Spherical Blocks Research Articles

On the Virasoro fusion and modular kernels at any irrational central charge

We propose a series representation for the Virasoro fusion and modular kernels at any irrational central charge. Two distinct, yet closely related formulas are needed for the cases c∈ \mathbb{C} \backslash (-∞,1]c∈ℂ∖(−∞,1] and c <1c<1. Our proposal for c <1c<1 agrees numerically with the fusion transformation of the four-point spherical conformal blocks, whereas our proposal for c∈ \mathbb{C} \backslash (-∞,1]c∈ℂ∖(−∞,1] agrees numerically with Ponsot and Teschner’s integral formula for the fusion kernel. The case of the modular kernel is studied as a special case of the fusion kernel.

Ag(Sn9-Sn9)]5- and [(η4-Sn9)Ag(η1-Sn9)]7-, as aggregates of spherical aromatic building blocks. Persistence of aromaticity upon cluster gathering.

Formation of cluster-based materials requires a fundamental understanding of the resulting cluster aggregation processes. The Sn94- Zintl-ion structure can be viewed as a building block featuring a spherical aromatic species, leading to a cluster gathering upon oxidative coupling and/or mediated by transition metals. Here, we evaluate the spherical aromatic properties of [Sn9-Sn9]6-, [Ag(Sn9-Sn9)]5- and [(η4-Sn9)Ag(η1-Sn9)]7-, as aggregates of two Sn9 building units held together via oxidative coupling and mediated by a Ag(I) transition metal center. Our results from magnetic criteria of aromaticity show that the inherent spherical aromatic characteristics of the parent Sn94- cluster are persistent in the overall aggregate where the enabled shielding cones ascribed to each Sn9 unit are able to interplay between them, leading to an overlap of the shielding regions. Hence, the two approaches for bringing cluster units together are able to retain the inherent spherical aromatic features for each Sn9 unit, leading to a cluster-based dimer where the parent properties remain. Thus, further cluster-based materials can be envisaged from aggregation upon oxidative coupling and/or mediated by transition metals, where the constituent building blocks retain their initial features, useful to guide the formation of more complex cluster-based aggregates.

A Cross-matching Service for Data Center of Xinjiang Astronomical Observatory

Cross-matching is a key technique to achieve fusion of multi-band astronomical catalogs. Due to different equipment such as various astronomical telescopes, the existence of measurement errors, and proper motions of the celestial bodies, the same celestial object will have different positions in different catalogs, making it difficult to integrate multi-band or full-band astronomical data. In this study, we propose an online cross-matching method based on pseudo-spherical indexing techniques and develop a service combining with high performance computing system (Taurus) to improve cross-matching efficiency, which is designed for the Data Center of Xinjiang Astronomical Observatory. Specifically, we use Quad Tree Cube to divide the spherical blocks of the celestial object and map the 2D space composed of R.A. and decl. to 1D space and achieve correspondence between real celestial objects and spherical patches. Finally, we verify the performance of the service using Gaia 3 and PPMXL catalogs. Meanwhile, we send the matching results to VO tools-Topcat and Aladin respectively to get visual results. The experimental results show that the service effectively solves the speed bottleneck problem of cross-matching caused by frequent I/O, and significantly improves the retrieval and matching speed of massive astronomical data.

Characterisation of the maximum entropy change in the process of drying materials based on a heat pump

This paper studies the maximum entropy change characteristics under different working condition parameters (e.g. inlet temperature, air volume, initial sludge temperature and sludge radius) based on the validated model. Spherical sludge blocks were used as drying materials, and heat was provided by a heat pump system. Theoretical models of mass balance, energy balance and entropy balance in the drying process are established, and the model is validated with experimental results. The results show that the change in sludge entropy during the drying process is mainly caused by irreversible moisture diffusion, heat transfer and pressure. There is a peak of entropy change when the entropy value initially climbs and then declines. The lower the peak of entropy change, the smaller the irreversible dissipation in the drying process; however, the entropy change is not the main factor of drying time. For every 5 ℃ increase in inlet drying temperature, the entropy change peak increases by 5.2 ∼ 18.6 % and the drying time is shortened by 27.5 %. The entropy changes the peak increase with the rise in inlet air volume, while the drying time initially shortens and then changes slightly, and the optimal air volume interval exists. For every 0.01 m decrease in sludge radius, the entropy change peak reduces by 9.4 ∼ 23.8 %, and the drying time is shortened by 19.8 ∼ 33.1 %. The change in the initial sludge temperature has little impact on the entropy of the drying process.

