Search NASA⌕ Search

SEARCH · Search NASA

Results for “Spatiotemporal phenomena”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Energy-conserving contact dynamics of nonspherical rigid-body particles

Understanding the contact dynamics of nonspherical particles is crucial for accurately modeling colloidal and granular systems where shape anisotropy dictates structural organization and transport properties. We here introduce an energy-conserving contact dynamics framework for arbitrary convex rigid-body particles by implementing vertex–boundary interactions in 2D and vertex–surface and edge–edge detection in 3D. The established formulation enables continuous force evaluation and prevents particle overlap while conserving total energy during translational and rotational motion. We demonstrate the framework’s stability and its utility to capture packing behavior, anisotropic diffusion, and equations of state of polygonal and polyhedral particles as examples. The framework establishes a robust and extensible foundation for investigating nonequilibrium dynamics of complex nonspherical particulate systems, enabling enhanced understanding of phenomena across spatiotemporal scales in self- and directed-assembly, granular flows, and hydrodynamics, potentially coupled with interactions that represent underlying physical mechanisms.

Discrete element method↗
DOE OSTI2025

Spatiotemporal Automatic Calibration of Infrastructure Lidar, Radar, and Camera with a Global Navigation Satellite System

Robust and accurate perception is important for modern intelligent transportation systems (ITS), which use sensors of various modalities for data fusion to create a digital twin of an intersection. Sensor calibration is an important process that creates a unified coordinate frame for the sensor output data so that it can be used for data fusion. Classical approaches for sensor calibration are time-consuming, require an overlapping field of view for feature matching, and are not feasible for ITS application as they cause disruptions in the flow of traffic. In this paper, we present a spatiotemporal automatic calibration approach to calibrate multiple infrastructure lidar, radar, and cameras installed at a traffic intersection. The approach uses global navigation satellite system (GNSS) positioning information shared by connected vehicles, and when the vehicle is detected by the sensor, we match the sensor detections with the GNSS coordinates. The proposed algorithm is evaluated with a real-world dataset utilizing detections from two radars, cameras, and lidars with a test vehicle instrumented with a post-processing kinematic (PPK)-corrected GNSS driving past the sensors installed at a four-way traffic intersection. The experimental results show that the proposed automatic calibration approach can achieve the transformation with a root mean squared error of less than 0.5 for radar and lidar and less than 2 for camera detections. The ability to rapidly calibrate sensors not only benefits initial installations, but can also be used for system health monitoring, while utilizing available connected vehicle data to test the real-time sensor fidelity and operational status.

ADVANCED PROPULSION SYSTEMS,ENERGY CONSERVATION, C↗
DOE OSTI2024

Bias Correction and Statistical Downscaling of Future Solar Irradiance Projections Using the NSRDB

Assessing renewable energy resources under future climate scenarios has been highlighted to understand potential impacts of future climate change in renewable generation on the power sector. Climate model projection has been recognized by the renewable energy community as a useful data set to analyze the impacts of future climate change on renewable resources. However, future climate projections generated from general circulation models (GCMs) contain inherent biases that need to be corrected for accurate analysis of future projections of climate variables. In addition, the coarse spatiotemporal resolution of GCMs needs to be improved for regional climate studies. In this work, we develop statistical methods to downscale future projections of global horizontal irradiance (GHI) in a computationally efficient way. Our approach builds statistical downscaling models that correct bias of climate projection of GHI and downscale the future GHI projection from daily-scale to hourly-scale. The National Solar Radiation Database (NSRDB) is used to calibrate the statistical models and validate the downscaled GHI projections across the contiguous United State (CONUS). Preliminary results show that the statistical approach efficiently downscales climate projections of GHI with a nBIAS of 3%, nMAE of 34 % and nRMSE of 46% calculated against NSRDB for CONUS. This study describes the implemented methodology and initial results as well as future research to create high-resolution climate data sets for solar energy applications.

analytical models↗
DOE OSTI2025

HPC-Driven Modeling with ML-Based Surrogates for Magnon-Photon Dynamics in Hybrid Quantum System

Here, we introduce a hybrid computational framework that merges HPC-based numerical solvers with physics-informed ML surrogates for efficient modeling of magnon-photon interactions. By running short-duration, high-fidelity Maxwell-LLG simulations and feeding their results into an ML model, we substantially cut simulation time while achieving accurate predictions across larger spatiotemporal domains.

