Boundary Collisions Research Articles

Enabling Predictive Redirection Reset Based on Virtual-Real Spatial Probability Density Distributions.

Redirected walking (RDW) allows users to explore vast virtual spaces by walking in confined real spaces, yet suffers from frequent boundary collisions due to physical constraints. The major solution is to use the reset strategy to steer users away from boundaries. However, most reset methods guide users to fixed spots or follow constant patterns, neglecting spatial features and users' movement trends. In this paper, we propose an innovative predictive reset method based on spatial probability density distribution to jointly involve impacts of spatial feature and walking intention for forecasting the user's possible positional distribution, and thereby determines the optimal reset direction by maximizing walking expectation. Given a space, we calculate the stationary layout energy to indicate traveling difficulties of all positions. Meanwhile, we exploit a novel intention inference model to anticipate the probability distribution of the user's presence across adjacent positions. Furthermore, we incorporate the obstacle energy attenuation to predict the obstacle avoidance behaviors. All aforementioned factors are amalgamated into a potential region energy map, and then we integrate energy maps of virtual and real spaces into a fusion energy map to enable the prediction considering both spaces simultaneously. Thus, the optimal reset direction is derived by maximizing the fusion energy. Simulation and user studies are conducted on a broad dataset containing plentiful virtual and real spaces. The results demonstrate that our method effectively reduces the physical collisions and increase the continuous walking distance compared to prevalent reset methods, while exhibiting superior applicability when combined with various RDW controllers. The source code and dataset are available at https://github.com/huiyuroy/Return2MaxPotentialEnergy.

A Segmented Redirection Mapping Method for Roadmaps of Large Constrained Virtual Environments.

Redirected walking (RDW) enables users to explore large virtual spaces by real walking in small real spaces. How to effectively reduce physical collisions and decrease user perceptions of redirection are important for most RDW methods. This paper proposes a segmented redirection mapping method to calculate and map the roadmap of a large virtual space with inner obstacles to a mapped roadmap within a small real space. We adopt a Voronoi-based pruning method to extract the roadmap of the virtual space and design an RDW platform to interactively modify the virtual roadmap. We propose a roadmap mapping method based on divide-and-conquer and dynamic planning strategies to subdivide the virtual roadmap into several sub-virtual roads that are mapped individually. By recording connections of different sub-virtual roads, our method is applicable to virtual roadmaps with loop structures. During mapping, we apply the reset and redirection gains of the RDW technique as optimal aims and restrict conditions to obtain the mapped roadmap, which has small path curving and contains as few resets as possible. By real walking along the mapped roadmap, users perceive moving along the virtual roadmap to explore the entire virtual space. The experiment shows that our method works effectively for various virtual spaces with or without inner obstacles. Furthermore, our method is flexible in obtaining mapped roadmaps of different real spaces when the virtual space is fixed. Compared to prevalent RDW methods, our method can significantly reduce physical boundary collisions and maintain user experience of virtual roaming.

Monte-Carlo Redirected Walking: Gain Selection Through Simulated Walks.

We present Monte-Carlo Redirected Walking (MCRDW), a gain selection algorithm for redirected walking. MCRDW applies the Monte-Carlo method to redirected walking by simulating a large number of simple virtual walks, then inversely applying redirection to the virtual paths. Different gain levels and directions are applied, producing differing physical paths. Each physical path is scored and the results used to select the best gain level and direction. We provide a simple example implementation and a simulation-based study for validation. In our study, when compared with the next best technique, MCRDW reduced incidence of boundary collisions by over 50% while reducing total rotation and position gain.

Dynamical Analysis of Border Collision Bifurcation in One-Cycle Controlled Single-Inductor Dual-Output Boost DC-DC Converters

In this paper, the evolution of three types of border collision bifurcations are investigated thoroughly for a high-order single-inductor double-output DC-DC converter with one-cycle control (OCC). Multi-piecewise inductor current with more than one border and cross-coupling effect between different output ports are prominent features of the system, resulting in unexpected period incrementing cascade and transition from periodicity to chaos as a parameter is varied. A high-order nonlinear iterative map model is proposed, which reveals the underlying mechanisms of those complicated nonstandard and unsmooth bifurcations in the multiple-output system. Additionally, theoretical analysis shows that those nonstandard bifurcations arise from the boundary collisions, and more specifically, a fixed point suddenly appears in the borderline between various regions. Besides eigenvalue loci changes abruptly at the bifurcation point, the characteristic of border collision bifurcation is the topology sequence changes. Furthermore, the parameter boundaries are given to provide useful guidance for design. Finally, PSpice circuit experiments are performed to verify the above theoretical and numerical results.