Universal Way to "Glue" Capsules and Gels into 3D Structures by Electroadhesion.

We demonstrate the use of electroadhesion (EA), i.e., adhesion induced by an electric field, to connect a variety of soft materials into 3D structures. EA requires a cationic and an anionic material, but these can be of diverse origin, including covalently cross-linked hydrogels made by polymerizing charged monomers or physical gels/capsules formed by the ionic cross-linking of biopolymers (e.g., alginate and chitosan). Between each cationic/anionic pair, EA is induced rapidly (in ∼10 s) by low voltages (∼10 V DC)─and the adhesion is permanent after the field is turned off. The adhesion is strong enough to allow millimeter-scale capsules/gels to be assembled in 3D into robust structures such as capsule-capsule chains, capsule arrays on a base gel, and a 3D cube of capsules. EA-based assembly of spherical building blocks can be done more precisely, rapidly, and easily than by any alternative techniques. Moreover, the adhesion can be reversed (by switching the polarity of the field)─hence any errors during assembly can be undone and fixed. EA can also be used for selective sorting of charged soft matter─for example, a 'finger robot' can selectively 'pick up' capsules of the opposite charge by EA and subsequently 'drop off' these structures by reversing the polarity. Overall, our work shows how electric fields can be used to connect soft matter without the need for an adhesive or glue.

Structural investigations of Au-Ni aerogels: morphology and element distribution.

The physical properties of nanomaterials are determined by their structural features, making accurate structural control indispensable. This carries over to future applications. In the case of metal aerogels, highly porous networks of aggregated metal nanoparticles, such precise tuning is still largely pending. Although recent improvements in controlling synthesis parameters like electrolytes, reductants, or mechanical stirring, the focus has always been on one particular morphology at a time. Meanwhile, complex factors, such as morphology and element distributions, are studied rather sparsely. We demonstrate the capabilities of precise morphology design by deploying Au-Ni, a novel element combination for metal aerogels in itself, as a model system to combine common aerogel morphologies under one system for the first time. Au-Ni aerogels were synthesized via modified one- and two-step gelation, partially combined with galvanic replacement, to obtain aerogels with alloyed, heterostructural (novel metal aerogel structure of interconnected nanoparticles and nanochains), and hollow spherical building blocks. These differences in morphology are directly reflected in the physisorption behavior, linking the isotherm shape and pore size distribution to the structural features of the aerogels, including a broad-ranging specific surface area (35-65 m2 g-1). The aerogels were optimized regarding metal concentration, destabilization, and composition, revealing some delicate structural trends regarding the ligament size and hollow sphere character. Hence, this work significantly improves the structural tailoring of metal aerogels and possible up-scaling. Lastly, preliminary ethanol oxidation tests demonstrated that morphology design extends to the catalytic performance. All in all, this work emphasizes the strengths of morphology design to obtain optimal structures, properties, and (performances) for any material application.

Articular Cartilage Regeneration through Bioassembling Spherical Micro-Cartilage Building Blocks.

Articular cartilage lesions are prevalent and affect one out of seven American adults and many young patients. Cartilage is not capable of regeneration on its own. Existing therapeutic approaches for articular cartilage lesions have limitations. Cartilage tissue engineering is a promising approach for regenerating articular neocartilage. Bioassembly is an emerging technology that uses microtissues or micro-precursor tissues as building blocks to construct a macro-tissue. We summarize and highlight the application of bioassembly technology in regenerating articular cartilage. We discuss the advantages of bioassembly and present two types of building blocks: multiple cellular scaffold-free spheroids and cell-laden polymer or hydrogel microspheres. We present techniques for generating building blocks and bioassembly methods, including bioprinting and non-bioprinting techniques. Using a data set of 5069 articles from the last 28 years of literature, we analyzed seven categories of related research, and the year trends are presented. The limitations and future directions of this technology are also discussed.

Structural Diversity in Multicomponent Nanocrystal Superlattices Comprising Lead Halide Perovskite Nanocubes.