Accuracy↗
DOE OSTI2020

Hierarchical Membrane Dynamics in Phase-Separated Model Membranes

Lipid membranes, the primary matrix of cell membranes, exhibit a hierarchy of dynamics from molecular motions to collective undulations, which control spatiotemporal membrane phenomena and regulate various cellular functions. Thus, understanding how various dynamic modes influence membrane behavior is crucial to uncovering the design rules of cell membranes and implementing them in future technologies. Previous membrane dynamics studies using neutron spin-echo spectroscopy (NSE) have shed light on the dependence of collective membrane fluctuations on viscoelastic membrane properties, demonstrating that thickness fluctuation modes (100ns) are dictated by membrane viscosity, which directly governs fast (ps) molecular diffusive motions. Here, we focus on phase-separating lipid membranes, composed of DMPC:DSPC mixtures, to understand the effect of domain formation/growth on hierarchical matrix dynamics using selective lipid deuteration and different neutron spectroscopy techniques. NSE measurements on DMPC:DSPC-d83 (70:30 mol%) show that bending rigidity of the DMPC-rich matrix graduallyincreases with decreasing temperature - as the fully-fluid membrane approaches the upper phase transition (i.e. with the formation of transient DSPC clusters) - and increases further in the phase coexistence region with the growth of DSPC domains. Comparatively, NSE measurements on DMPC-d54:DSPC-d83 vesicles show pronounced matrix thickness fluctuations in the fully-fluid phase and drastic suppression of this fluctuation mode in the gel-fluid coexistence phase, even when the DMPC-rich matrix is still in its fluid phase. This suppression in fluctuations suggests an increase in the matrix viscosity with the growth of gel DSPC domains, which is further investigated by selectively measuring lipid diffusion in the DMPC-rich matrix using neutron backscattering spectroscopy. Comparisons of the experimental results with coarse-grained MD simulationsillustrate the underlying coupling mechanisms. Overall, these observations indicate a clear mechanical and viscoelastic coupling betweenlipid domains and their host matrix, suggesting that domain formation influences membrane properties beyond local effects.

Carrillo, Jan Michael↗
DOE OSTI2024

Flashback Studies of High-Hydrogen Flames using High-Speed OH Planar Laser-Induced Fluorescence

Flame flashback is a crucial challenge during the application of high-hydrogen fuels for the development of next-generation lean premixed combustors. The fundamentals of stable flame configuration, flashback phenomena, and spatiotemporal information of flame dynamics in a premixed, swirl-stabilized burner are investigated experimentally at atmospheric pressure conditions using high-repetition-rate nanosecond (ns)-duration hydroxyl radical planar laser-induced fluorescence (OH-PLIF) measurements. The inlet conditions are varied systematically with respect to equivalence ratio (ϕ), hydrogen percentage in a hydrogen-methane mixture (50%–90%) and pre-mixer velocities and the experiments are performed on the burner modified to provide optical access to the premixing section. Signal interferences such as saturation effects, background chemiluminescence, and laser non-uniformity issues were minimized or corrected during data acquisition and subsequent data processing steps. A stable flame characterization was performed at 20 kHz-repetition-rate for varied pre-mixer velocities, hydrogen content and ϕ in the reactant mixture and lift-off length (L) investigation showed dependence on each of these parameters. Flame dynamics such as flame flashback events, local ignition, local extinction, flame curvature as well as the main reaction zone of the combustion mechanism are well characterized. Flashback ϕ showed an expected linearly increasing trend with increasing pre-mixer velocity and decreasing hydrogen content and the conclusions drawn aligned well with detailed L investigation. Such spatially and temporally resolved kHz-rate OH-PLIF is a promising technique to observe rapidly occurring flashback dynamics and can further validate turbulence-chemistry interaction models of swirling flames.