Speeding up simulations by slowing down particles: Speed-limited particle-in-cell simulation

Based on the particle-in-cell (PIC) plasma simulation method, the speed-limited PIC (SLPIC) method delivers faster kinetic plasma simulation in cases where the particle distributions evolve slowly compared with the maximum stable PIC timestep. SLPIC thus offers more feasible, fully kinetic simulation in regimes that historically have required fluid approaches, such as magnetohydrodynamic (MHD), two-fluid, or Boltzmann electron treatments. In particular, SLPIC allows an explicit time advance with steps much larger than the inverse plasma frequency, avoiding the instability explicit PIC faces with large timesteps. SLPIC avoids this instability by slowing down fast particles (e.g., electrons) in a way that is rigorously underpinned by an approximate Vlasov equation; unlike MHD, two-fluid, and Boltzmann electron approaches, SLPIC does not fundamentally neglect any first-principles plasma physics, although the choices of the grid cell size, timestep, and number of macroparticles per cell naturally limit the physical phenomena that can be accurately represented. SLPIC can be implemented with minor modifications of a standard PIC code and does not require an implicit time advance. It enables large timesteps in first-principles kinetic plasma simulation of appropriately slow phenomena, and it can handle many of the same complications as PIC, such as boundary conditions and collisions. In an argon plasma sheath test problem, a SLPIC simulation achieved a speed-up of a factor of 160 over the corresponding PIC simulation, without loss of accuracy.

A dynamic geo-based resource selection algorithm for LTE-V2V communications

The geography-based (geo-based) resource selection algorithm is one of the feasibility schemes of third-generation partnership project (3GPP). However, most researches about it ignore the impacts of boundary interference and vehicle density. Therefore, this paper firstly puts forward an enhanced geo-based resource selection algorithm (EGRSA). This algorithm can eliminate the boundary interference through randomizing subframes of each sub resource pool. On the basis of EGRSA, the dynamic geo-based resource selection algorithm (DGRSA) is proposed to guarantee the reliability of communication when vehicle density is nonuniform. In DGRSA, mapping relationships are changed dynamically by grouping and optimal matching, and the size of each sub resource pool can also be adjusted. The system level simulation results indicate that the EGRSA is able to improve the packet reception ratio (PRR) and reduce the number of boundary collisions. Meanwhile, the proposed DGRSA further promotes the PRR when vehicle density is in a non-uniformity distribution because of traffic jam.

A framework of boundary collision data aggregation into neighbourhoods

A large portion of the total number of motor collisions can be boundary collisions; therefore, exaggerated or underestimated numbers for boundary collisions aggregated into neighbourhoods may hamper road safety analyses and management. In this paper, we propose a systematic framework for boundary collision aggregation. First, an entropy-based histogram thresholding method is utilized to determine the boundary zone size and identify boundary collisions. Next, the collision density probability distribution is then established, based on the collisions in each neighbourhood. Last, an effective boundary collision aggregation method, called the collision density ratio (CDR), is used to aggregate boundary collisions into neighbourhoods. The proposed framework is applied to collision data in the City of Edmonton for a case study. The experimental results show that the proposed entropy-based histogram thresholding method can identify boundary collision with the high precision and recall, and the proposed CDR method is more effective than the existing methods, the half-to-half ratio method and the one-to-one ratio method, to aggregate boundary collisions into neighbourhoods.

