Three-dimensional Physical Space Research Articles

Efficient parallel solver for rarefied gas flow using GSIS

Recently, the general synthetic iterative scheme (GSIS) has been proposed to find the steady-state solution of the Boltzmann equation in the whole range of gas rarefaction, where its fast-converging and asymptotic-preserving properties lead to the significant reduction of iteration numbers and spatial cells in the near-continuum flow regime. However, the efficiency and accuracy of GSIS have only been demonstrated in two-dimensional problems with small numbers of spatial cells and discrete velocities. Here, a large-scale parallel computing strategy is designed to extend the GSIS to three-dimensional flow problems, including the supersonic flows which are usually difficult to solve by the discrete velocity method. Since the GSIS involves the calculation of the mesoscopic kinetic equation which is defined in six-dimensional phase-space, and the macroscopic high-temperature Navier–Stokes–Fourier equations in three-dimensional physical space, the proper partition of the spatial and velocity spaces, and the allocation of CPU cores to the mesoscopic and macroscopic solvers, are the keys to improving the overall computational efficiency. These factors are systematically tested to achieve optimal performance, up to 100 billion spatial and velocity grids. For hypersonic flows around the Apollo reentry capsule, the X38-like vehicle, and the space station, our parallel solver can obtain the converged solution within one hour.

A new derivation of the Minkowski metric

The four dimensional spacetime continuum, as first conceived by Minkowski, has become the dominant framework within which to describe physical laws. In this paper, we show how this four-dimensional structure is a natural property of physical three-dimensional space, if modeled with Clifford geometric algebra . We find that Minkowski spacetime can be embedded within a larger eight dimensional structure. This then allows a generalisation of the invariant interval and the Lorentz transformations. Also, with this geometric oriented approach the fixed speed of light, the laws of special relativity and a generalised form of Maxwell’s equations, arise naturally from the intrinsic properties of the algebra without recourse to physical arguments. We also find new insights into the nature of time, which can be described as two-dimensional. Some philosophical implications of this approach as it relates to the foundations of physical theories are also discussed.

Kinematics and Dynamics of a Particle in Gravitation Field

It is accepted that three-dimensional physical space is a hypersurface with a Riemannian metric in four-dimensional space. The metric tensor of this three-dimensional space is defined by Einstein's equations. Another coordinate of four-dimensional space is time. In this space, the equations of the world line of a particle with a mass m are defined under certain initial conditions: the starting point of the space and the vector of the particle's initial velocity. This approach removes all the problems and contradictions noted in the monograph [1], and the resulting equations adequately describe, for example, the curvilinear motion of planets without energy change.

Non-verbal Aspects of Collaboration in Virtual Worlds: a CSCW Taxonomy-development Proposal Integrating the Presence Dimension

Virtual worlds, particularly those able to provide a three-dimensional physical space, have features that make them suitable to support collaborative activities. These features distinguish virtual worlds from other collaboration tools, but current taxonomies of the field of Computer-Supported Cooperative Work do not account for several distinctive features of virtual worlds, namely those related with non-verbal communication. We intended to find out how the use of an avatar, gestures, spatial sounds, etc., influence collaboration in order to be able to include non-verbal communication in taxonomies of the field Computer-Supported Cooperative Work. Several cases of collaboration in virtual worlds are analysed, to find the impact of these non-verbal characteristics of virtual worlds. We proposed adding the concept of Presence to taxonomies of Computer-Supported Cooperative Work and contribute with guidance for future taxonomy development that includes it as a new dimension. This new dimension of Presence is subdivided into "avatar" and "physical space" subdimensions. In turn, these are divided into "physical appearance", "gestures, sounds and animations" and "focus, nimbus and aura"; "environment" and "objects / artefacts". This new taxonomy-development proposal may contribute to inform better design of virtual worlds in support of cooperative work.

Early Detection of Cyanobacterial Blooms and Associated Cyanotoxins using Fast Detection Strategy.

