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DOE OSTI2023

Linear Viscoelastic Properties of Putative Cyclic Polymers Synthesized by Reversible Radical Recombination Polymerization (R3P)

Linear viscoelastic properties in both melt and solution states are reported for a series of poly(3,6-dioxa-1,8-octanedithiol) (polyDODT) made by reversible radical recombination polymerization (R 3 P) under conditions designed to produce linear (LDODT), cyclic (RDODT) and linear-cyclic mixtures (LRDODT). PolyDODT is amorphous (T g < -50 °C) and highly flexible (entanglement molecular weight M e,lin ≈ 1850 g/mol for LDODT). PolyDODT’s low T g and low M e,lin enable characterization over a wide dynamic range and a wide range of dimensionless weight-average molecular weight Z w = M w /M e,lin . Measurements at temperatures from -57 °C to 100 °C provide up to 18 deades of reduced frequency, which is necessary to characterize RDODT melts with Z w from 23 to 300. The two highest molecular weight polymers in the present RDODT series have such high M w (406k and 556k g/mol) that mass spectrometry, NMR spectroscopy, and even chemical assays for chain ends are unable to rule out up to 2 mol% linear contaminant. By studying the samples in solution (using dilution to reduce Z w ) we could compare their dynamics with those of previously established high-purity polystyrene (PS) rings (limited to Z w ≤ 13.6). RDODT solutions with Z w < 15 (concentrations <5wt% for RDODT-406k and 556k) have dynamic moduli G^* that accord with LCCC-purified PS rings in terms of the frequency dependence (including the absence of a plateau), the progression of shapes of G* as a function of Z w , and the linear scaling of their zero-shear viscosity η0 with M w . The shape of G* as a function of Z w for solutions of RDODT-406k and -556k also accord with lower M w RDODT melts (which have ≤ 1.3mol% linear contaminant). Thus, measurement of the linear viscoelastic properties of appropriate concentrations of high M w (>200k g/mol) putative cyclic polymers, in which linear chains evade spectroscopic detection, may provide an alternative means (though not fully proven) of validation of sample purity. When Z w > 15 (including all seven RDODT melts and eight of their solutions), G* has a rubbery plateau. This suggests that the onset of entanglement-like behavior in rings requires 4-5-fold greater Z w than is required for linear chains. Further, the plateau moduli of RDODT samples are indistinguishable from G N o of the corresponding LDODT (melt or matched-concentration solutions). In entangled linear polymers, the observation that G N o is independent of Z w follows from limitations on lateral fluctuations due to neighboring chains becoming independent of position along a given chain. The present results for RDODT suggest that this holds for sufficiently long endless chains, too. While the RDODT have the same G N o as entangled LDODT, when Z w > 60 the terminal relaxation, if reached at all, of RDODT extends to orders of magnitude lower frequency than an entangled linear polymer of the same Z w . Consequently, the viscosity of RDODT with Z w > 60 increases with Z w much more strongly than the 3.4-power observed for entangled linear polymers. Lastly, these novel polymers, with disulfide-linked backbone and broad relaxation time distribution may prove important in relation to biodegradable elastomers and materials with exceptional low-frequency dissipation, extending at least 12 decades below the onset of the rubbery plateau.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2021

Climatology of Linear Mesoscale Convective System Morphology in the United States based on Random Forests Method

This study uses machine learning methods, specifically the random forest (RF), on a radar-based mesoscale convective system (MCS) tracking dataset to classify the five types of linear MCS morphology in the contiguous United States during the period 2004-2016. The algorithm is trained using radar- and satellite-derived spatial and morphological parameters, and reanalysis environmental information from 5-26yr manually identified nonlinear and five linear MCS modes. The algorithm is then used to automate the classification of linear MCSs over 8 years with high accuracy, providing a systematic, long-term climatology of linear MCSs. Results reveal that nearly 40% of MCSs are classified as linear MCSs, in which half of the linear events belong to the type of system having a leading convective line. The occurrence of linear MCSs shows large annual and seasonal variations. On average, 113 linear MCSs occur annually during the warm season (through March to October), with most of these events clustered from May through August in the central eastern Great Plains. MCS characteristics, including duration, propagation speed, orientation, and system cloud size, have large variability among the different linear modes. The systems having a trailing convective line and the systems having a back-building area of convection typically move more slowly and have higher precipitation rate, and thus have higher potential in producing extreme rainfall and flash flooding. Analysis of the environmental conditions associated with linear MCSs show that the storm-relative flow is of most importance in determining the organization mode of linear MCSs.