Experimental Investigations on the Coefficient of Restitution of Single Particles

Particle-based modeling approaches, such as the discrete element method, require the definition of accurate contact (collision) models. An essential parameter within these models is the coefficient of restitution (e), which mathematically defines the ratio of postcollision to precollision relative velocity during the collision of two materials. More generally, the coefficient of restitution provides a way of accounting for the kinetic energy lost during the collision of materials. This becomes important during particle–particle and particle–boundary collisions in both dry granular and multiphase flow models. This work studies e for particle–boundary type collisions through detailed experimental investigations of falling spheres colliding with thin stationary plates over a range of impact velocities. The results of these studies are also examined against analytical formulations for the coefficient of restitution. Experiments are performed on various sphere–plate material combinations, which include several tribologically relevant materials, such as low-carbon steel, tungsten carbide, and NiTiNOL 60. Experimental results for metallic material combinations displayed a decreasing trend in e for increased impact velocities. These metallic combinations also showed the lowest overall e values, whereas collisions involving glass showed the highest e values.

Size Independence of Statistics for Boundary Collisions of Random Walks and Its Implications for Spin-Polarized Gases

A bounded random walk exhibits strong correlations between collisions with a boundary. For a one-dimensional walk, we obtain the full statistical distribution of the number of such collisions in a time t. In the large t limit, the fluctuations in the number of collisions are found to be size independent (independent of the distance between boundaries). This occurs for any interboundary distance, from less to greater than the mean free path, and means that this boundary effect does not decay with increasing system size. As an application, we consider spin-polarized gases, such as 3-helium, in the three-dimensional diffusive regime. The above results mean that the depolarizing effect of rare magnetic impurities in the container walls is orders of magnitude larger than a Smoluchowski assumption (to neglect correlations) would imply. This could explain why depolarization is so sensitive to the container's treatment with magnetic fields prior to its use.

Heat fluctuations and phonon hydrodynamics in nanowires

We evaluate the second moments of the fluctuations of the total longitudinal heat flux in cylindrical nanowires described by phonon hydrodynamics with boundary conditions accounting for phonon boundary collisions. It is found that the second moments exhibit an explicit dependence on the boundary conditions and, therefore, may provide a suitable tool for analyzing phonon boundary collisions. Furthermore, an analogous dependence is also manifested in the relative probability of forward and backward fluctuations of the heat flux in a nonequilibrium steady state, thus providing a complementary tool of research for phonon boundary collisions.

Analysis of Outflow Boundary Collisions in North-Central Alabama

Abstract Ninety-four outflow boundary (OB) collisions were documented in north-central Alabama over the summers of 2005–07 using the Advanced Radar for Meteorological and Operational Research (ARMOR) dual-polarimetric radar located at the Huntsville, Alabama, airport. These data were used to extend and verify previous research and to look for new correlations among the various factors that lead to convective initiation (CI) from OB collisions more frequently. For this study, CI is defined as the first occurrence of a ≥35-dBZ radar echo at an elevation angle of 0.8° and within 10 km of the point of collision, from a convective cloud. The radar reflectivity and angle of collision between both OBs along with time of day at which CI occurs most often were analyzed. Also, the presence of cumulus clouds along either/both OBs, or within the area of collision, was examined using Geostationary Operational Environmental Satellite-12 (GOES-12) visible imagery. A more detailed analysis of 23 of the 94 OBs that passed over the Mobile Integrated Profiling System instruments examines the relation among radar reflectivity, updraft magnitude, and water vapor enhancements. This analysis indicates that OB updraft magnitude is positively correlated with OB reflectivity factor. The main findings are that when OBs collide in a more head-on manner, when both colliding OBs have radar reflectivity values of 15 dBZ or greater, or when cumulus clouds preexist along at least one OB, CI is produced at a greater rate. These results, using a much larger dataset than had previously been used for colliding OBs, are subsequently compared with two existing studies.