Fast detection of cyanobacteria and cyanotoxins is achieved using a Fast Detection Strategy (FDS). Only 24 h are needed to unravel the presence of cyanobacteria and related cyanotoxins in water samples and in an organic matrix, such as bivalve extracts. FDS combines remote/proximal sensing techniques with analytical/bioinformatics analyses. Sampling spots are chosen through multi-disciplinary, multi-scale, and multi-parametric monitoring in a three-dimensional physical space, including remote sensing. Microscopic observation and taxonomic analysis of the samples are performed in the laboratory setting, which allows for the identification of cyanobacterial species. Samples are then extracted with organic solvents and processed with LC-MS/MS. Data obtained by MS/MS are analyzed using a bioinformatic approach using the online platform Global Natural Products Social (GNPS) to create a network of molecules. These networks are analyzed to detect and identify toxins, comparing data of the fragmentation spectra obtained by mass spectrometry with the GNPS library. This allows for the detection of known toxins and unknown analogues that appear related in the same molecular network.

Folded space of machine listening

The paper investigates new machine listening technologies through a comparison of phenomenological and empirical/media-archeological approaches. While phenomenology associates listening with subjectivity, empiricism takes into account the technical operations involved with listening processes in both human and non-human apparatuses. Based on this theoretical framework, the paper undertakes a media-archeological investigation of two algorithms employed in copyright detection: “acoustic fi ngerprinting” and “audio watermarking”. In the technical operations of sound recognition algorithms, empirical analysis suggests the coexistence of a multiplicity of spatialities: from the “sound event”, which occurs in three-dimensional physical space, to its mathematical representation in vector space, and to the one-dimensional informational space of data processing and machine-to-machine communication. Recalling Deleuze’s defi nition of “the fold”, we defi ne these coexistent spatial dimensions in techno-culturally mediated sound as “the folded space” of machine listening. We go on to argue that the issue of space in machine listening consists of the virtually infi nite variability of the sound event being subjected to automatic recognition. The diffi culty lies in conciliating the theoretically enduring information transmitted by sound with the contingent manifestation of sound affected by space. To make machines able to deal with the site-specifi city of sound, recognition algorithms need to reconstruct the three-dimensional space on a signal processing level, in a sort of reverse-engineering of the sound phenomenon that recalls the concept of “implicit sonicity” defi ned by Wolfgang Ernst. While the metaphors and social representations adopted to describe machine listening are often anthropomorphic – and the very term “listening”, when referring to numerical operations, can be seen as a metaphor in itself – we argue that both human listening and machine listening are co-defi ned in a socio-technical network, in which the listening space no longer coincides with the position of the listening subject, but is negotiated between human and nonhuman agencies.

The geometry of property

Our legal regimes are crafted in a way that asserts control over a certain physical three-dimensional space. Some property regimes assert dominion over a vertical three-dimensional column, such as ownership of land that includes certain resources that are vertically related to it above and below the ground. Other property regimes, however, control resources on the horizontal axis. For example, legal control over a footpath exerts a kind of horizontal dominion over the space of and around the footpath. This article offers a conceptual framework for unpacking the spatial geometry of our property regimes and underscores its significance for policy and institutional design. It shows, importantly, that the compatibility between the space over which a regime holds control, and the space that is occupied by a particular resource, has profound implications. A misalignment between the two – for example, when a vertical regime is applied to a horizontal resource – implicates how well the regime functions. After laying out the conceptual framework, the article illustrates its application to a contemporary problem of extracting wind energy.

The Geometry of Property

Our legal regimes are crafted in a way that asserts control over a certain physical three-dimensional space. Some property regimes assert dominion over a vertical three-dimensional column, such as ownership of land that includes certain resources that are vertically related to it above and below the ground. Other property regimes, however, control resources on the horizontal axis. For example, legal control over a footpath exerts a kind of horizontal dominion over the space of and around the footpath. This Article offers a conceptual framework for unpacking the spatial geometry of our property regimes and underscores its significance for policy and institutional design. It shows, importantly, that the compatibility between the space over which a regime holds control and the space that is occupied by a particular resource, has profound implications. A misalignment between the two – for example, when a vertical regime is applied to a horizontal resource – implicates how well the regime functions. After laying out the conceptual framework, the Article illustrates its application to a contemporary problem of extracting wind energy.