Cui, Wenjun↗

DOE OSTI2021

Composite entanglement topology and extensional rheology of symmetric ring-linear polymer blends

Extensive molecular simulations are applied to characterize the equilibrium dynamics, entanglement topology, and nonlinear extensional rheology of symmetric ring-linear polymer blends with systematically varied ring fraction ϕR. Chains with degree of entanglement Z≈14 are mixed to produce 10 well-entangled systems with ϕR varying from neat linear to neat ring melts. Z is large enough that except for very large ϕR, the rings are threaded by multiple linear chains in equilibrium. Primitive path analysis is used to visualize and quantify the structure of the composite ring-linear entanglement network. We measure the quantity of ring-linear threading and linear-linear entanglement as a function of ϕR and identify with simple arguments a ring fraction ϕR≈0.4 where the topological constraints of the composite entanglement network are maximized. These topological analyses are used to rationalize the ϕR-dependence of ring and linear chain dynamics, conformations, and rheology. Simulations of startup uniaxial elongation flows demonstrate the extensional stress overshoot observed in recent filament stretching experiments and characterize how it depends on the blend composition and entanglement topology. The overshoot is driven by an overstretching and recoil of ring polymers due to the convective unthreading of rings from linear chains.

O’Connor, Thomas C.↗

DOE OSTI2022

On the Convergence of Inexact Predictor-Corrector Methods for Linear Programming

Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear system of equations at each iteration. In common applications of linear programming, particularly in machine learning and scientific computing, the size of this linear system can become prohibitively large, requiring the use of iterative solvers, which provide an approximate solution to the linear system. However, approximately solving the linear system at each iteration of an IPM invalidates the theoretical guarantees of common IPM analyses. To remedy this, we theoretically and empirically analyze (slightly modified) predictor-corrector IPMs when using approximate linear solvers: our approach guarantees that, when certain conditions are satisfied, the number of IPM iterations does not increase and that the final solution remains feasible. We also provide practical instantiations of approximate linear solvers that satisfy these conditions for special classes of constraint matrices using randomized linear algebra.

Dexter, Gregory↗

DOE OSTI2026

The Linear Point Standard Ruler with DESI DR1 and DR2 Data

The linear point, a purely geometric feature in the monopole of the two-point correlation function, has been proposed as an alternative standard ruler. Compared to the peak in the correlation function, it is more robust to late-time nonlinear effects at the percent level. In light of improved simulations and high quality data, we revisit the robustness of the linear point and use it as an alternative to template-based fitting approaches typically used in BAO analyses. We present the linear point measurements on galaxy samples from the first and second data releases (DR1 and DR2) of the DESI survey. We convert the linear point into a dimensionless parameter $α_{iso,LP}$, defined as the ratio of the linear point in the fiducial cosmology and the observed value, analogous to the isotropic BAO scaling parameter $α_{iso}$ used in previous BAO measurements. Using the 2nd generation of AbacusSummit mock catalogs, we find that linear point measurements are more precise when calculated in the post-reconstruction regime with 15-60% smaller uncertainties than those pre-reconstruction. We find a systematic shift in the linear point measurements compared against the isotropic BAO measurements in mocks; we attribute this to the isotropic damping parameter responsible for smearing the linear point in the nonlinear regime. We propose a sample-dependent correction that mitigates the impact of late-time nonlinear effects. While this introduces a cosmology dependence in an otherwise model-independent measurement, this is necessary given the sub-percent precision dictated by current cosmological surveys. Comparing $α_{iso,LP}$ with isotropic BAO measurements made on the DESI DR1 and DR2 galaxy samples, we find excellent agreement after applying this correction, particularly post-reconstruction. We discuss future scope regarding cosmological inference with linear point measurements.