Nanocrystal (NC) self-assembly is a versatile platform for materials engineering at the mesoscale. The NC shape anisotropy leads to structures not observed with spherical NCs. This work presents a broad structural diversity in multicomponent, long-range ordered superlattices (SLs) comprising highly luminescent cubic CsPbBr3 NCs (and FAPbBr3 NCs) coassembled with the spherical, truncated cuboid, and disk-shaped NC building blocks. CsPbBr3 nanocubes combined with Fe3O4 or NaGdF4 spheres and truncated cuboid PbS NCs form binary SLs of six structure types with high packing density; namely, AB2, quasi-ternary ABO3, and ABO6 types as well as previously known NaCl, AlB2, and CuAu types. In these structures, nanocubes preserve orientational coherence. Combining nanocubes with large and thick NaGdF4 nanodisks results in the orthorhombic SL resembling CaC2 structure with pairs of CsPbBr3 NCs on one lattice site. Also, we implement two substrate-free methods of SL formation. Oil-in-oil templated assembly results in the formation of binary supraparticles. Self-assembly at the liquid–air interface from the drying solution cast over the glyceryl triacetate as subphase yields extended thin films of SLs. Collective electronic states arise at low temperatures from the dense, periodic packing of NCs, observed as sharp red-shifted bands at 6 K in the photoluminescence and absorption spectra and persisting up to 200 K.

Analytical Solution for Fractional Well Flow in a Double-Porosity Aquifer with Fractional Transient Exchange between Matrix and Fractures

An analytical solution is presented for groundwater flow to a well in an aquifer with double-porosity behavior and transient transfer between fractures and matrix. The solution is valid for fractional flow dimensions including linear, cylindrical or spherical flow to the well and for fractional inter-porosity diffusive transfer including release from storage in infinite slabs, infinite cylinders or spherical matrix blocks. Approximations are also presented for small and large times that are easy to evaluate in practice. The solution can be used to analyze pumping tests via coupling with a parameter estimation code. The utility of the method is demonstrated by a practical example using data from a pumping test performed in a fractured chalk aquifer. The analytical solution allows the accurate modeling of pumping tests and the estimation of aquifer parameters that are statistically significant and physically relevant.

Elaborate Size-Tuning of Silica Aerogel Building Blocks Enables Laser-Driven Lighting.

Silica aerogels with accurate building-block control are realized by adjusting the surfactant concentration during the synthesis process. The resulting silica-aerogel monolith with spherical building blocks of ≈24-40nm, together with a deliberately created hole along the incident light direction, shows an incredibly promising application in monochromatic laser-driven lighting. The resulting coefficient of illuminance variation is as low as 8.1%, significantly outperforming commercially available ground-glass diffusers (139.0%) and polymer diffusers (249.1%); the speckle contrast is lower, as well as better, than that can be recognized by the human eye (4%), and the illuminance uniformity in the range of 0.770-0.862 is much better (higher) than that indoor workplace lighting required by the International Organization for Standardization. Lighting with any color in the visible spectrum, including white, can be obtained by using three primary color lasers (450, 532, and 638nm) with different powers simultaneously as the light source. The resulting silica aerogel, which has excellent thermal stability, high laser-damage threshold, outstanding mechanical performance, and superhydrophobicity, can be further applied to long-distance and noncontact laser-driven lighting in rain or underwater without any additional encapsulation components.

Investigating the influence of block rotation and shape on the impact process

A block impact model based on the elasto-viscoplastic macro element approach is developed for regular base prismatic blocks. This model upgrades a previously conceived model for spherical boulders introducing (i) a rotational degree of freedom; (ii) a moment-rotation relationship; (iii) a toppling mechanism. The model can improve rockfall simulations by considering block geometry and the exchange between translational and rotational energies. Model parameters were calibrated by using laboratory tests on vertical impacts. Parametric analyses were carried out to investigate for both vertical and inclined impacts, the effects of block shape and orientation. The influence of these factors on the impact force, the maximum penetration depth as well as the exchange between translational and rotational energies is discussed. A comparison with the available results for small and large scale laboratory tests shows model capabilities and put in evidence the “nonlinear” relationship between maximum acceleration (or equivalently the maximum contact force) and impact translational velocity. For vertical impacts the trend of the maximum penetration depth is a function of the block shape. Prismatic blocks can experience larger values of maximum penetration than spherical blocks characterized by coincident masses and kinetic energies. In case of bouncing of a prismatic block the increment of normal maximum displacement with respect to spherical blocks ranges from about 66% for triangular base prisms to 132% for hexagonal base blocks. In case of no bouncing, the increments range from about 82% for triangular blocks to −32% for hexagonal blocks. Maximum normal forces also depend on block shape and orientation. In case of a vertex impact with no bouncing, triangular blocks show a decrement in the maximum force of about 43% with respect to the spherical block. The increment of initial block angular velocity generates a reduction in both maximum penetration depths and impact forces.