Surface Boundaries of the Southern Plains: Their Role in the Initiation of Convective Storms

Abstract The nature of the different types of surface boundaries that appear in the southern plains of the United States during the convectively active season is reviewed. The following boundaries are discussed: fronts, the dryline, troughs, and outflow boundaries, The boundaries are related to their environment and to local topography. The role these boundaries might play in the initiation of convective storms is emphasized. The various types of boundary-related vertical circulations and their dynamics are discussed. In particular, quasigeostrophic and semigeostrophic dynamics, and the dynamics of solenoidal circulations, density currents, boundary layers, and gravity waves are considered. Miscellaneous topics pertinent to convective storms and their relationship to surface boundaries such as along-the-boundary variability, boundary collisions, and the role of vertical shear are also discussed. Although some cases of storm initiation along surface boundaries have been well documented using research datasets collected during comprehensive field experiments, much of what we know is based only on empirical forecasting and nowcasting experience. It is suggested that many problems relating to convective-storm formation need to be explored in detail using real datasets with new observing systems and techniques, in conjunction with numerical simulation studies, and through climatological studies.

Onset of diffusive behavior in confined transport systems

We investigate the onset of diffusive behavior in polygonal channels for disks of finite size, modeling simple microporous membranes. It is well established that the point-particle case displays anomalous transport, because of slow correlation decay in the absence of defocusing collisions. We investigate which features of point-particle transport survive in the case of finite-sized particles (which undergo defocusing collisions). A similar question was investigated by Lansel, Porter, and Bunimovich [Chaos 16, 013129 (2006)], who found that certain integrals of motion and multiple ergodic components, characteristic of the point-particle case, remain in "mushroom"-like systems with few finite-sized particles. We quantify the time scales over which the transport of disks shows features typical of the point particles, or is driven toward diffusive behavior. In particular, we find that interparticle collisions drive the system toward diffusive behavior more strongly than defocusing boundary collisions. We illustrate how, and at what stage, typical thermodynamic behavior (consistent with kinetic theory) is observed, as particle numbers grow and mean free paths diminish. These results have both applied (e.g., nanotechnological) and theoretical interest.

Particle screening phenomena in an oblique multi-level tumbling reservoir: a numerical study using discrete element simulation

Due to their wide usage in industrial and technological processes, granular materials have captured great interest in recent research. The related studies are often based on numerical simulations and it is challenging to investigate computational phenomena of granular systems. Particle screening is an essential technology of particle separation in many industrial fields. This paper presents a numerical model for studying the particle screening process using the discrete element method that considers the motion of each particle individually. Dynamical quantities like particle positions, velocities and orientations are tracked at each time step of the simulation. The particular problem of interest is the separation of round shape particles of different sizes using a rotating tumbling vertical cylinder while the particulate material is continuously fed into its interior. This rotating cylinder can be designed as a uniform or stepped multi level obliqued vertical vessel and is considered as a big reservoir for the mixture of particulate material. The finer particles usually fall through the sieve openings while the oversized particles are rebounded and ejected through outlets located around the machine body. Particle–particle and particle–boundary collisions will appear under the tumbling motion of the rotating structure. A penalty method, which employs spring-damper models, will be applied to calculate the normal and frictional forces. As a result of collisions, the particles will dissipate kinetic energy due to the normal and frictional contact losses. The particle distribution, sifting rate of the separated particles and the efficiency of the segregation process have been studied. It is recognized that the screening phenomenon is very sensitive to the machines geometrical parameters, i.e. plate inclinations, shaft eccentricities and aperture sizes in the sieving plates at different levels of the structure. The rotational speed of the machine and the feeding rate of the particles flow have also a great influence on the transportation and segregation rates of the particles. In an attempt to better understand the mechanism of the particle transport between the different layers of the sifting system, different computational studies for achieving optimal operation have been performed.

An Observational Study of Atmospheric Bore Formation from Colliding Density Currents

Observations from east-central Florida during the Convection and Precipitation/Electrification (CaPE) experiment are used to investigate the factors that influence atmospheric bore formation from colliding density currents. Ten cases involving the collision of a gust front with a sea-breeze front are analyzed with Doppler radar and sounding and surface mesonet data. The gust fronts in these collisions were generally deeper, denser, and faster propagating than their sea-breeze-front counterparts. Seven of the 10 cases produced dual boundaries that moved away from each other in a relative sense after the collision. Post-collision boundaries moving in the same direction and oriented similarly to the pre-collision gust front occurred in all 10 cases. They transported mass in the manner of a density current in six cases, while the others behaved more like bores or bore–density current hybrids, as they were characterized by little or no mass transport. Similarity of gust-front and sea-breeze-front propagation speed prior to the collision was the best indicator of bore character in post-collision boundaries induced by gust fronts. Sea-breeze-front-induced post-collision boundaries occurred in the seven cases in which the pre-collision sea-breeze front was nonstationary. These post-collision boundaries exhibited no purely mass transport behavior and were all categorized as bores or bore/density current hybrids. The potential ability to predict dual zones of convergence emanating from boundary collisions as demonstrated in this study may be of value to convective nowcasting in Florida and perhaps other locales, as 70% of the observed post-collision boundaries initiated new convection or enhanced existing convection.