Uberoi, N. [Yale U.] (ORCID:0000000275179629)↗

DOE OSTI2021

Jet wake from linearized hydrodynamics

We explore how to improve the hybrid model description of the particles originating from the wake that a jet produced in a heavy ion collision leaves in the droplet of quark-gluon plasma (QGP) through which it propagates, using linearized hydrodynamics on a background Bjorken flow. Jet energy and momentum loss described by the hybrid model become currents sourcing linearized hydrodynamics. By solving the linearized hydrodynamic equations numerically, we investigate the development of the wake in the dynamically evolving droplet of QGP, study the effect of viscosity, scrutinize energy-momentum conservation, and check the validity of the linear approximation. We find that linearized hydrodynamics works better in the viscous case because diffusive modes damp the energy-momentum perturbation produced by the jet. We calculate the distribution of particles produced from the jet wake by using the Cooper-Frye prescription and find that both the transverse momentum spectrum and the distribution of particles in azimuthal angle are similar in shape in linearized hydrodynamics and in the hybrid model. Their normalizations are different because the momentum-rapidity distribution in the linearized hydrodynamics analysis is more spread out, due to sound modes. Since the Bjorken flow has no transverse expansion, we explore the effect of transverse flow by using local boosts to add it into the Cooper-Frye formula. After including the effects of transverse flow in this way, the transverse momentum spectrum becomes harder: more particles with transverse momenta bigger than 2 GeV are produced than in the hybrid model. Although we defer implementing this analysis in a jet Monte Carlo, as would be needed to make quantitative comparisons to data, we gain a qualitative sense of how the jet wake may modify jet observables by computing proxies for two example observables: the lost energy recovered in a cone of varying open angle, and the fragmentation function. We find that linearized hydrodynamics with transverse flow effects added improves the description of the jet wake in the hybrid model in just the way that comparison to data indicates is needed. Our study illuminates a path to improving the description of the wake in the hybrid model, highlighting the need to take into account the effects of both transverse flow and the broadening of the energy-momentum perturbation in spacetime rapidity on particle production.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Threading–Unthreading Transition of Linear-Ring Polymer Blends in Extensional Flow

Adding small amounts of ring polymers to a matrix of their linear counterparts is known to increase the zero-shear-rate viscosity because of linear-ring threading. Uniaxial extensional rheology measurements show that, unlike its pure linear and ring constituents, the blend exhibits an overshoot in the stress growth coefficient. By combining these measurements with ex-situ small-angle neutron scattering and nonequilibrium molecular dynamics simulations, this overshoot is shown here to be driven by a transient threading–unthreading transition of rings embedded within the linear entanglement network. Prior to unthreading, embedded rings deform affinely with the linear entanglement network and produce a measurably stronger elongation of the linear chains in the blend compared to the pure linear melt. Thus, rings uniquely alter the mechanisms of transient elongation in linear polymers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Linear delta systems, hexapod systems, and related methods

A linear delta system includes a support frame, rails mounted to the support frame, linear actuators, each linear actuator configured to translate along a longitudinal length of a respective rail, pairs of parallel rods each coupled to the linear actuators, a platform coupled to a longitudinal end of each of the pairs of parallel rods opposite the respective linear actuator, and an object coupled to the platform. Longitudinal axes of the rails are oriented parallel to each other and lie within a common plane or an uncommon plane. A method of forming a linear delta system includes mounting rails to a support frame, the rails having longitudinal axes that are parallel to each other and lying within a common plane, coupling a linear actuator to each of the rails, coupling a pair of parallel rods to each linear actuator, and coupling a platform to the pairs of parallel rods.

