endemic mite Paratarsotomus macropalpis was filmed in the field on a concrete substrate and in the lab to analyze stride frequency, gait and running speed under different temperature conditions and during turning. At ground temperatures ranging from 45 to 60 °C, mites ran at a mean relative speed of 192.4 ± 2.1 body lengths (BL) s(-1), exceeding the highest previously documented value for a land animal by 12.5%. Stride frequencies were also exceptionally high (up to 135 Hz), and increased with substrate temperature. Juveniles exhibited higher relative speeds than adults and possess proportionally longer legs, which allow for greater relative stride lengths. Although mites accelerated and decelerated rapidly during straight running (7.2 ± 1.2 and -10.1 ± 2.1 m s(-2), respectively), the forces involved were comparable to those found in other animals. Paratarsotomus macropalpis employs an alternating tetrapod gait during steady running. Shallow turns were accomplished by a simple asymmetry in stride length. During tight turns, mites pivoted around the tarsus of the inside third leg (L3), which thus behaved like a grappling hook. Pivot turns were characterized by a 42% decrease in turning radius and a 40% increase in angular velocity compared with non-pivot turns. The joint angle amplitudes of the inner L2 and L3 were negligible during a pivot turn. While exceptional, running speeds in P. macropalpis approximate values predicted from inter-specific scaling relationships.

Exceptional locomotory performance in Paratarsotomus macropalpis mites (878.1)

The Southern California erythracarid mite species, Paratarsotomus macropalpis, was filmed using a high frame‐rate video camera in the field to analyze speed, stride frequency, acceleration and deceleration. We also recorded higher resolution lab footage of mites starting, stopping and turning to analyze gait and kinematic mechanisms. Mites running in the field on concrete substrates at high temperatures (40°C to 60°C) were shown to travel at mean relative speed of 192.4 bl s−1 (body lengths per second), exceeding the highest currently documented speed for land animals (171 bl s−1). Despite this exceptional value, it conforms broadly with predictions based on interspecific scaling. Stride frequencies were also exceptionally high (as fast as 135 Hz), and increased significantly with substrate temperature. Mites accelerate and decelerate rapidly (mean values of 7.2 ms−2 and −10.1 ms−2, respectively), although the forces involved are simiilar to those found in other running animals. Calculations show that air resistance is a minor contributor to deceleration; the forces are likely borne by a combination of muscle and cuticle ligament strain. During normal running, adjacent and opposite tarsi are 180 degrees out of phase. This gait cycle is preserved during turning, although the two front pairs of tarsi initiate acceleration cycles and duty factors increase for inner tarsi during turns.Grant Funding Source: Supported by the Howard Hughes Medical Institute

Decompression as a Treatment for Odontogenic Cystic Lesions of the Jaw

To evaluate the effectiveness of decompression as the primary treatment of odontogenic cystic lesions of the jaw involving factors that affect relative shrinking speed and bone regeneration. A total of 32 patients with odontogenic cystic lesions of the jaw underwent decompression with customized thermoplastic resin stents. Clinical examinations and pre- and postdecompression panoramic radiographs were analyzed. The mean relative speed of shrinkage of radicular cysts (RCs; 3.37 cm(2)/month) was faster than those of keratocystic odontogenic tumors (KCOTs; 2.87 cm(2)/month) and unicystic ameloblastomas (UABs; 2.71 cm(2)/month). The relative shrinking size increased linearly in a time-dependent manner for KCOTs (r = 0.849, P < .001), RCs (r = 0.681, P = .319), and UABs (r = 0.146, P = .730); a similar relation was detected between the primary radiolucent area of cystic lesions before decompression and relative shrinking speed after decompression in KCOTs (r = 0.481, P = .032), RCs (r = 0.260, P = .673), and UABs (r = 0.370, P = .366), but patient age did not affect the relative speed of shrinkage (P > .05). Furthermore, the increase in bone density was more significant in RCs than in KCOTs (P = .026) and UABs (P = .012) after decompression. Decompression was effective in reducing odontogenic cystic lesions of the jaw and increasing bone density. For aggressive lesions, secondary definitive surgery was necessary.