Dynamics of inelastic collapse.

We consider a particle randomly accelerated by Gaussian white noise on the half-line x>0. The collisions of the particle with the wall at x=0 are inelastic. The velocities just before and after reflection are related by v(f)=-rv(i), where r is the coefficient of restitution. Cornell, Swift, and Bray have shown that for r<r(c)=e(-pi/sqrt[3])=0.163, there is inelastic collapse, i.e., boundary collisions localize the particle at x=0. The probability that the particle is not yet absorbed at the boundary after a time t decays, for long times, as t(-straight theta(r)). The exponent straight theta(r) is calculated exactly. We also consider the case of "partial-survival" boundary conditions, i.e., elastic reflection with probability p and absorption with probability 1-p, and derive the analogous persistence exponent straight phi(p). The exact exponents satisfy the Swift-Bray conjecture straight theta(r)=straight phi(r(2straight theta(r))).

Statistics of a confined, randomly accelerated particle with inelastic boundary collisions

We consider the one-dimensional motion of a particle randomly accelerated by Gaussian white noise on the line segment $0lxl1.$ The reflections of the particle from the boundaries at $x=0,1$ are inelastic. The velocities just before and after reflection are related by ${v}_{f}=\ensuremath{-}{\mathrm{rv}}_{i},$ where r is the coefficient of restitution. Cornell, Swift, and Bray [Phys. Rev. Lett. 81, 1142 (1998)] have argued that there is an inelastic collapse transition in this system. For $rg{r}_{c}{=e}^{\ensuremath{-}\ensuremath{\pi}/\sqrt{3}}$ the particle moves throughout the interval $0lxl1,$ while for $rl{r}_{c}$ the particle is localized at $x=0$ or $x=1.$ In this paper the equilibrium distribution function $P(x,v)$ is analyzed for $rg{r}_{c}$ by solving the steady-state Fokker-Planck equation, and the results are compared with numerical simulations.

BASIN BOUNDARY COLLISION AS A MODEL OF DISCONTINUOUS CHANGE IN ECOSYSTEMS

It has long been recognized that gradual secular changes in environmental parameters may lead to discontinuous changes in ecosystems. The dominant model ex- plaining such changes has been the presence of alternative attractors and their basins. We discuss a related model, that of basin boundary collisions, that may also produce discon- tinuous changes in an environmental variable. The alternative model suggests that the underlying structure of the basins themselves may be gradually changed by the changing environmental factor. Consequently, the basin of the chaotic attractor may disappear, because it intersects the alternative basin; hence the term basin boundary collision. The implications of this model can be dramatic, such as sudden and unpredictable extinctions or dramatic and unexpected changes in ecosystem syndromes. Furthermore, where this model applies, ancillary phenomena such as a lag in time of the ecosystem change or the existence of so- called chaotic transients may be important. Also discussed are the implications of these results in a world in which slowly changing forcing parameters are well known (e.g., gradual increases of CO2 in the atmosphere, and gradual changes in political attitudes about con- servation).

The mean free path of gas molecules in the transition régime

Comparison is made between the electrical and thermal conductivities of solids and the transport properties of gases, with special reference to boundary limiting effects. The transition from continuum to molecular behaviour of gases is explored using a modified mean free path. Relative intermolecular and boundary collisions are calculated and it is proposed that, by assuming the transport process to be partially continuum and partially molecular, according to such frequencies, there results a plausible account for some of the observed `anomalies' in gas flow characteristics in the transition régime.