Parajuli, Pradeep↗
DOE OSTI2022

Exploratory Precipitation Metrics: Spatiotemporal Characteristics, Process-Oriented, and Phenomena-Based

Abstract Precipitation sustains life and supports human activities, making its prediction one of the most societally relevant challenges in weather and climate modeling. Limitations in modeling precipitation underscore the need for diagnostics and metrics to evaluate precipitation in simulations and predictions. While routine use of basic metrics is important for documenting model skill, more sophisticated diagnostics and metrics aimed at connecting model biases to their sources and revealing precipitation characteristics relevant to how model precipitation is used are critical for improving models and their uses. This paper illustrates examples of exploratory diagnostics and metrics including 1) spatiotemporal characteristics metrics such as diurnal variability, probability of extremes, duration of dry spells, spectral characteristics, and spatiotemporal coherence of precipitation; 2) process-oriented metrics based on the rainfall–moisture coupling and temperature–water vapor environments of precipitation; and 3) phenomena-based metrics focusing on precipitation associated with weather phenomena including low pressure systems, mesoscale convective systems, frontal systems, and atmospheric rivers. Together, these diagnostics and metrics delineate the multifaceted and multiscale nature of precipitation, its relations with the environments, and its generation mechanisms. The metrics are applied to historical simulations from phases 5 and 6 of the Coupled Model Intercomparison Project. Models exhibit diverse skill as measured by the suite of metrics, with very few models consistently ranked as top or bottom performers compared to other models in multiple metrics. Analysis of model skill across metrics and models suggests possible relationships among subsets of metrics, motivating the need for more systematic analysis to understand model biases for informing model development.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Discrete Time-Crystalline Order Enabled by Quantum Many-Body Scars: Entanglement Steering via Periodic Driving

The control of many-body quantum dynamics in complex systems is a key challenge in the quest to reliably produce and manipulate large-scale quantum entangled states. Recently, quench experiments in Rydberg atom arrays [Bluvstein et al. Science 371, 1355 (2021)] demonstrated that coherent revivals associated with quantum many-body scars can be stabilized by periodic driving, generating stable subharmonic responses over a wide parameter regime. We analyze a simple, related model where these phenomena originate from spatiotemporal ordering in an effective Floquet unitary, corresponding to discrete time-crystalline behavior in a prethermal regime. Unlike conventional discrete time crystals, the subharmonic response exists only for Néel-like initial states, associated with quantum scars. We predict robustness to perturbations and identify emergent timescales that could be observed in future experiments. Our results suggest a route to controlling entanglement in interacting quantum systems by combining periodic driving with many-body scars.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Spatiotemporal control of high-intensity laser pulses with a plasma lens

Spatiotemporal control encompasses a variety of techniques for producing laser pulses with dynamic intensity peaks that move independently of the group velocity. This controlled motion of the intensity peak offers a new approach to optimizing laser-based applications and enhancing signatures of fundamental phenomena. Here, we demonstrate spatiotemporal control with a plasma optic. A chirped laser pulse focused by a plasma lens exhibits a moving focal point, or “flying focus,” that can travel at an arbitrary, predetermined velocity. Unlike currently used conventional or adaptive optics, a plasma lens can be located close to the interaction region and can operate at an orders of magnitude higher, near-relativistic intensity. Published by the American Physical Society 2024

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

High-Speed OH-PLIF Diagnostics of Flame Flashback in Low Swirl Hydrogen-Enriched Flames