Lo spazio e il tempo per le foreste resilienti

Forests are now universally thought of as Complex Adaptive Systems. The adaptive capacity of these ecosystems is directly proportional to their resistance, resilience and adaptability/plasticity. These attributes are, in turn, a function of the degree of biocomplexity (compositional, structural and functional/relational) obtained by the system itself. Because a forest can reach a high level of complexity, an adequate three-dimensional physical space and a very long time span must be ensured. Managed forests are often limited in surface (due to physical or ecological fragmentation) and in height (due to too early and intense cuts, which does not allow the canopy to occupy all the available biospace) making them more simplified and therefore less resilient. As regards time, the diversity between human time and forest time is not often taken into account, attempting to accelerate, in an unnatural way, the growth and succession of the structural phases. Speed is the enemy of complexity, especially relational complexity, on which the ability of forests to respond to external disturbances is based. Global change and the new challenges for the planet’s future require a decisive change in the criteria and methods of forest management, also considering the great value of ecosystems left to undisturbed natural evolution.

Wavelet-spectral analysis of droplet-laden isotropic turbulence

The spectrum of turbulence kinetic energy for homogeneous turbulence is generally computed using the Fourier transform of the velocity field from physical three-dimensional space to wavenumber $k$. This analysis works well for single-phase homogeneous turbulent flows. In the case of multiphase turbulent flows, instead, the velocity field is non-smooth at the interface between the carrier fluid and the dispersed phase; thus, the energy spectra computed via Fourier transform exhibit spurious oscillations at high wavenumbers. An alternative definition of the spectrum uses the wavelet transform, which can handle discontinuities locally without affecting the entire spectrum while additionally preserving spatial information about the field. In this work, we propose using the wavelet energy spectrum to study multiphase turbulent flows. Also, we propose a new decomposition of the wavelet energy spectrum into three contributions corresponding to the carrier phase, droplets and interaction between the two. Lastly, we apply the new wavelet-decomposition tools in analysing the direct numerical simulation data of droplet-laden decaying isotropic turbulence (in absence of gravity) of Dodd & Ferrante (J. Fluid Mech., vol. 806, 2016, pp. 356–412). Our results show that, in comparison to the spectrum of the single-phase case, the droplets (i) do not affect the carrier-phase energy spectrum at high wavenumbers ($k_{m}/k_{min}\geqslant 128$), (ii) increase the energy spectrum at high wavenumbers ($k_{m}/k_{min}\geqslant 256$) by increasing the interaction energy spectrum at these wavenumbers and (iii) decrease the energy at low wavenumbers ($k_{m}/k_{min}\leqslant 16$) by increasing the dissipation rate at these wavenumbers.

Quadcopter Flight Control Using a Non-invasive Multi-Modal Brain Computer Interface.

Brain-Computer Interfaces (BCIs) translate neuronal information into commands to control external software or hardware, which can improve the quality of life for both healthy and disabled individuals. Here, a multi-modal BCI which combines motor imagery (MI) and steady-state visual evoked potential (SSVEP) is proposed to achieve stable control of a quadcopter in three-dimensional physical space. The complete information common spatial pattern (CICSP) method is used to extract two MI features to control the quadcopter to fly left-forward and right-forward, and canonical correlation analysis (CCA) is employed to perform the SSVEP classification for rise and fall. Eye blinking is designed to switch these two modes while hovering. Real-time feedback is provided to subjects by a global camera. Two flight tasks were conducted in physical space in order to certify the reliability of the BCI system. Subjects were asked to control the quadcopter to fly forward along the zig-zag pattern to pass through a gate in the relatively simple task. For the other complex task, the quadcopter was controlled to pass through two gates successively according to an S-shaped route. The performance of the BCI system is quantified using suitable metrics and subjects are able to acquire 86.5% accuracy for the complicated flight task. It is demonstrated that the multi-modal BCI has the ability to increase the accuracy rate, reduce the task burden, and improve the performance of the BCI system in the real world.