Discontinuous percolation in diffusion-limited cluster aggregation

Recently, the diffusion-limited cluster aggregation (DLCA) model was restudied as a real-world example of showing discontinuous percolation transitions (PTs). Because a larger cluster is less mobile in Brownian motion, it comes into contact with other clusters less frequently. Thus, the formation of a giant cluster is suppressed in the DLCA process. All clusters grow continuously with respect to time, but the largest cluster grows drastically with respect to the number of cluster merging events. Here, we study the discontinuous PT occurring in the DLCA model in more general dimensions such as two, three, and four dimensions. PTs are also studied for a generalized velocity, which scales with cluster size s as vs ∝ sη. For Brownian motion of hard spheres in three dimensions, the mean relative speed scales as s−1/2 and the collision rate σvs scales as ∼s1/6. We find numerically that the PT type changes from discontinuous to continuous as η crosses over a tricritical point ηc ≈ 1.2 (in two dimensions), ηc ≈ 0.8 (in three dimensions), and ηc ≈ 0.4 (in four dimensions). We illustrate the root of this crossover behavior from the perspective of the heterogeneity of cluster size distribution. Finally, we study the reaction-limited cluster aggregation (RLCA) model in the Brownian process, in which cluster merging takes place with finite probability r. We find that the PTs in two and three dimensions are discontinuous even for small r such as r = 10−3, but are continuous in four dimensions.

Corrigendum

Biological ReviewsVolume 84, Issue 2 p. 347-347 Free Access Corrigendum This article corrects the following: Use, misuse and extensions of “ideal gas” models of animal encounter John M. C. Hutchinson, Peter M. Waser, Volume 82Issue 3Biological Reviews pages: 335-359 First Published online: July 10, 2007 First published: 16 April 2009 https://doi.org/10.1111/j.1469-185X.2008.00072.xCitations: 1AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat The paper by J. M. C. Hutchinson (majmch@googlemail.com) and P. M. Waser (2007) contains the following errors. 1) On p. 343, formula (23) should read instead of . 2) On p. 350, in the caption to Fig. 9, the trajectory of the herring relative to the jellyfish should have length rather than . Nevertheless the derived formula (29) is correct and the quantitative results in this section were calculated with the correct version. 3) On p. 351, in the caption to Fig. 10, the trajectory of the ship relative to the bird should likewise have length rather than . This error has not affected other parts of the text (e.g. formula (31) remains correct). 4) On p. 338, in the last sentence of the caption to Fig. 1, 4vt/π should be the mean relative trajectory length, not mean relative speed, which is given correctly in formula (1) as 4v/π. The authors wish to apologise for any inconvenience caused by their carelessness. REFERENCE Hutchinson, J. M. C. & Waser, P. M. (2007). Use, misuse and extensions of “ideal gas” models of animal encounter. Biological Reviews 82, 335– 359. Wiley Online LibraryPubMedWeb of Science®Google Scholar Citing Literature Volume84, Issue2May 2009Pages 347-347 ReferencesRelatedInformation