This paper reports flashback events observed in hydrogen-enriched flames stabilized in a low swirl burner (LSB) at atmospheric pressure and temperature conditions. The fundamentals of hydrogen-rich stable flames and spatiotemporal investigation of flashback phenomena were observed experimentally using a high-repetition-rate nanosecond (ns)-duration hydroxyl radical planar laser-induced fluorescence (OH-PLIF) diagnostic. Testing was conducted in an optically accessible pre-mixing section of a LSB with inlet pre-mixing velocities ranging from 5 to 10 m/s for methane and hydrogen (50 – 90% by mole) blends. Swirlers with two different turning angles, 26o and 33o, and three different perforated plate hole diameters, 1.08, 1.12 and 1.16 mm, with measured swirl numbers varying from 0.43 to 0.49 were used in this study at atmospheric temperature and pressure inlet conditions. The flashback propensity showed a dependence on the proximity of the lifted flame to the burner exit (termed as lift-off length, L) which was dependent on the pre-mixer velocity (V), hydrogen content (XH2) and equivalence ratio (ϕ) at constant temperature and pressure conditions. High-speed OH-PLIF images revealed lifted flames were first observed at low ϕ/ XH2 condition which then changed to a M-shaped flame attached to burner rim with the increase in ϕ/ XH2. Further increases in ϕ/XH2, depending upon other inlet parameters, triggered flame flashback into the pre-mixing section. Flashback occurred when burning began in the outer shear layer and the leading flame brush propagated into the nozzle. Such spatiotemporally resolved high-speed OH-PLIF imaging provides insights on different stages of flashback in a LSB – flashback initiation, transition of flame propagation from burner exit to the swirler and flashback to flame holding transition. Flame ϕ at flashback showed an expected linearly increasing trend with increasing V and decreasing XH2 and the conclusions drawn aligned well with detailed investigations. For identical inlet conditions, flashback propensity decreased with increasing perforated-plate hole diameter and increasing swirler vane angle.

Parajuli, Pradeep↗
DOE OSTI2026

Flame Characterization and Flashback Studies of Hydrogen-Enriched Low-Swirl Flames Using High-Speed OH-PLIF

Here, this paper reports the flashback mechanism observed in hydrogen-enriched flames stabilized in a low-swirl burner (LSB) at atmospheric temperature and pressure. The fundamentals of hydrogen-rich stable flames and spatiotemporal information of flashback phenomena were observed experimentally using a high-repetition-rate nanosecond (ns)-duration hydroxyl planar laser-induced fluorescence (OH-PLIF) diagnostic. Testing was conducted for methane and hydrogen (50–90%H 2 , by mole) blends in an optically accessible LSB premixer with measured swirl numbers varying from 0.43 to 0.49. The flashback propensity showed dependence on liftoff length, which was dependent on premixer velocity (𝑉), hydrogen content (𝑋 H 2 ), and equivalence ratio (𝜙) at constant temperature and pressure. High-speed OH-PLIF images revealed that lifted flames were first observed at low 𝜙/𝑋 H 2 conditions, which were changed to an M-shaped flame attached to the burner rim with an increase in 𝜙/𝑋 H 2 . A further increase in 𝜙/𝑋 H 2 triggered the flame flashback into the premixer. Flame 𝜙 at flashback (𝜙 FB ) showed an expected linearly increasing trend with increasing 𝑉 and decreasing 𝑋 H 2 , and the conclusions drawn aligned well with detailed liftoff length investigations. The 𝜙 FB increased with increasing perforated plate hole diameter and increasing swirler vane angle. The vane angle had little effect on flashback tendency at high premixer velocity.

combustion↗
DOE OSTI2024

Flame Flashback Investigations in Hydrogen-Enriched Low Swirl Flames using High-Speed Hydroxyl (OH) Planar Laser-Induced Fluorescence

This study reports flashback mechanism observed in hydrogen-enriched flames stabilized in a low swirl burner (LSB) at atmospheric pressure and temperature conditions. The fundamentals of hydrogen-rich stable flames and spatiotemporal investigation of flashback phenomena were observed experimentally using a high-repetition-rate nanosecond (ns)-duration hydroxyl radical planar laser-induced fluorescence (OH-PLIF) diagnostic. Testing was conducted in an optically accessible pre-mixing section of LSB with inlet pre-mixing velocities from 5 to 10 m/s for methane and hydrogen (50 – 90% by mole) blends. Swirlers with two different turning angles, 26 and 33 degrees and three different perforated plate hole diameters, 1.08, 1.12 and 1.16 mm with measured swirl numbers varying from 0.43 to 0.49 were used. The flashback propensity showed dependence on the proximity of the lifted flame to the burner exit which was dependent on pre-mixer velocity, hydrogen content and equivalence ratio (ER). High-speed OH-PLIF images revealed lifted flames were first observed at low ER condition which is changed to M-shaped flame attached to burner rim with the increase in ER. Then, further increase in ER triggers flame flashback into the nozzle. Flashback occurred when burning occurs in the outer shear layer and the leading flame brush ingresses into the nozzle.

