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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.

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At least 739 records · Page 41
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Charging-driven coarsening and melting of a colloidal nanoparticle monolayer at an ionic liquid–vacuum interface

In this work, we induce and investigate the coarsening and melting dynamics of an initially static nanoparticle colloidal monolayer at an ionic liquid–vacuum interface, driven by a focused, scanning electron beam. Coarsening occurs through grain interface migration and larger-scale motions such as grain rotations, often facilitated by sliding dislocations. The progressive decrease in area fraction that drives melting of the monolayer is explained using an electrowetting model whereby particles at the interface are solvated once their accumulating charge recruits sufficient counterions to subsume the particle. Subject to stochastic particle removal from the monolayer, melting is recapitulated in simulations with a Lennard-Jones potential. This new driving mechanism for colloidal systems, whose dynamical timescales we show can be controlled with the accelerating voltage, opens the possibility to manipulate particle interactions dynamically without need to vary particle intrinsic properties or surface treatments. Furthermore, the decrease in particle size availed by electron imaging presents opportunities to observe force and time scales in a lesser-explored regime intermediate between typical colloidal and molecular systems.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Anisotropic interactions for continuum modeling of protein–membrane systems

In this work, a model for anisotropic interactions between proteins and cellular membranes is proposed for large-scale continuum simulations. The framework of the model is based on dynamic density functional theory, which provides a formalism to describe the lipid densities within the membrane as continuum fields while still maintaining the fidelity of the underlying molecular interactions. Within this framework, we extend recent results to include the anisotropic effects of protein–lipid interactions. As applications, we consider two membrane proteins of biological interest: a RAS–RAF complex tethered to the membrane and a membrane embedded G protein-coupled receptor. A strong qualitative and quantitative agreement is found between the numerical results and the corresponding molecular dynamics simulations. Combining the scope of continuum level simulations with the details from molecular level particle simulations enables research into protein–membrane behaviors at a more biologically relevant scale, which crucially can also be accessed via experiment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Dynamic population balance in molecular-level simulations of hypersonic flows

This report summarizes the work towards developing stochastic weighted particle methods (SWPM) for future application in hypersonic flows. Extensive changes to Sandia’s direct simulation Monte Carlo (DSMC) solver, SPARTA (Stochastic Particle Real Time Analyzer), were made to enable the necessary particle splitting and reduction capabilities for SWPM. The results from one-dimensional Couette and Fourier flows suggest that SWPM can reproduce the correct transport for a large range of Knudsen numbers with adequate accuracy. The associated velocity and temperature profiles are in good agreement with DSMC. An issue with particle placement during particle number reduction, is identified, to which, a simple but effective solution based on minimizing the center of mass error is proposed. High Mach wheel flows are simulated using the SWPM and DSMC methods. SWPM is capable of providing nearly an order of magnitude increase in efficiency over DSMC while retaining high accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Parametrizations of coupled betatron motion for strongly coupled lattices

The coupling of transverse motion is a natural occurrence in particle accelerators, either in the form of a residual coupling arising from imperfections or originating by design from strong systematic coupling fields. While the first can be treated perturbatively, the latter requires a robust approach adapted to strongly coupled optics, and a parametrization of the linear optics must be performed to explore beam dynamics in such peculiar lattices. This work highlights the key physical interpretations of the main parametrization formalisms to describe linear coupled optics, along with explicit links and comparisons of these parametrizations. Concepts rarely illustrated in other works, such as forced mode flips and local coupling, are explored in detail, clarifying some anomalies that can arise in lattice functions. The analytical methods have been implemented in a reference Python package and connected with ray-tracing and integration codes to explore examples of strongly coupled lattices, which are discussed in detail to highlight the key physical interpretations of the parametrizations and characteristics of the lattices.

