Results for “probability generating function” — Page 16

DOE OSTI2025

Voltage Probability Density Function Shaping Control Strategy Considering Grid Operational Uncertainties

It is well-known that power systems operation always affected by various uncertainties which make the bus voltage a random process that can be characterized by its probability density function (PDF) at any time instant. In this context, this paper presents a novel PDF-based voltage control framework for power systems. By modeling voltage as a stochastic process, we formulate a stochastic differential equationthat captures grid uncertainties. The associated Fokker-Planck-Kolmogorov equation is derived to describe the evolution of the voltage PDF, which enables the formulation of a PDF-shaping control strategy. To simplify the PDF control formulation, a B-spline neural network is introduced for real-time estimation and regulation of the voltage distribution. The proposed PDF control law updates voltage references for energy storage systems and synchronous generators using real-time PDF measurements and feedback signals. The proposed method is validated on a modified Kundur’s two-area system. Simulation results demonstrate that the controller can significantly improve the voltage stability under stochastic conditions, highlighting its effectiveness in modern inverter-rich grids.

Gui, Yonghao [ORNL] (ORCID:0000000250435534)↗

DOE OSTI2020

A Phenomenological Model for Cavitation

A phenomenological model of cavitation is presented, based on observations that both large relative negative pressures and large negative time derivatives of pressure are required for cavitation onset. We simulated two cavitation experiments to generate cavitation scaling parameters for relative pressure drop and rate of pressure drop. Our results show the model, while simple, is effective at reproducing results from laboratory experiments of cavitation. The parameters were then used in conjunction with a human surrogate computational model to predict, at any position within the head, the probability of intracranial cavitation caused by exposure to a blast event. The results suggest that the magnitude of blast overpressure observed in field data is sufficient to cause intracranial cavitation. Our analysis indicates that the helmeted head, when compared to the unhelmeted head configuration, results in a decrease but not elimination of cavitation exposure. When density functions of cavitation probability versus cumulative brain volume are combined with an injury severity model, the results show helmet efficacy at low and moderate risk levels. However, the convergence of unhelmeted and helmeted probability density functions at high-to-excessive risk thresholds indicates the helmet offers diminishing protection at elevated exposure levels, relative to the unhelmeted baseline. Future investigation and collaboration with neuroscience subject matter experts are needed to contextualize the current computational results. While the present work contributes specific and quantified predictions of intracranial cavitation location and severity, more research is required to apply our results to clinical settings with population-based brain injury subjects and controls. The relationship between our intracranial cavitation predictions with their anticipated clinical sequelae remains a topic in need of exploration.

60 APPLIED LIFE SCIENCES↗

NASA NTRS1986

Three component plasma electron distribution in the intermediate ionized coma of Comet Giacobini-Zinner

The observation of three distinct components of the electron distribution function measured in the intermediate ionized coma (IIC) and plasma tail of Comet Giacobini-Zinner is reported. It is believed that the cold component represents electrons produced close to the comet nucleus by ionization of cometary matter and subsequent cooling by Coulomb collisions. The second component also appears to be composed of electrons produced by photoionization of cometary neutrals, but sufficiently far from the nucleus that the distributions are largely unaffected by Coulomb interactions. The hot component is probably a population of electrons originating in the solar wind. Throughout the IIC, the electrostatic potential of the spacecraft was very low (less than 0.8 eV), implying that ICE generated very little impact-produced plasma during its passage.

Zwickl, R. D.↗

DOE OSTI2023

Oracle-Preserving Latent Flows

A fundamental task in data science is the discovery, description, and identification of any symmetries present in the data. We developed a deep learning methodology for the simultaneous discovery of multiple non-trivial continuous symmetries across an entire labeled dataset. The symmetry transformations and the corresponding generators are modeled with fully connected neural networks trained with a specially constructed loss function, ensuring the desired symmetry properties. The two new elements in this work are the use of a reduced-dimensionality latent space and the generalization to invariant transformations with respect to high-dimensional oracles. The method is demonstrated with several examples on the MNIST digit dataset, where the oracle is provided by the 10-dimensional vector of logits of a trained classifier. We find classes of symmetries that transform each image from the dataset into new synthetic images while conserving the values of the logits. We illustrate these transformations as lines of equal probability (“flows”) in the reduced latent space. These results show that symmetries in the data can be successfully searched for and identified as interpretable non-trivial transformations in the equivalent latent space.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1985