Crawford, Anthony L.↗

DOE OSTI2025

Projection-based multifidelity linear regression for data-scarce applications

Surrogate modeling for systems with high-dimensional quantities of interest remains challenging, particularly when training data are costly to acquire. This work develops multifidelity methods for multiple-input multiple-output linear regression targeting data-limited applications with high-dimensional outputs. Multifidelity methods integrate many inexpensive low-fidelity model evaluations with limited, costly high-fidelity evaluations. We introduce two projection-based multifidelity linear regression approaches with linear and nonlinear features that leverage principal component basis vectors for dimensionality reduction and combine multifidelity data through: (i) a direct data augmentation using low-fidelity data, and (ii) a data augmentation incorporating explicit linear corrections between low-fidelity and high-fidelity data. The data augmentation approaches combine high-fidelity and low-fidelity data into a unified training set and train the linear regression model through weighted least squares with fidelity-specific weights. We introduce a proximity-based weighting scheme with automatic weight selection strategy through cross-validation. Here, the proposed multifidelity linear regression methods are demonstrated on approximating the surface pressure field of a hypersonic vehicle in flight and the temperature field on an aircraft disc braking system. In an ultra low-data regime of no more than twelve high-fidelity samples, multifidelity linear regression achieves approximately 2% – 12% improvement in median accuracy and a higher R 2 score relative to single-fidelity methods at comparable computational cost.

data augmentation↗

DOE OSTI2022

Approximating a linear multiplicative objective in watershed management optimization

Implementing management practices in a cost-efficient manner is critical for regional efforts to reduce the amount of pollutants entering the Chesapeake Bay. We study the problem of selecting a subset of practices that minimizes pollutant load—subject to budgetary and environmental constraints—as simulated in a widely used regulatory watershed model. Mimicking the computation of pollutant load in the regulatory model, we formulate this problem as a continuous optimization model with a linear multiplicative objective function and linear constraints. To lay the groundwork for incorporating additional stakeholder requirements in the future, especially those that would require integer variables, we present and study a continuous linear optimization model that approximates the nonlinear model. The linear model, which requires an exponential number of variables, arises naturally as an alternative model for the same underlying physical process. We examine the theoretical behavior of these optimization models and investigate restrictions of the linear model to handle its large number of variables. Through extensive computational tests on real and randomly generated instances, we demonstrate that the linear model and its restrictions provide optimal solutions close to those of the nonlinear model in practice, despite poor approximation properties in the worst case. We conclude that the linear model—together with our approach to handling its large number of variables—provides a viable framework from which to extend the optimization model to better meet the needs of the Chesapeake Bay watershed management stakeholders.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

A new tubular ironless linear induction motor using non-interrupted winding method

The ironless linear induction motor device can be used for any application which requires a large motion span or rotation restrictedly by the ironless feature due to the strong magnetic field environment. One of the possible applications is ITER diagnostics shutters. The tokamak reactor systems have a severe radiation issue during the operation. The traditional Kapton-insulated wires have significantly lower radiation resistance than an expected large radiation dose at ITER Motion Stark Effect (MSE) shutter location. Furthermore, the traditional single-sided linear induction motor winds the wire to make the N-turn pitch coils independently and then connect them in series to make a one-phase winding. Therefore, it is a big challenge to make so many radiation-protection connectors in such a limited space as inside the vacuum vessel of fusion reactors. The approved mineral-insulated kinds of cables need a large bend radius for the end turns, so the traditional single-sided linear motor with two-layer three-phase windings need to be upgraded to the tubular linear motors. The new proposed tubular ironless linear induction motor can not only overcome the large bend radius issue with the mineral-insulated cables but also allow the motor coils wound continuously around the tubular-shaped stator, forward and backward N times to make a N-turn winding for each phase, in order to resolve the radiation protection issue with the winding connection. The 3D transient Maxwell electromagnetic model with a tubular three-phase linear induction motor has been analyzed. Furthermore, this paper will present the detailed design and winding method of ironless linear induction motor actuators, and results of the 3D transient numerical simulation of the actuator performance.

Ironless↗

DOE OSTI2022

Influence of wind turbine design parameters on linearized physics-based models in OpenFAST

Abstract. While most physics involved in wind energy are nonlinear, linearization of the underlying nonlinear wind system equations is often important for understanding the system response and exploiting well-established methods and tools for analyzing linear systems. Linearized models are important for eigenanalysis (to derive structural natural frequencies, damping ratios, and mode shapes), controls design (based on linear state-space models), etc. In controls co-design, wherein methods often rely on linearized time-domain models of the physics, the physical structure (often called the plant) and controller are designed and optimized concurrently, so it is important to understand how changes to the physical design affect the linearized system. This work summarizes efforts done to understand the impact of design parameter variations in the physical system (e.g., mass, stiffness, geometry, and aerodynamic and hydrodynamic coefficients) on the linearized system using OpenFAST.