47 OTHER INSTRUMENTATION↗
NASA NTRS2013

Representation of Nucleation Mode Microphysics in a Global Aerosol Model with Sectional Microphysics

In models, nucleation mode (1 nm<Dp <10 nm) particle microphysics can be represented explicitly with aerosol microphysical processes or can be parameterized to obtain the growth and survival of nuclei to the model's lower size boundary. This study investigates how the representation of nucleation mode microphysics impacts aerosol number predictions in the TwO-Moment Aerosol Sectional (TOMAS) aerosol microphysics model running with the GISS GCM II-prime by varying its lowest diameter boundary: 1 nm, 3 nm, and 10 nm. The model with the 1 nm boundary simulates the nucleation mode particles with fully resolved microphysical processes, while the model with the 10 nm and 3 nm boundaries uses a nucleation mode dynamics parameterization to account for the growth of nucleated particles to 10 nm and 3 nm, respectively.We also investigate the impact of the time step for aerosol microphysical processes (a 10 min versus a 1 h time step) to aerosol number predictions in the TOMAS models with explicit dynamics for the nucleation mode particles (i.e., 3 nm and 1 nm boundary). The model with the explicit microphysics (i.e., 1 nm boundary) with the 10 min time step is used as a numerical benchmark simulation to estimate biases caused by varying the lower size cutoff and the time step. Different representations of the nucleation mode have a significant effect on the formation rate of particles larger than 10 nm from nucleated particles (J10) and the burdens and lifetimes of ultrafinemode (10 nm≤Dp ≤70 nm) particles but have less impact on the burdens and lifetimes of CCN-sized particles. The models using parameterized microphysics (i.e., 10 nm and 3 nm boundaries) result in higher J10 and shorter coagulation lifetimes of ultrafine-mode particles than the model with explicit dynamics (i.e., 1 nm boundary). The spatial distributions of CN10 (Dp ≥10 nm) and CCN(0.2 %) (i.e., CCN concentrations at 0.2%supersaturation) are moderately affected, especially CN10 predictions above ∼700 hPa where nucleation contributes most strongly to CN10 concentrations. The lowermost-layer CN10 is substantially improved with the 3 nm boundary (compared to 10 nm) in most areas. The overprediction in CN10 with the 3 nm and 10 nm boundaries can be explained by the overprediction of J10 or J3 with the parameterized microphysics, possibly due to the instantaneous growth rate assumption in the survival and growth parameterization. The errors in CN10 predictions are sensitive to the choice of the lower size boundary but not to the choice of the time step applied to the microphysical processes. The spatial distribution of CCN(0.2 %) with the 3 nm boundary is almost identical to that with the 1 nm boundary, but that with the 10 nm boundary can differ more than 10-40% in some areas. We found that the deviation in the 10 nm simulations is partly due to the longer time step (i.e., 1 h time step used in the 10 nm simulations compared to 10 min time step used in the benchmark simulations), but, even with the same time step, the 10 nm cutoff showed noticeably higher errors than the 3 nm cutoff. In conclusion, we generally recommend using a lower diameter boundary of 3 nm for studies focused on aerosol indirect effects but down to 1 nm boundary for studies focused on CN10 predictions or nucleation.

microphysics↗
NASA NTRS1993

Design and testing of a unique randomized gravity, continuous flow bioreactor

A rotating, null gravity simulator, or Couette bioreactor was successfully used for the culture of mammalian cells in a simulated microgravity environment. Two limited studies using Lipomyces starkeyi and Streptomyces clavuligerus were also conducted under conditions of simulated weightlessness. Although these studies with microorganisms showed promising preliminary results, oxygen limitations presented significant limitations in studying the biochemical and cultural characteristics of these cell types. Microbial cell systems such as bacteria and yeast promise significant potential as investigative models to study the effects of microgravity on membrane transport, as well as substrate induction of inactive enzyme systems. Additionally, the smaller size of the microorganisms should further reduce the gravity induced oscillatory particle motion and thereby improve the microgravity simulation on earth. Focus is on the unique conceptual design, and subsequent development of a rotating bioreactor that is compatible with the culture and investigation of microgravity effects on microbial systems. The new reactor design will allow testing of highly aerobic cell types under simulated microgravity conditions. The described reactor affords a mechanism for investigating the long term effects of reduced gravity on cellular respiration, membrane transfer, ion exchange, and substrate conversions. It offers the capability of dynamically altering nutrients, oxygenation, pH, carbon dioxide, and substrate concentration without disturbing the microgravity simulation, or Couette flow, of the reactor. All progeny of the original cell inoculum may be acclimated to the simulated microgravity in the absence of a substrate or nutrient. The reactor has the promise of allowing scientists to probe the long term effects of weightlessness on cell interactions in plants, bacteria, yeast, and fungi. The reactor is designed to have a flow field growth chamber with uniform shear stress, yet transfer high concentrations of oxygen into the culture medium. The system described allows for continuous, on line sampling for production of product without disturbing fluid and particle dynamics in the reaction chamber. It provides for the introduction of substrate, or control substances after cell adaptation to simulated microgravity has been accomplished. The reactor system provides for the nondisruptive, continuous flow replacement of nutrient and removal of product. On line monitoring and control of growth conditions such as pH and nutrient status are provided. A rotating distribution valve allows cessation of growth chamber rotation, thereby preserving the simulated microgravity conditions over longer periods of time.