An APL program for the distribution of energy deposition by charged particles passing through thin absorbers

An APL program which numerically evaluates the probability density function (PDF) for the energy deposited in a thin absorber by a charged particle is proposed, with application to the construction, pointing, and control of spacecraft. With this program, the PDF of the restricted energy loss distribution of Watts (1973) is derived, and Vavilov's (1957) distribution is obtained by proper parameter selection. The method is demonstrated with the example of the effect of charged particle induced radiation on the Hubble Space Telescope (HST) pointing accuracy. A Monte Carlo study simulates the photon noise caused by charged particles passing through the photomultiplier tube window, and the stochastic variation of energy loss is introduced into the simulation by generating random energy losses from a power law distribution. The program eliminates annoying loop procedures, and model parameter sensitivity can be studied using the graphical output.

Howell, L. W.↗

NASA NTRSDate not supplied

CLINICAL DECISION SUPPORT: PATH TO FUNCTIONAL REQUIREMENTS

Long-duration, deep-space exploration missions present significant challenges to crew health and performance. These challenges include the individual and combined effects of microgravity, radiation exposure, isolation, limited resources (mass, volume, power, data and crew time), limited options for evacuation and those associated with delayed or constrained communications, all of which demand greater crew autonomy. Specifically, as the communication delays intensify the further we explore space, the unqualified need for Earth-independent medical operations focused on autonomous diagnosis, treatment and prevention will be key to mission continuation and success. To augment the requisite knowledge, skills and abilities (KSAs) of a time-constrained crew operating under stressful conditions, combatting fatigue, and facing a potential medical crisis, a robust clinical decision support system (CDSS) is a probable solution that would facilitate, guide and inform Earth-independent medical operations, while assisting crewmembers through various clinical presentations. The Exploration Medical Capability (ExMC) Element of the Human Research Program (HRP) is expanding the boundaries of space medical systems to advance the care of astronauts on future exploration missions beyond low Earth orbit. ExMC is actively identifying and testing next-generation medical care and crew health maintenance technologies. The Clinical Decision Support (CDS) project addresses gap Medical-701 within the Inflight Medical Conditions risk: “Enhance medical capabilities within an exploration medical system.” Though mass, volume, and power will face increasing constraints, the projected computational capabilities of spacecraft systems will increase exponentially as information technology continues to advance this decade and beyond. Hence, data, software and computational resources will play an essential and synergistic role in maintaining crew health, wellness and performance in deep space missions. The focus of the CDS project is to develop recommended requirements for an in-vehicle CDSS that acts as a ‘virtual assistant’ for delivering optimal health, performance and medical care during exploration missions. The CDSS is envisioned as an integrated, software-based tool deployed on a laptop computer or handheld device. The CDSS will assist the crew and ground support when interacting with knowledge/databases (e.g. records, pharmacy, schedule), instrumentation (e.g. imaging, physiological monitoring devices), and habitat (e.g. wellness system, task performance system) and vehicle systems (e.g. environmental system, communication system). In addition, the human interface will employ a context-based approach that accounts for the crew’s situation. Thus, extraneous and clinically/operationally non-relevant information are reduced to avoid an increase in cognitive load. The framework of an ideal spaceflight CDSS is to include core and advanced analytical features that incorporate work from collaborators yet maintain a flexible platform for integrating new technology in the future. In fiscal year 2021 (FY21), the CDS project identified requirements through two primary mechanisms: (i) the development of software implementation prototypes and (ii) the application of systems engineering processes. The CDS project developed and tested a series of increasingly complex system prototypes that were based on use cases derived from the CDSS concept of operations (ConOps). These software implementations yielded insights on CDSS functionality as well as lessons learned that provided the initial requirements for CDSS capability. By applying a systems engineering (SE) approach, medical scenarios provided in the ConOps and the use cases for software implementation underwent functional decomposition to identify CDSS functionality. Also, systems-based modeling language (SysML) tools such as activity diagrams were developed from the same ConOps and use cases to identify CDSS functionality. The lessons learned from software implementation defined both specific requirements and broad areas of requirements. Within these defined broad requirement areas, further analysis of the SE products identified specific capability that resulted in the final functional requirements. In summary, the software prototypes, functional decomposition of the ConOps and use cases, and SysML diagrams provided the basis for the CDSS requirements developed in FY21. In the upcoming year, these requirements will be refined for their final ExMC baseline review in latter FY22.