Parajuli, Pradeep↗
DOE OSTI2025

Data-Driven Analysis of Multipactor Dynamics via Dynamic Mode Decomposition

Multipactor effect is a performance-limiting kinetic plasma effect that can occur in high-power microwave and radio frequency (RF) devices. Multipactor effect is of special concern in vacuum or near-vacuum conditions such as those in particle accelerators and spaceborne devices. In this work, we present a data-driven reduced-order model (ROM) based on dynamic mode decomposition (DMD) for modeling of multipactor effects. We study multipactor effects and the resulting nonlinear harmonic generation by processing high-fidelity data generated from electromagnetic particle-in-cell (EMPIC) simulations using the DMD algorithm. We also investigate time-delay embedding extensions of DMD with improved generalizability and accuracy for modeling the electron plasma current density behavior. Here, the results show that DMD provides valuable insights into multipactor phenomena by extracting relevant modal spatiotemporal patterns and frequencies. In addition, DMD offers the potential to time extrapolate EMPIC simulations at a minimal cost, thereby reducing overall simulation time.

43 PARTICLE ACCELERATORS↗
DOE OSTI2020

A combined SECM and electrochemical AFM approach to probe interfacial processes affecting molecular reactivity at redox flow battery electrodes

Redox flow batteries are attractive technologies for grid energy storage since they use solutions of redox-active molecules that enable a superior scalability and the decoupling of power and energy density. However, the reaction mechanisms of the redox active components at RFB electrodes are complex, and there is currently a pressing need to understand how interfacial processes impact the kinetics and operational reversibility of RFB systems. Here, we developed a combined electrochemical imaging methodology rooted in scanning electrochemical microscopy (SECM) and atomic force microscopy (AFM) for exploring the impact of electrode structure and conditioning on the electron transfer properties of model redox-active dialkoxybenzene derivatives, 2,5-di-tert-butyl-1,4-bis(2-methoxyethoxy)benzene (C1) and 2,3-dimethyl-1,4-dialkoxybenzene (C7). Using AFM and secondary-ion mass spectrometry (SIMS), we observed the formation of interfacial films with distinct mechanical properties compared to those of cleaved graphitic surfaces, and exclusively during reduction of electrogenerated radical cations. These films had an impact on the median rate and distribution of the electron transfer rate constant at the basal plane of multilayer and single layer graphene electrodes, displaying kinetically-limited values that did not yield the activation expected per the Butler–Volmer model with a transfer coefficient ~0.5. These changes were dependent on redoxmer structure: furthermore, SECM showed strong attenuation of C7 kinetics by a surface layer on MLG and SLG, while C1 kinetics were only affected by SLG. SECM and AFM results together show that these limiting films operate exclusively on the basal plane of graphite, with the edge plane showing a relative insensitivity to cycling and operation potential. Ultimately, this integrated electrochemical imaging methodology creates new opportunities to understand the unique role of interfacial processes on the heterogeneous reactivity of redoxmers at electrodes for RFBs, with a future role in elucidating phenomena at high active concentrations and spatiotemporal variations in electrode dynamics.

25 ENERGY STORAGE↗
DOE OSTI2022

Unified many-worlds browsing of arbitrary physics-based animations

Manually tuning physics-based animation parameters to explore a simulation outcome space or achieve desired motion outcomes can be notoriously tedious. This problem has motivated many sophisticated and specialized optimization-based methods for fine-grained (keyframe) control, each of which are typically limited to specific animation phenomena, usually complicated, and, unfortunately, not widely used. In this paper, we propose Unified Many-Worlds Browsing (UMWB), a practical method for sample-level control and exploration of physics-based animations. Our approach supports browsing of large simulation ensembles of arbitrary animation phenomena by using a unified volumetric WORLDPACK representation based on spatiotemporally compressed voxel data associated with geometric occupancy and other low-fidelity animation state. Beyond memory reduction, the WORLDPACK representation also enables unified query support for interactive browsing: it provides fast evaluation of approximate spatiotemporal queries, such as occupancy tests that find ensemble samples ("worlds") where material is either IN or NOT IN a user-specified spacetime region. WORLDPACKS also support real-time hardware-accelerated voxel rendering by exploiting the spatially hierarchical and temporal RLE raster data structure. Our UMWB implementation supports interactive browsing (and offline refinement) of ensembles containing thousands of simulation samples, and fast spatiotemporal queries and ranking. We show UMWB results using a wide variety of physics-based animation phenomena---not just JELL-O ® .