Lassiter, Carroll B.↗
DOE OSTI2011

Comment on 'Mapping of localized spin-wave excitations by near-field Brillouin light scattering' [Appl. Phys. Lett. 97, 152502 (2010)].

The authors reported in their letter some outstanding experimental results of spin excitations in nano-particles investigated by near-field Brillouin scattering. They conclude from their observations that existing theories -- in particular micromagnetic simulations -- do not correctly describe the behavior of the spin modes. Since excellent agreement has been reported between spin-wave mode frequencies obtained from Brillouin scattering experiments and those obtained from micromagnetic-based simulations, it is somewhat surprising that the simulations should fail for the particles investigated in Ref. 1. In the literature, there is also evidence of various kinds and degrees of mode localization when exchange competes with dipolar interactions. When dipolar long-range interactions are taken into account, the eigenmodes can be seen as the superposition of plane waves, leading to different localizations and in particular to the appearence of bulk-dead modes. We have simulated the normal modes of the particles used in Ref. 1, with the dynamical matrix method; the results are shown in Fig. 1 for different values of the applied field. In addition to the lowest frequency non-localized mode (1-BA), several localized modes are present. Large particles exhibit modes with oscillations along the field direction;8 for such modes, we use the label n-BA-loc, with n the number of nodes. While the profile of the pure end-mode, i.e., 0-BA-loc, has its maximum at the edge with the amplitude monotonously decreasing toward the interior of the ellipse, as correctly described by the authors, the localized modes with n > 0, not considered by them, do not have this characteristic: see inset of Fig. 1. Based on Fig. 1, we believe that the assumption that the mode they observe is 'the' localized spin mode is not correct. Instead, we believe that the mode detected in the experiment at H > 700 Oe is a combinations (due to non-linear excitation conditions of the experiment) of several n-BA-loc modes, with n?>?0. In this picture, the sharp peaks of the n-BA-loc modes are smoothed in the experimental measurements, thanks to the superposition of modes with different nodal lines. Finally, at 350 Oe, the measured profile and frequency suggest that the mode seen in the experiment may be well due to the 1-BA mode. The observed change in mode profile at 350 Oe is substantiated by the frequency behavior shown in Fig. 3(b) of Ref. 1, where it can be observed that the frequency of the low-field point does not lie on the same curve as the high-field points. In summary, before concluding that micromagnetic-based simulations of spin wave modes in nano-particles are unreliable, we believe that it is necessary to await either the simulation of large particles using small cell sizes or for more exhaustive experiments reaching lower frequencies on particles of varying size. The comparison of calculations with experiment would greatly benefit if the authors were to provide the field dependence of all the modes detected in their experiment (in order to achieve a proper assignment).