clinical decision support↗

NASA NTRSDate not supplied

Clinical Decision Support: Path to Functional Requirements

Long-duration, deep-space exploration missions present significant challenges to crew health and performance. These challenges include the individual and combined effects of microgravity, radiation exposure, isolation, limited resources (mass, volume, power, data and crew time), limited options for evacuation and those associated with delayed or constrained communications, all of which demand greater crew autonomy. Specifically, as the communication delays intensify the further we explore space, the unqualified need for Earth-independent medical operations focused on autonomous diagnosis, treatment and prevention will be key to mission continuation and success. To augment the requisite knowledge, skills and abilities (KSAs) of a time-constrained crew operating under stressful conditions, combatting fatigue, and facing a potential medical crisis, a robust clinical decision support system (CDSS) is a probable solution that would facilitate, guide and inform Earth-independent medical operations, while assisting crewmembers through various clinical presentations. The Exploration Medical Capability (ExMC) Element of the Human Research Program (HRP) is expanding the boundaries of space medical systems to advance the care of astronauts on future exploration missions beyond low Earth orbit. ExMC is actively identifying and testing next-generation medical care and crew health maintenance technologies. The Clinical Decision Support (CDS) project addresses gap Medical-701 within the Inflight Medical Conditions risk: “Enhance medical capabilities within an exploration medical system.” Though mass, volume, and power will face increasing constraints, the projected computational capabilities of spacecraft systems will increase exponentially as information technology continues to advance this decade and beyond. Hence, data, software and computational resources will play an essential and synergistic role in maintaining crew health, wellness and performance in deep space missions. The focus of the CDS project is to develop recommended requirements for an in-vehicle CDSS that acts as a ‘virtual assistant’ for delivering optimal health, performance and medical care during exploration missions. The CDSS is envisioned as an integrated, software-based tool deployed on a laptop computer or handheld device. The CDSS will assist the crew and ground support when interacting with knowledge/databases (e.g. records, pharmacy, schedule), instrumentation (e.g. imaging, physiological monitoring devices), and habitat (e.g. wellness system, task performance system) and vehicle systems (e.g. environmental system, communication system). In addition, the human interface will employ a context-based approach that accounts for the crew’s situation. Thus, extraneous and clinically/operationally non-relevant information are reduced to avoid an increase in cognitive load. The framework of an ideal spaceflight CDSS is to include core and advanced analytical features that incorporate work from collaborators yet maintain a flexible platform for integrating new technology in the future. In fiscal year 2021 (FY21), the CDS project identified requirements through two primary mechanisms: (i) the development of software implementation prototypes and (ii) the application of systems engineering processes. The CDS project developed and tested a series of increasingly complex system prototypes that were based on use cases derived from the CDSS concept of operations (ConOps). These software implementations yielded insights on CDSS functionality as well as lessons learned that provided the initial requirements for CDSS capability. By applying a systems engineering (SE) approach, medical scenarios provided in the ConOps and the use cases for software implementation underwent functional decomposition to identify CDSS functionality. Also, systems-based modeling language (SysML) tools such as activity diagrams were developed from the same ConOps and use cases to identify CDSS functionality. The lessons learned from software implementation defined both specific requirements and broad areas of requirements. Within these defined broad requirement areas, further analysis of the SE products identified specific capability that resulted in the final functional requirements. In summary, the software prototypes, functional decomposition of the ConOps and use cases, and SysML diagrams provided the basis for the CDSS requirements developed in FY21. In the upcoming year, these requirements will be refined for their final ExMC baseline review in latter FY22.

Clinical decision support↗

NASA NTRS1973

Mars - Crustal structure inferred from Bouguer gravity anomalies.