Experimental study of different typical shape falling-rocks impacting on the sand cushion and dimensionless analysis

An experimental study on the impact force and penetration of falling rocks with three typical shapes, including spherical, conical and flat shapes, against the cushion was carried out. The experimental results show that the shape of the falling rock has a significant influence on the impact results. Under the same conditions, the flat blocks have the highest impact force, the lowest penetration depth and the shortest peak impact time, and the opposite for the conical falling rocks, with spherical blocks are between the two. The dimensionless analysis method was adopted to convert the mass, velocity, shape, size of the falling rock, the strength and density of the cushion layer into the dimensionless strength impact factor I, density impact factor λ and shape impact factor ψ. The correlation analysis between the impact factors and penetration test data shows that: (1) The effects of the impact factors I and λ on the final depth of penetration zm/d are similar. (2) The analysis of the impact factors I and λ effects on penetration depth shows that I and λ are relatively independent. The pattern of the I effects on the depth of penetration is generally consistent for different λ values.

Predicting the fragmentation survival probability of brittle spheres upon impact from statistical distribution of material properties

Fragmentation of rocks upon impact during rockfall is a phenomenon that is poorly understood, scarcely researched and difficult to predict. However, to adequately predict the outcomes of rockfall events, it is essential to know whether a given block is likely to fragment given the impact conditions and what will be the outcome of the fragmentation process; that is, the number, size and trajectory of fragments. To date, there is no model or data that can be used to fully answer these questions. This paper presents the first theoretical model that can predict the fragmentation survival probability of brittle spherical blocks upon dynamic impact (i.e. drop tests) from the statistical distribution of material properties, determined from a range of standard quasi-static tests. Considering that survival probabilities tend to follow a Weibull distribution, the model focuses on predicting the two Weibull parameters, commonly known as the shape parameter (m) and the scale parameter (here, the critical kinetic energy). The model is based on theoretically-derived conversion factors used to turn the critical work required to fail disc samples in quasi-static indirect tension into the critical kinetic energy to cause failure of spheres at impact in drop tests. The mechanistic conversion factors specifically account for the shape and size of the specimens tested and the increase of strength under dynamic loading (strain rate effect). Three series of drop tests were conducted (on spheres of three different diameters) and complemented by extensive material characterisation testing in order to validate the novel predictive model. The variability of material properties was characterised, and it was found that the material strength found by the characterisation tests generally follows a Weibull form, but the survival probability distribution of the drop tests seems to be linear. The predicted conversion factors were first compared against their experimental counterparts before validating the prediction of survival probability of the spheres upon dynamic impact (in drop tests). It was found that it is possible to predict the survival probability of artificial rock of three different diameters (50 mm, 75 mm, 100 mm) and two different strengths upon impact solely from the statistical information coming from Brazilian tests and with an average relative error of less than 9%.

Continuity of terrestrial water storage variability and trends across mainland China monitored by the GRACE and GRACE-Follow on satellites

Terrestrial water storage (TWS) plays an important role in the global water cycle. Measuring dynamic changes in TWS is essential for water resources management, weather-related hazard monitoring and agricultural production. The Gravity Recovery and Climate Experiment (GRACE) and its following mission (GRACE-Follow on) have provided monthly terrestrial water storage anomalies (TWSA) at a quasi-global scale since April 2002. This study bridges the data gap between the two generations of satellites using Random Forest (RF), Support Vector Machine (SVM) and Artificial Neural Network models over mainland China. We systematically examine the spatiotemporal continuity of GRACE and GRACE-Follow on missions based on the spherical harmonics (SH) and mass concentration blocks (mascons) solutions as well as GLDAS-Noah data across mainland China during 2002–2020. Results show that the GRACE-Follow on data of CSR SH/CSR mascons reduces the uncertainty of TWSA in China from 5.26/6.96 to 3.83/4.65 mm/month, respectively. ML-predicted TWSA fits well with in-situ observations during the gap between GRACE and GRACE-Follow on satellites. Modeled TWSA also shows continuity between GRACE and GRACE-Follow on satellites. During the period 2002–2020, reconstructed TWSA significantly decreased from − 0.03 mm/a to − 1.06 mm/a (p < 0.05) with spatial heterogeneity for the whole of China. In many areas of China, TWSA increased rapidly in the range of 5–15 mm/a (p < 0.05), while north and southwest China experienced a decrease between − 5 and − 25 mm/a (p < 0.05). This study provides bridged GRACE data and reveals the variability of TWSA in mainland China, which may contribute to a better understanding of climate change and water resources management.