17 WIND ENERGY↗

DOE OSTI2026

Multibody for Everybody (M4E) - A Linearization Approach to Enable Frequency Domain Analysis, Time Integration and Control Co-Design

1.1 Background/Objectives: Marine energy represents a promising yet underexploited source of power. To increase the harvested power, significant efforts have been made to improve wave energy converter (WEC) modeling capabilities and optimize power take-off (PTO) performance; however, these efforts have often treated WEC dynamics, PTO design, and controller development sequentially. In contrast, control co-design (CCD) is emerging as a promising strategy to address these issues directly, creating a growing need for fast analysis tools suitable for repeated simulation and parametric studies [1]. To support this need, this work presents the Multibody for Everybody (M4E) [2] linearization module, which employs a symbolic toolbox to provide deeper insight of WEC design parameters. The objective is to demonstrate that a minimal-coordinate linearization of articulated WEC dynamics can provide accurate wave response predictions and substantial computational savings relative to nonlinear time-domain simulation, while preserving compatibility with broader wave-energy analysis workflows, enabling CCD. 1.2 Approach/Activities: The proposed approach linearizes the equations of motion, generated by M4E, in minimal coordinates about a selected operating point and combines the resulting system with frequencydomain hydrodynamic terms to incorporate the reduced mass, damping, stiffness, and forcing operators. The linearized model is used for both impedance-based response amplitude operator (RAO) prediction and rapid regular-wave time integration. The methodology is demonstrated on a single-flap device and a FOSWEC configuration, with linearized M4E responses compared against the corresponding nonlinear M4E simulations and WEC-Sim results. Regular-wave time histories, RAO trends, and runtime differences are assessed. The framework is also compatible with broader wave-energy workflows, including coupling to WecOptTool, although that capability is not the focus of this work [3]. 1.3 Results/Lessons: The linearized M4E model reproduces key regularwave response characteristics such as integration and Response Amplitude over multiple frequencies. This module matches nonlinear M4E and WEC-Sim results while substantially reducing integration cost. Thus, the proposed framework can serve as a rapid analysis layer for articulated WEC design, parameter studies, and controls-oriented workflows. The analysis is most appropriate in the near-equilibrium regime, about the linearization point.

16 TIDAL AND WAVE POWER↗

DOE OSTI2022

Automated Experiments of Local Non–Linear Behavior in Ferroelectric Materials

An automated experiment in multimodal imaging to probe structural, chemical, and functional behaviors in complex materials and elucidate the dominant physical mechanisms that control device function is developed and implemented. Here, the emergence of non-linear electromechanical responses in piezoresponse force microscopy (PFM) is explored. Non-linear responses in PFM can originate from multiple mechanisms, including intrinsic material responses often controlled by domain structure, surface topography that affects the mechanical phenomena at the tip-surface junction, and the presence of surface contaminants. Using an automated experiment to probe the origins of non-linear behavior in ferroelectric lead titanate (PTO) and ferroelectric Al 0.93 B 0.07 N films, it is found that PTO shows asymmetric nonlinear behavior across a/c domain walls and a broadened high nonlinear response region around c/c domain walls. In contrast, for Al 0.93 B 0.07 N, well-poled regions show high linear piezoelectric responses, when paired with low non-linear responses regions that are multidomain show low linear responses and high nonlinear responses. It is shown that formulating dissimilar exploration strategies in deep kernel learning as alternative hypotheses allows for establishing the preponderant physical mechanisms behind the non-linear behaviors, suggesting that automated experiments can potentially discern between competing physical mechanisms. Furthermore, this technique can also be extended to electron, probe, and chemical imaging.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Measuring Topological Constraint Relaxation in Ring-Linear Polymer Blends