Computer Science↗
DOE OSTI2021

Non-linear hydrologic organization

We revisit three variants of the well-known Stommel diagrams that have been used to summarize knowledge of characteristic scales in time and space of some important hydrologic phenomena and modified these diagrams focusing on spatiotemporal scaling analyses of the underlying hydrologic processes. In the present paper we focus on soil formation, vegetation growth, and drainage network organization. We use existing scaling relationships for vegetation growth and soil formation, both of which refer to the same fundamental length and timescales defining flow rates at the pore scale but different powers of the power law relating time and space. The principle of a hierarchical organization of optimal subsurface flow paths could underlie both root lateral spread (RLS) of vegetation and drainage basin organization. To assess the applicability of scaling, and to extend the Stommel diagrams, data for soil depth, vegetation root lateral spread, and drainage basin length have been accessed. The new data considered here include timescales out to 150 Myr that correspond to depths of up to 240 m and horizontal length scales up to 6400 km and probe the limits of drainage basin development in time, depth, and horizontal extent.

58 GEOSCIENCES↗
DOE OSTI2025

Oscillatory redox behavior in oxides: Cyclic surface reconstruction and reactivity modulation via the Mars–van Krevelen mechanism

The breaking of translational symmetry at oxide surfaces gives rise to coordinatively unsaturated cations/anions and surface restructuring—key factors that govern surface reactivity. Using direct in situ environmental transmission electron microscopy (TEM) observations along with atomistic modeling, we report oscillatory redox behavior in CuO under H 2 , where cyclic surface reconstruction and reactivity modulation occur via the Mars–van Krevelen (MvK) mechanism. We observe self-switching between oxygen-rich and oxygen-deficient surface reconstructions, alternately activating and deactivating the surface for H 2 O formation. During periods of chemical inactivity, the oxygen-deficient surface undergoes slow reoxidation via lattice oxygen diffusing from subsurface and bulk reservoirs, restoring the active oxygen-rich surface termination. The inherent disparity in chemical activity among undercoordinated surface ions, along with sluggish subsurface-to-surface oxygen replenishment, drives this oscillatory redox cycle, modulating H2-induced loss of lattice oxygen at the surface and its delayed replenishment from the subsurface. This creates spatiotemporally separated redox steps at the oxide surface. The phenomena and atomistic insights presented here have significant implications for manipulating the surface reactivity of oxides by tuning the separation of these redox steps.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Variational multiscale reinforcement learning for discovering reduced order closure models of nonlinear spatiotemporal transport systems

Abstract A central challenge in the computational modeling and simulation of a multitude of science applications is to achieve robust and accurate closures for their coarse-grained representations due to underlying highly nonlinear multiscale interactions. These closure models are common in many nonlinear spatiotemporal systems to account for losses due to reduced order representations, including many transport phenomena in fluids. Previous data-driven closure modeling efforts have mostly focused on supervised learning approaches using high fidelity simulation data. On the other hand, reinforcement learning (RL) is a powerful yet relatively uncharted method in spatiotemporally extended systems. In this study, we put forth a modular dynamic closure modeling and discovery framework to stabilize the Galerkin projection based reduced order models that may arise in many nonlinear spatiotemporal dynamical systems with quadratic nonlinearity. However, a key element in creating a robust RL agent is to introduce a feasible reward function, which can be constituted of any difference metrics between the RL model and high fidelity simulation data. First, we introduce a multi-modal RL to discover mode-dependant closure policies that utilize the high fidelity data in rewarding our RL agent. We then formulate a variational multiscale RL (VMRL) approach to discover closure models without requiring access to the high fidelity data in designing the reward function. Specifically, our chief innovation is to leverage variational multiscale formalism to quantify the difference between modal interactions in Galerkin systems. Our results in simulating the viscous Burgers equation indicate that the proposed VMRL method leads to robust and accurate closure parameterizations, and it may potentially be used to discover scale-aware closure models for complex dynamical systems.

97 MATHEMATICS AND COMPUTING↗