36 MATERIALS SCIENCE↗
DOE OSTI2016

Hydraulic jumps in inhomogeneous strongly coupled toroidal dust flows

The inhomogeneous flow of strongly coupled dust particles in a toroidal particle trap with harmonic radial confinement is analyzed in the incompressible fluid limit. It is shown that the flow can spontaneously generate shock-like events, which are similar to the hydraulic jump in open channel flows. A definition of the Froude number for this model is given and the critical speed is recovered as the group velocity of surface waves. This hydraulic model is compared with molecular-dynamics simulations, which show that a sudden bifurcation of the flow lines and a localized temperature peak appear just at the point where the critical condition for the hydraulic jump is located.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2024

Experimental Validation of Charged Lunar Dust Dynamics Simulants

The goal of this work is to experimentally verify the electrostatic interaction physics that have been incorporated into the discrete element method (DEM) modeling software package during the FY20 CIF project titled “Charged Particle Dynamics in the Lunar Environment.” Current state-of-the-art (SOA) granular gas dynamics models used to explain rocket plume impingement physics have not taken into account the natural or induced electrostatic environment of the lunar surface, nor the effect of charged regolith grains being present in the plume plasma. This work improved upon the SOA by adding long-range and contact inter-particle electrostatic interactions to a granular mechanics DEM modeling software package. Tribocharging mechanics between spherical particles has been experimentally examined along with the natural electrostatic plasma environments produced via emission from an electron gun and ultraviolet lamp.

Jay Phillips↗
DOE OSTI2015

Multiscale Universal Interface: A concurrent framework for coupling heterogeneous solvers

Graphical abstract: - Abstract: Concurrently coupled numerical simulations using heterogeneous solvers are powerful tools for modeling multiscale phenomena. However, major modifications to existing codes are often required to enable such simulations, posing significant difficulties in practice. In this paper we present a C++ library, i.e. the Multiscale Universal Interface (MUI), which is capable of facilitating the coupling effort for a wide range of multiscale simulations. The library adopts a header-only form with minimal external dependency and hence can be easily dropped into existing codes. A data sampler concept is introduced, combined with a hybrid dynamic/static typing mechanism, to create an easily customizable framework for solver-independent data interpretation. The library integrates MPI MPMD support and an asynchronous communication protocol to handle inter-solver information exchange irrespective of the solvers' own MPI awareness. Template metaprogramming is heavily employed to simultaneously improve runtime performance and code flexibility. We validated the library by solving three different multiscale problems, which also serve to demonstrate the flexibility of the framework in handling heterogeneous models and solvers. In the first example, a Couette flow was simulated using two concurrently coupled Smoothed Particle Hydrodynamics (SPH) simulations of different spatial resolutions. In the second example, we coupled the deterministic SPH method with the stochastic Dissipative Particle Dynamics (DPD) method to study the effect of surface grafting on the hydrodynamics properties on the surface. In the third example, we consider conjugate heat transfer between a solid domain and a fluid domain by coupling the particle-based energy-conserving DPD (eDPD) method with the Finite Element Method (FEM)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Wakefield Simulations for the Laser Acceleration Experiment at SLAC

Laser-driven acceleration in dielectric photonic band gap structures can provide gradients on the order of GeV/m. The small transverse dimension of the structure, on the order of the laser wavelength, presents interesting wakefield-related issues. Higher order modes can seriously degrade beam quality, and a detailed understanding is needed to mitigate such effects. On the other hand, wakefields also provide a direct way to probe the interaction of a relativistic bunch with the synchronous modes supported by the structure. Simulation studies have been carried out as part of the effort to understand the impact on beam dynamics, and to compare with data from beam experiments designed to characterize candidate structures. In this paper, we present simulation results of wakefields excited by a sub-wavelength bunch in optical photonic band gap structures.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Quantum Simulation of the First-Quantized Pauli-Fierz Hamiltonian