Bouguer gravity has been computed for the equatorial region of Mars by differencing free air gravity and the gravity predicted from topographic variations. The free air gravity was generated from an eighth-order set of spherical harmonic coefficients. The gravity from topographic variations was generated by integrating a two-dimensional Green's function over each contour level. The Bouguer gravity indicates crustal inhomogeneities on Mars that are postulated to be variations in crustal thickness. The Tharsis ridge is a region of thick continental type crust. The gravity data, structural patterns, topography, and surface geology of this region lead to the interpretation of the Tharsis topographic high as a broad crustal upwarp possibly associated with local formation of lower-density crustal material and subsequent rise of a thicker crust. The Amazonis region is one of several basins of relatively thin crust, analogous to terrestrial ocean basins. The Libya and Hellas basins, which are probable impact features, are also underlain by thin crust and are possible regions of mantle upwelling.

Phillips, R. J.↗

DOE OSTI2025

Superspin renormalization and slow relaxation in random spin systems

We develop an excited-state real-space renormalization group (RSRG-X) formalism to describe the dynamics of conserved densities in randomly interacting spin-12 systems. Our formalism is suitable for systems with U(1) and Z2 symmetries, and we apply it to chains of randomly positioned spins with dipolar XX+YY interactions, as arise in Rydberg quantum simulators and other platforms. The formalism generates a sequence of effective Hamiltonians that provide approximate descriptions for dynamics on successively smaller energy scales. These effective Hamiltonians involve “superspins”: two-level collective degrees of freedom constructed from (anti)aligned microscopic spins. Conserved densities can then be understood as relaxing via coherent collective spin flips. For the well-studied simpler case of randomly interacting nearest-neighbor XX+YY chains, the superspins reduce to single spins. Our formalism also leads to a numerical method capable of simulating the dynamics up to an otherwise inaccessible combination of large system size and late time. Focusing on disorder-averaged infinite-temperature autocorrelation functions, in particular the spin survival probability Sp¯(t), we demonstrate quantitative agreement between our algorithm and exact diagonalization (ED) at low but nonzero frequencies. Such agreement holds for chains with nearest-neighbor, next-nearest-neighbor, and long-range dipolar interactions. Our results indicate decay of Sp¯(t) slower than any power law and feature no significant deviation from the ∼1/ln2(t) asymptote expected from the infinite-randomness fixed-point of the nearest-neighbor model. We also apply the RSRG-X formalism to two-dimensional long-range systems of moderate size and find slow late-time decay of Sp¯(t).

Zhao, Yi J↗

NASA NTRS1993

The compositional structure and the effects of exothermicity in a nonpremixed planar jet flame

Results are presented of direct numerical simulation (DNS) of a randomly perturbed compressible, spatially developing two-dimensional planar jet under the influence of a finite rate chemical reaction of the type F + O yields product. The objectives of the simulations are to assess the compositional structure of the flame and to determine the influence of reaction exothermicity by means of statistical sampling of the DNS generated data. It is shown that even with this idealized kinetics model the simulated results exhibit features in accord with experimental data. These results indicate that the Damkohler number is an important parameter in determining the statistical composition of the reacting field and that the results are not very sensitive to the mechanism by which this parameter is varied. It is demonstrated that as the intensity of mixing is increased and the effect of finite rate chemistry is more pronounced, the magnitudes of the ensemble mean and variance of the product mass fraction decrease and those of the reactants' mass fraction increase. Also, at higher mixing rates the joint probability density functions of the reactants' mass fractions shift towards higher values within the composition domain, indicating a lower reactedness.

Steinberger, C. J.↗

NASA NTRS1986

Combustion characteristics in the transition region of liquid fuel sprays

A number of important effects have been observed in the droplet size transition region in spray combustion systems. In this region, where the mechanism of flame propagation is transformed from diffusive to premixed dominated combustion, the following effects have been observed: (1) maxima in burning velocity; (2) extension of flammability limits; (3) minima in ignition energy; and (4) minima in NOx formation. A monodisperse aerosol generator has been used to form and deliver a well controlled liquid fuel spray to the combustion test section where measurements of ignition energy have been made. The ignition studies were performed on monodisperse n-heptane sprays at atmospheric pressure over a range of equivalence ratios and droplet diameters. A capacitive discharge spark ignition system was used as the ignition source, providing independent control of spark energy and duration. Preliminary measurements were made to optimize spark duration and spark gap, optimum conditions being those at which the maximum frequency or probability of ignition was observed. Using the optimum electrode spacing and spark duration, the frequency of ignition was determined as a function of spark energy for three overall equivalence ratios (0.6, 0.8, and 1.0) and for initial droplet diameters of 25, 40, 50, 60, and 70 micro m.