Effect of arbitrary blade tip design on tip leakage flow

Tip geometry modification is frequently used to suppress the tip leakage flow in the turbine cascade however a universally beneficial tip geometry modification design has not been fully discovered. In this paper, the two-surface coupling arbitrary blade tip design method in three-dimensional physical space which satisfies the simple trigonometric function law is proposed and the mathematical parametric description is presented. The effects of different arbitrary blade tips on tip leakage flow have been studied numerically in a highly loaded axial turbine cascade. The aerodynamic performance of different tips is assessed by the tip leakage mass flow rate and the total pressure loss coefficient at the exit section. The Kriging model and genetic optimization algorithm are used to optimize the arbitrary blade tips to obtain the optimal arbitrary blade tip. Compared with the flat tip, the tip leakage mass flow rate is decreased by 10.57% and the area-average total pressure loss coefficient at the exit section is reduced by 8.91% in the optimal arbitrary blade tip.

Can we study 3D grid codes non-invasively in the human brain? Methodological considerations and fMRI findings

Recent human functional magnetic resonance imaging (fMRI) and animal electrophysiology studies suggest that grid cells in entorhinal cortex are an efficient neural mechanism for encoding knowledge about the world, not only for spatial location but also for more abstract cognitive information. The world, be it physical or abstract, is often high-dimensional, but grid cells have been mainly studied on a simple two-dimensional (2D) plane. Recent theoretical studies have proposed how grid cells encode three-dimensional (3D) physical space, but it is unknown whether grid codes can be examined non-invasively in humans. Here, we investigated whether it was feasible to test different 3D grid models using fMRI based on the direction-modulated property of grid signals. In doing so, we developed interactive software to help researchers visualize 3D grid fields and predict grid activity in 3D as a function of movement directions. We found that a direction-modulated grid analysis was sensitive to one type of 3D grid model – a face-centred cubic (FCC) lattice model. As a proof of concept, we searched for 3D grid-like signals in human entorhinal cortex using a novel 3D virtual reality paradigm and a new fMRI analysis method. We found that signals in the left entorhinal cortex were explained by the FCC model. This is preliminary evidence for 3D grid codes in the human brain, notwithstanding the inherent methodological limitations of fMRI. We believe that our findings and software serve as a useful initial stepping-stone for studying grid cells in realistic 3D worlds and also, potentially, for interrogating abstract high-dimensional cognitive processes.

Space and Time as a Consequence of Ghirardi-Rimini-Weber Quantum Jumps

Abstract The Ghirardi-Rimini-Weber theory of spontaneous collapse offers a possible resolution of the quantum measurement problem. In this theory, the wave function of a particle spontaneously and repeatedly localises to one or the other random position in space, as a consequence of the hypothesised quantum jumps. In between jumps, the wave function undergoes the usual Schrödinger evolution. In the present paper, we suggest that these jumps take place in Hilbert space, with no reference to physical space and a physical three-dimensional space arises as a consequence of localisation of macroscopic objects in the universe. That is, collapse of the wave-function is responsible for the origin of space. We then suggest that similar jumps take place for a hypothetical time operator in Hilbert space and classical time, as we know it emerges from localisation of this time operator, for macroscopic objects. More generally, the jumps are suggested to take place in an operator space-time in Hilbert space, leading to an emergent classical space-time.

Classical transitions with the topological number changing in the early Universe

We consider classical dynamics of two real scalar fields within a model with the potential having a saddle point. The solitons of such model are field configurations that have the form of closed loops in the field space. We study the formation and evolution of these solitons, in particular, the conditions at which they could be formed even when the model potential has only one minimum. These non-trivial field configurations represent domain walls in the three-dimensional physical space. The set of these configurations can be split into disjoint equivalence classes. We provide a simple expression for the winding number of an arbitrary closed loop in the field space and discuss the transitions that change the winding number. We also show that non-trivial field configurations could be responsible for the energy density excess that could evade the CMB constraints but could be important at scales which are responsible for the formation of galaxies and the massive primordial black holes.