Dynamic response of flexible rockfall barriers with different block shapes

Flexible rockfall barriers are commonly constructed on steep hillsides to mitigate rockfall. The evaluation of the dynamic response of proprietary flexible rockfall barriers is conventionally performed using full-scale field tests by dropping a block onto the barriers in accordance with the European test standard ETAG 027. The block typically has a spherical or polyhedral shape and cannot reproduce more complex rockfall scenarios encountered in the field. Little attention has been paid to the effects of the block shape on the impact force and structural response. This paper aims to quantitatively reveal the influence of the block shape on the dynamic response of flexible rockfall barriers. First, an ellipsoidal model is established to approximately simulate the block, and the sphericity is employed as the representative index of the block’s shape. A full-scale test on a typical flexible barrier system is carried out and then used to calibrate an advanced three-dimensional finite element model. Finally, the dynamic responses of flexible rockfall barriers are analyzed and discussed, focusing on the effects of the block’s shape. The numerical results show that the sphericity will obviously influence the maximum elongation of flexible barriers, the peak impact force, the peak force of the upslope anchor cable, the peak force of the lower main support cable, the axial peak force of the post, and the peak shear force at the post foundation. The assumption of spherical or polyhedral blocks in the test standard could lead to the defensive failure of flexible rockfall barriers in some impact scenarios.

Influence of the particle shape on the impact force of lahar on an obstacle

Lahars represent natural phenomena that can generate severe damage in densely populated urban areas. The evaluation of pressures generated by these mass flows on constructions (buildings, infrastructure…) is crucial for civil protection and assessment of physical vulnerability. The existing tools to model the spread of flows at large scale in densely populated urban areas remain inaccurate in the estimation of mechanical efforts. A discrete numerical model is developed for evaluating debris flow (DF) impact pressures at the local scale of one structure. The large-sized solid particles are modelled explicitly using Distinct Element Method (DEM) and the fine-grained solid particles are integrated in a fluid phase which generates two effects on the movement of particles, i.e. buoyancy and drag. Fluid velocity field and the fluid free surface are obtained from Computational Fluid Dynamics (CFD) code then imported in the DEM simulation in a one way coupling scheme. In this paper, the influence of particle shape on the impact forces generated on the obstacle is investigated: spherical particles and polygonal rigid blocks (r-blocks) are considered. The shape of the particle influences the contact surface and therefore the impact pressure. With an angular shape and several facets like r-blocks, the impact pressure on an obstacle is more important for a flow with the same characteristics.

Morphology of poly(lactide)‐block‐poly(dimethylsiloxane)‐block‐polylactide high‐χ triblock copolymer film studied by grazing incidence small‐angle X‐ray scattering

AbstractThe morphologies of poly(lactide)‐block‐poly(dimethylsiloxane)‐block‐polylactide (PLA‐b‐PDMS‐b‐PLA) triblock copolymer films were studied using a combination of grazing‐incidence small‐angle X‐ray scattering, X‐ray reflectivity and scanning electron microscopy. This block copolymer is characterized by a high Flory–Huggins interaction parameter which leads to the self‐assembly of periodic high‐resolution nanodomains. In this article, we performed a detailed analysis of GISAXS patterns, in the frame of the Distorted Wave Born Approximation, in order to determine the morphology of blocks and their spatial arrangement. For a low volume fraction of PLA (17%), a three‐dimensional hexagonal lattice of PLA spherical blocks is revealed, while, for a PLA fraction twice larger, in‐plane (parallel) PLA lying cylinders adopt a two‐dimensional centered rectangular lattice. Moreover, the in‐depth electron density profile of the polymer film for the cylindrical morphology was extracted from the XRR data, revealing the presence of interfacial layers at the top surface and at the interface with the Si substrate.