We provide an explicit recursive divide-and-conquer approach for simulating quantum dynamics and derive a discrete first-quantized nonrelativistic QED Hamiltonian based on the many-particle Pauli-Fierz Hamiltonian. We apply this recursive divide-and-conquer algorithm to this Hamiltonian and compare it to a concrete simulation algorithm that uses qubitization. Our divide-and-conquer algorithm, using lowest-order Trotterization, scales for fixed grid spacing as O ~ ( Λ N 2 η 2 t 2 / ϵ ) for grid size N , η particles, simulation time t , field cutoff Λ , and error ϵ . Our qubitization algorithm scales as O ~ ( N ( η + N ) ( η + Λ 2 ) t log ( 1 / ϵ ) ) . This shows that even a naive partitioning and low-order splitting formula can yield, through our divide-and-conquer formalism, superior scaling to qubitization for large Λ . We compare the relative costs of these two algorithms on systems that are relevant for applications such as the spontaneous emission of photons and the photoionization of electrons. We observe that for different parameter regimes, one method can be favored over the other. Finally, we give new algorithmic and circuit-level techniques for gate optimization, including a new way of implementing a group of multicontrolled- X gates that can be used for better analysis of circuit cost. Published by the American Physical Society 2024

Mukhopadhyay, Priyanka (ORCID:0000000164639100)↗
DOE OSTI2015

Stochastic dynamics of penetrable rods in one dimension: Entangled dynamics and transport properties

The dynamical properties of a system of soft rods governed by stochastic hard collisions (SHCs) have been determined over a varying range of softness using molecular dynamics simulations in one dimension and analytic theory. The SHC model allows for interpenetration of the system’s constituent particles in the simulations, generating overlapping clustering behavior analogous to the spatial structures observed in systems governed by deterministic bounded potentials. Through variation of an assigned softness parameter δ, the limiting ranges of intermolecular softness are bridged, connecting the limiting ensemble behavior from hard to ideal (completely soft). Various dynamical and structural observables are measured from simulation and compared to developed theoretical values. The spatial properties are found to be well predicted by theories developed for the deterministic penetrable-sphere model with a transformation from energetic to probabilistic arguments. While the overlapping spatial structures are complex, the dynamical properties can be adequately approximated through a theory built on impulsive interactions with Enskog corrections. Our theory suggests that as the softness of interaction is varied toward the ideal limit, correlated collision processes are less important to the energy transfer mechanism, and Markovian processes dominate the evolution of the configuration space ensemble. For interaction softness close to hard limit, collision processes are highly correlated and overlapping spatial configurations give rise to entanglement of single-particle trajectories.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Sensitivity of puff dynamics and airborne droplet nuclei distribution to variations in violent expiration events

Here, we use large eddy simulations to investigate the puff and droplet dynamics from violent expiratory events such as coughs and sneezes in the first few seconds following an ejection. For each of the eleven simulations considered, over 60,000 droplets are ejected and individually tracked using the point-particle Euler–Lagrange approach. We test the sensitivity of the puff and droplet dynamics to various parameters including the ejection volume, momentum, and orientation. We also explore the effect of the mouth shape on the aforementioned dynamics by considering elliptical and circular inlet cross-sections. The results from the simulations compare favorably with a recent theoretical framework put forth by Balachandar et al. in terms of the puff size and propagation velocity. More importantly however, the theory is able to accurately predict the number and size spectra of the potentially virus-laden droplet nuclei that remain airborne within the puff. We observe that the ejection angle and mouth shape do not significantly affect the puff and droplet dynamics. Additionally, we quantify the carrying capacity of the detached puff portions in terms of the number and size spectra of droplets/droplet nuclei suspended within.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2018

On Collisions Times of ‘Self-Sorting’ Interacting Particles in One-Dimension with Random Initial Positions and Velocities

We investigate a one-dimensional system of N particles, initially distributed with random positions and velocities, interacting through binary collisions. The collision rule is such that there is a time after which the N particles do not interact and become sorted according to their velocities. When the collisions are elastic, we derive asymptotic distributions for the final collision time of a single particle and the final collision time of the system as the number of particles approaches infinity, under different assumptions for the initial distributions of the particles’ positions and velocities. For comparison, a numerical investigation is carried out to determine how a non-elastic collision rule, which conserves neither momentum nor energy, affects the median collision time of a particle and the median final collision time of the system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

A unified gas-kinetic scheme for continuum and rarefied flows IV: Full Boltzmann and model equations