Local random configuration-tree theory for string repetition and facilitated dynamics of glass

We derive a microscopic theory of glassy dynamics based on the transport of voids by micro-string motions, each of which involves particles arranged in a line hopping simultaneously displacing one another. Disorder is modeled by a random energy landscape quenched in the configuration space of distinguishable particles, but transient in the physical space as expected for glassy fluids. We study the evolution of local regions with m coupled voids. At a low temperature, energetically accessible local particle configurations can be organized into a random tree with nodes and edges denoting configurations and micro-string propagations respectively. Such trees defined in the configuration space naturally describe systems defined in two- or three-dimensional physical space. A micro-string propagation initiated by a void can facilitate similar motions by other voids via perturbing the random energy landscape, realizing path interactions between voids or equivalently string interactions. We obtain explicit expressions of the particle diffusion coefficient and a particle return probability. Under our approximation, as temperature decreases, random trees of energetically accessible configurations exhibit a sequence of percolation transitions in the configuration space, with local regions containing fewer coupled voids entering the non-percolating immobile phase first. Dynamics is dominated by coupled voids of an optimal group size, which increases as temperature decreases. Comparison with a distinguishable-particle lattice model (DPLM) of glass shows very good quantitative agreements using only two adjustable parameters related to typical energy fluctuations and the interaction range of the micro-strings.

Transitions between topologically non-trivial configurations

We study formation and evolution of solitons within a model with two real scalar fields with the potential having a saddle point. The set of these configurations can be split into disjoint equivalence classes. We give a simple expression for the winding number of an arbitrary closed loop in the field space and discuss the evolution scenarios that change the winding number. These non-trivial field configurations lead to formation of the domain walls in the three-dimensional physical space.

Visualization during Crystallization in Minkowski Spacetime

It was achieved a visual representation of information about the crystallization process in the multidimensional space, which creates prerequisites for the development of software systems to solve a wide class of problems. With the geometric interpretation Minkowski space-time, quasi-Lorentz and Einstein's concept concerning the concept of giving time physical sense, simulated the process of formation of crystals in the four-dimensional space. The 4D model space combines the physical three-dimensional space of the factors affecting the formation of crystals, and time. Visualization of the crystallization process in spacetime plays an important role, as having great cognitive and probative value, and contributes to a better understanding of crystallization processes, creates conditions to control the properties of materials in the process of crystallization.

Large Eddy Simulation of flame edge evolution in a spark-ignited methane–air jet

The unsteady evolution of lifted methane–air jet flames following spark ignition is computed using Large Eddy Simulation (LES). A presumed joint Probability Density Function (PDF) approach is used for the sub-grid combustion modelling accounting for both premixed and non-premixed mode contributions. Two flames, one with high and another with low jet velocities are investigated and the computed temporal variation of flame leading point agrees quite well with the measured data for both the transient evolution and final lift-off height. The joint PDF of the axial and radial stabilisation locations shows that these locations are correlated with the jet exit velocity. The flame leading point evolution in the three-dimensional physical space is visualised using its trajectory, starting from the ignition location to the final lift-off height. A spiral-shaped path is observed for both velocity cases showing different flame propagation behaviours at different heights from the jet exit. These observations are explained on a physical basis.

The XXL Survey

The XXL Survey is the largest homogeneous and contiguous survey carried out with XMM-Newton. Covering an area of 50 square degrees distributed over two fields, it primarily investigates the large-scale structures of the Universe using the distribution of galaxy clusters and active galactic nuclei as tracers of the matter distribution. Given its depth and sky coverage, XXL is particularly suited to systematically unveiling the clustering of X-ray clusters and to identifying superstructures in a homogeneous X-ray sample down to the typical mass scale of a local massive cluster. A friends-of-friends algorithm in three-dimensional physical space was run to identify large-scale structures. In this paper we report the discovery of the highest redshift supercluster of galaxies found in the XXL Survey. We describe the X-ray properties of the clusters members of the structure and the optical follow-up. The newly discovered supercluster is composed of six clusters of galaxies at a median redshift z around 0.43 and distributed across approximately 30 by 15 arc minutes (10 by 5 Mpc on sky) on the sky. This structure is very compact with all the clusters residing in one XMM pointing; for this reason this is the first supercluster discovered with the XXL Survey. Spectroscopic follow-up with WHT (William Herschel Telescope) and NTT (New Technology Telescope) confirmed a median redshift of z = 0.43. An estimate of the X-ray mass and luminosity of this supercluster and of its total gas mass put XLSSC-e at the average mass range of superclusters; its appearance, with two members of equal size, is quite unusual with respect to other superclusters and provides a unique view of the formation process of a massive structure.