Polymers are an effective test bed for studying topological constraints in condensed matter due to a wide array of synthetically available chain topologies. When linear and ring polymers are blended together, emergent rheological properties are observed as the blend can be more viscous than either of the individual components. This emergent behavior arises since ring-linear blends can form long-lived topological constraints as the linear polymers thread the ring polymers. Here, in this work, we demonstrate how the Gauss linking integral can be used to efficiently evaluate the relaxation of topological constraints in ring-linear polymer blends. For majority-linear blends, the relaxation rate of topological constraints depends primarily on reptation of the linear polymers, resulting in the diffusive time τ d,R for rings of length N R blended with linear chains of length N l to scale as τ d,R ~ N$^2_R$N$^{3.4}_L$.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Programmatic Advantages of Linear Equivalent Seismic Models

Underground explosions nonlinearly deform the surrounding earth material and can interact with the free surface to produce spall. However, at typical seismological observation distances the seismic wavefield can be accurately modeled using linear approximations. Although nonlinear algorithms can accurately simulate very near field ground motions, they are computationally expensive and potentially unnecessary for far field wave simulations. Conversely, linearized seismic wave propagation codes are orders of magnitude faster computationally and can accurately simulate the wavefield out to typical observational distances. Thus, devising a means of approximating a nonlinear source in terms of a linear equivalent source would be advantageous both for scenario modeling and for interpretation of seismic source models that are based on linear, far-field approximations. This allows fast linear seismic modeling that still incorporates many features of the nonlinear source mechanics built into the simulation results so that one can have many of the advantages of both types of simulations without the computational cost of the nonlinear computation. In this report we first show the computational advantage of using linear equivalent models, and then discuss how the near-source (within the nonlinear wavefield regime) environment affects linear source equivalents and how well we can fit seismic wavefields derived from nonlinear sources.

58 GEOSCIENCES↗

DOE OSTI2025

Enabling Efficient Sparse Computations using Linear Algebra Aware Compilers

This project developed the LAPIS compiler framework, built on the Multilevel Intermediate Representation (MLIR), to optimize sparse linear algebra operations and support performance portability across diverse architectures. The main innovation of LAPIS is the Kokkos dialect, which allows for lowering codes from a high productivity language to different architectures in an elegant way. The dialect also allows the conversion of lower-level MLIR code to C++ Kokkos code, facilitating the integration of scientific machine learning (SciML) models into applications. To extend LAPIS for distributed memory architectures, a new partition dialect was created to manage the distribution of sparse tensors and express communication patterns for sparse linear algebra operations. This dialect also supports the distributed execution of operators and includes algorithmic optimizations to minimize communication to improve performance. The project also demonstrates that MLIR can enable effective linear algebra-level optimizations, improving performance on different GPUs for both sparse and dense linear algebra kernels. Key applications of LAPIS include sparse linear algebra and graph kernels, TenSQL, a relational database management solution built on GraphBLAS, and the development of subgraph isomorphism and monomorphism kernels, showcasing performance portability. In summary, the LAPIS framework supports productivity, performance, portability, and distributed memory execution, while also enabling linear algebra-level optimizations that are challenging in traditional programming languages, with successful applications ranging from simple sparse linear algebra to complex graph kernels.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Improved quantum algorithms for linear and nonlinear differential equations

We present substantially generalized and improved quantum algorithms over prior work for inhomogeneous linear and nonlinear ordinary differential equations (ODE). Specifically, we show how the norm of the matrix exponential characterizes the run time of quantum algorithms for linear ODEs opening the door to an application to a wider class of linear and nonlinear ODEs. In [1], a quantum algorithm for a certain class of linear ODEs is given, where the matrix involved needs to be diagonalizable. The quantum algorithm for linear ODEs presented here extends to many classes of non-diagonalizable matrices including singular matrices. The algorithm here is also exponentially faster than the bounds derived in [1] for certain classes of diagonalizable matrices. Our linear ODE algorithm is then applied to nonlinear differential equations using Carleman linearization (an approach taken recently by us in [2]). The improvement over that result is two-fold. First, we obtain an exponentially better dependence on error. This kind of logarithmic dependence on error has also been achieved by [3], but only for homogeneous nonlinear equations. Second, the present algorithm can handle any sparse matrix (that models dissipation) if it has a negative log-norm (including non-diagonalizable matrices), whereas [2] and [3] additionally require normality.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