Fluid dynamic equations are valid in their respective modeling scales, such as the particle mean free path scale of the Boltzmann equation and the hydrodynamic scale of the Navier–Stokes (NS) equations. With a variation of the modeling scales, theoretically there should have a continuous spectrum of fluid dynamic equations. Even though the Boltzmann equation is claimed to be valid in all scales, many Boltzmann solvers, including direct simulation Monte Carlo method, require the cell resolution to the order of particle mean free path scale. Therefore, they are still single scale methods. In order to study multiscale flow evolution efficiently, the dynamics in the computational fluid has to be changed with the scales. A direct modeling of flow physics with a changeable scale may become an appropriate approach. The unified gas-kinetic scheme (UGKS) is a direct modeling method in the mesh size scale, and its underlying flow physics depends on the resolution of the cell size relative to the particle mean free path. The cell size of UGKS is not limited by the particle mean free path. With the variation of the ratio between the numerical cell size and local particle mean free path, the UGKS recovers the flow dynamics from the particle transport and collision in the kinetic scale to the wave propagation in the hydrodynamic scale. The previous UGKS is mostly constructed from the evolution solution of kinetic model equations. Even though the UGKS is very accurate and effective in the low transition and continuum flow regimes with the time step being much larger than the particle mean free time, it still has space to develop more accurate flow solver in the region, where the time step is comparable with the local particle mean free time. In such a scale, there is dynamic difference from the full Boltzmann collision term and the model equations. This work is about the further development of the UGKS with the implementation of the full Boltzmann collision term in the region where it is needed. The central ingredient of the UGKS is the coupled treatment of particle transport and collision in the flux evaluation across a cell interface, where a continuous flow dynamics from kinetic to hydrodynamic scales is modeled. The newly developed UGKS has the asymptotic preserving (AP) property of recovering the NS solutions in the continuum flow regime, and the full Boltzmann solution in the rarefied regime. In the mostly unexplored transition regime, the UGKS itself provides a valuable tool for the non-equilibrium flow study. The mathematical properties of the scheme, such as stability, accuracy, and the asymptotic preserving, will be analyzed in this paper as well.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Roles of Hydrogen Bonds and Alignment in Oriented Attachment of Gibbsite Nanoparticles: Insights from Molecular Dynamics

Oriented attachment (OA) of nanoparticles is an important crystal growth pathway in the synthesis of hierarchical structures. Although a significant understanding of OA has been made, the effect of atomistic misalignment and the roles of solvent/particle and particle/particle interactions on the structure–energy relationship during an OA remain elusive. In this study, we perform molecular dynamics simulations to calculate the potential of mean force (PMF) profile for gibbsite particle translation on a gibbsite slab with 1 or 2 intervening water layers (1W or 2W). The structures of the gibbsite surfaces and the confined water are analyzed to determine how the number and type of hydrogen bonds (H-bonds) influence the free energy profile during the translation. The PMF profile exhibits a periodicity of length 5.078 Å, consistent with the gibbsite unit cell size along the translation direction. The changes in the surface–water and water–water hydrogen bond network and water and surface OH groups’ orientations during the translation are strongly coupled with the changes in the PMF profile in the 1W case. However, when increasing the number of intervening water layers from 1W to 2W, the particle/slab misalignment becomes a dominant factor controlling the behavior of the PMF profile. We also establish a method to quantify misalignment between the particle and the slab, which exhibits a strong correlation with the free energy for the 2W case. These results shed more light into the roles of particle/slab misalignment and hydrogen bond network in the OA of mineral particles in aqueous solution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Diagnosis of bubble evolution in laser-wakefield acceleration via angular distributions of betatron x-rays

We present an indirect method to diagnose the electron beam behaviors and bubble dynamic evolution in a laser-wakefield accelerator. Four kinds of typical bubble dynamic evolution and, hence, electron beam behaviors observed in Particle-In-Cell simulations are identified correspondingly by simultaneous measurement of distinct angular distributions of the betatron radiation and electron beam energy spectra in experiment. The reconstruction of the bubble evolution may shed light on finding an effective way to better generate high-quality electron beams and enhanced betatron X-rays.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