The performance of complex-structure fractured reservoirs considering natural and induced matrix block size, shape, and distribution

This paper introduces an analytical approach for the performance of the fractured reservoir considering the impact of the matrix block size, shape, and distribution. The objective is better understanding the roles of the variable interporosity flow systems, fracture flowing systems, and reservoir matrix heterogeneity in the responses of the wellbore pressure drop, flow rate, cumulative production, and productivity index. This understanding could help to eliminate the uncertainties and increase the accuracy in characterizing the conventional and unconventional reservoirs where very complex structures of a significant disorder in the matrix block size, shape and distribution could be existed in the porous media.The study uses the well documented multilinear flow model to describe the pressure distribution in the naturally fractured reservoirs depleted by multiple hydraulic fractures considering different matrix block sizes, shapes, and distributions. The analytical models of the flow rate, cumulative production, and the productivity index are also developed in this study from the multilinear flow model. The reservoirs of interest are assumed to have stimulated porous media extending between hydraulic fracture and unstimulated volume extending beyond the fracture tips toward the reservoir boundary. The unstimulated reservoir volume is assumed consisting of uniformly distributed single matrix block size and shape because there is no impact for the hydraulic fracturing process. While the stimulated reservoir volume is considered consisting of a variable matrix block size, shape, and distribution because of the impact of hydraulic fracture propagation. The petrophysical properties of the two porous media, as well as the storativity and interporosity flow coefficient, are assumed functions of the matrix characteristics in the two volumes. The matrix block dimensions (radius or length) are correlated exponentially with the distance from the hydraulic fracture face toward the no-flow boundary between these fractures. Three fracture-matrix fluid flux functions are developed for the reservoirs where the matrix blocks could have a spherical, slab, and cylindrical configuration.The study has reached several conclusions. A positive impact on the reservoir performance is seen when the matrix block size becomes small or when the small size matrix blocks control the distribution of the blocks in the porous media. Reservoir performance is enhanced also when there are several matrix block sizes compared to a single size or very few sizes. It is observed that the reservoirs with spherical blocks may give better performance than the reservoir with slab or cylindrical matrix blocks. In terms of matrix block size and distribution, heterogeneous reservoirs may have a higher productivity index than homogenous reservoirs. The variable matrix block size and distribution in the stimulated reservoir volume is more beneficial than the unstimulated volume. The novel point presented in this paper is developing several analytical models for the wellbore pressure drop, flow rate, cumulative production, and productivity index of hydraulically fractured reservoirs with a consideration given to the matrix block size, shape, and distribution.

Possibilities of modernization of wheel motor blocks of locomotives

The task of modernizing the wheel-motor blocks of locomotives with a wheel diameter of 1050 mm with asynchronous and collector traction motors is considered. As a result of the analysis, it was found that the design of the traverse suspension of the collector engines is outdated and contains wearing surfaces that are difficult to protect from contamination, while due to the limited dimensions the attempt to use a hinged suspension of the “Earring” type, the silent blocks on the axes were stuck. For drives with asynchronous motors, an increase in the rotational speed is limited by the cantilever location of the gear, at which the gear rotates and the end of the motor shaft can be turned. An engine suspension design with three spherical silent blocks, a liquid with ferromagnetic nanoparticles and a permanent magnet is proposed. It eliminates jamming of the silent blocks on the axes during transverse movements of the engine and ensures interchangeability of the wheel-motor blocks for upgraded and non-upgraded trolleys. To improve the reliability of traction transmission, it is proposed to position the gear between the rotary bearings. To reduce the wear of traction gear teeth, the design of an elastic gear wheel with chevron teeth was proposed. A patent for an invention and a patent for a utility model have been obtained for the proposed technical solutions.

Electromagnetic field visualization in virtual reality

We developed two virtual reality demonstrations for electromagnetism. For statics, we use spherical building blocks and superposition to calculate the electric field of a user-generated configuration of charge. The electric field information is displayed on a three-dimensional grid using vector arrows. A second demonstration displays field information for electromagnetic fields generated by a particle moving along a user-generated path (at arbitrary speed). We used the Unity game creation engine to efficiently develop the demonstrations, and tested them on an HTC Vive VR headset with handheld controllers.