Istrian Coastal Countercurrent and its Year-to-Year Variability

In this paper we demonstrate the existence of a descending surface current which usually appears in August along the Istrian coast line and runs counter to the general Adriatic-wide cyclonic flow. This is achieved by computing the relative (with respect to the 30-dbar surface) geostrophic currents as well as absolute currents and net transports from hydrographic data collected monthly to seasonally at six stations of the Po-Rovinj profile in the northern Adriatic. We name it the Istrian Coastal Countercurrent (ICCC). Its mean relative speed is high, 7cms−1(relative currents at the profile on average stay below 5cms−1in winter and below 8cms−1in summer), inducing a net outflow near the Istrian coast.The ICCC was strong in 1968, 1977, 1983, 1984, 1988, 1989, 1991, 1992, 1996 and 1997, weak or absent in 1971–1973, 1982, 1986, 1993–1995. Whenever the ICCC was well pronounced, specific dynamic and hydrographic features—pointing to a possible existence of an anticyclonic gyre off Rovinj—were observed. The existence of the ICCC is confirmed by direct current measurements, which show that the descending coastal current was intense in 1977 and 1983, and that it did not develop in 1976, 1978 and 1987.The intensity of the ICCC in August over the 1966–1992 interval was significantly correlated to the air–sea heat flux observed with the −7 months time lag in combination with the Po River discharge rate with the −1 month time lag and to the sea surface temperature recorded in the area with the −5 months time lag. On the correlation basis a weak or non-existent ICCC is hindcasted for 1976, 1978 and 1987. It seems that high intensity of the ICCC coincides with oceanographic conditions which favour near anoxia or mucilage events, observed in northern Adriatic in 1977, 1988, 1989, 1991 and 1997.

A Linear Altitude Rule for Safer and More Efficient Enroute Air Traffic

Current regulations designate cruising altitudes in discrete steps of 1000 ft (or 2000 ft above FL290, but those will eventually be reduced to 1000 ft also). By concentrating all enroute traffic into a few altitudes, this discrete altitude rule makes the enroute air traffic system less fail-safe and less fault-tolerant than it could be. The linear altitude rule proposed in this paper designates cruising altitudes as a linear function of heading or course. This rule spreads the traffic vertically and provides a default vertical separation that is proportional to path crossing angle. Monte Carlo simulation of enroute traffic with no air traffic control shows that the linear altitude rule greatly reduces both the collision rate and the mean relative speed of collisions. It also improves the efficiency of conflict resolution. It reduces the amount of altitude change required to resolve conflicts vertically, particularly for large-angle, high-speed conflicts, because those conflicts will have almost the required vertical separation by default. The inherent safety superiority of the linear altitude rule may also allow the horizontal separation standard to be reduced, which would increase airspace capacity and reduce the magnitude of speed or heading changes required to resolve conflicts horizontally.

Drag coefficients of spherical liquid droplets Part 2: Turbulent gaseous fields

The drag of non-evaporating, spherical, liquid droplets was measured in turbulent flow fields at parametric ranges relevant to spray combustion, characterized by the droplet Reynolds number, and the intensity and spatial scales of turbulence. The experimental apparatus comprised a wind-tunnel and a piezo-electric droplet generator. The procedure was to inject water droplets of uniform size co-currently and continuously with vertical turbulent air flows while droplet velocity was measured at different elevations using laser-Doppler velocimetry. Turbulence was characterized using hot-wire anemometry prior to droplet injection. Drag coefficients were calculated using these main measurements and the law of conservation of mechanical energy. Reynolds numbers were investigated in the range 10–100, in terms of the equivalent spherical diameter of a droplet, and the mean relative speed between the ambient gaseous field and the droplets. Weber numbers were much less than unity so droplets were effectively spherical. Relative intensities of turbulence were investigated in the range 20–65 percent, in terms of the mean relative speed. Spatial scales of turbulence were large in comparison to the droplets; the ratio between the spatial integral scale and the droplet diameter was in the range 11–38, and the Kolmogorov scale was comparable in size or smaller than the droplet diameter. Experimental data showed that the drag in turbulent fields under these conditions is not significantly different than that of solid spheres in a quiescent field at the same Reynolds number.

Rovibrational-state-dependent collisions of C2H4-Kr at low temperatures

Light-induced drift experiments at temperatures between 130 and 300 K have been performed on C2H4 With Kr as a collision partner. The experimental results for various rovibrational transitions in the nu 7 fundamental vibrational band are expressed in terms of the relative change in collision rate upon excitation, Delta nu / nu , as a function of the mean relative speed grms between the collision partners. For low grms, the collision rate nu is found to depend strongly on the rotational states involved. For high grms, the rotational dependence is relatively weak, and the values of Delta nu / nu converge to what is interpreted as the pure vibrational contribution.