Cernansky, N. P.↗

NASA NTRS2015

Directed Design of Experiments for Validating Probability of Detection Capability of NDE Systems (DOEPOD)

Directed Design of Experiments for Validating Probability of Detection Capability of NDE Systems (DOEPOD) Manual v.1.2 The capability of an inspection system is established by applications of various methodologies to determine the probability of detection (POD). One accepted metric of an adequate inspection system is that there is 95% confidence that the POD is greater than 90% (90/95 POD). Design of experiments for validating probability of detection capability of nondestructive evaluation (NDE) systems (DOEPOD) is a methodology that is implemented via software to serve as a diagnostic tool providing detailed analysis of POD test data, guidance on establishing data distribution requirements, and resolving test issues. DOEPOD demands utilization of observance of occurrences. The DOEPOD capability has been developed to provide an efficient and accurate methodology that yields observed POD and confidence bounds for both Hit-Miss or signal amplitude testing. DOEPOD does not assume prescribed POD logarithmic or similar functions with assumed adequacy over a wide range of flaw sizes and inspection system technologies, so that multi-parameter curve fitting or model optimization approaches to generate a POD curve are not required. DOEPOD applications for supporting inspector qualifications is included.

Generazio, Edward R.↗

NASA NTRSDate not supplied

Reversibly Assembled Microparticles for Sustained Applications on the Moon and Mars

A sustained presence in any extra-terrestrial environment will require the capability to generate materials, goods, and ultimately vehicles, construction supplies and habitats to be tenable. As an example, NASA, in collaboration with Made In Space, Inc., recently reported the results of extensive research toward enabling3D printing in space. The extensive characterization and comparison of 3D printed articles suggested that, overall, articles generated in the International Space Station microgravity environment were comparable to those generated on Earth. The benefit of in-space manufacturing can be increased through utilization of recyclable materials. A recent analysis of a hypothetical 1,100 day round trip mission to Mars determined that significant mass savings and increase in mission probability of success could be achieved through in-space manufacturing with recyclable materials. NASA’s project ESPUR (Enabling Sustained Presence Using Recyclables), through support from NASA Langley’s Innovative Research and Development Fund, is investigating novel, polymer-coated, epoxy microparticle systems as an enabling technology to realize in-space manufacturing using recyclable feedstocks. Building from previously reported results, further progress toward synthesis of the polymer coating containing click chemical functionalities will be described here. Finite elemental analysis (FEA) has been utilized, in light of scale-free/small world considerations in an effort to identify compositions most likely to yield robust macroscopic geometries. Initial results will be described here. Finally, potential mass savings and life cycle of this recyclable materials technology will be discussed.

Click Chemistry↗

NASA NTRS1980

Aerodynamic aspects of shock containing jet plumes

Aerodynamic and acoustic measurements of shock-free and shock-containing plumes were acquired for several supersonic free-jet model nozzles. The purpose was to investigate important features of the broadband shock noise generation process. The aerodynamic measurements include the variation of shock cell spacing and strength as a function of nozzle pressure ratio, and longitudinal turbulent-mass-flux axial development as determined by a hot-film probe. In addition, correlations of the hot-film probe with a near-field microphone were obtained. These measurements provide useful information concerning the relation of peak shock noise frequency and level with variations in shock cell spacing and strength. In general, it is shown that a distinction must be made between plumes containing weak and strong imbedded shocks. Strong shocks diminish the level of emitted shock noise and influence the behavior of the jet mixing noise process. The probable location and spectral content for the shock-shear layer interaction mechanism is indicated by the correlations. Numerical inviscid plume comparisons with experimental data are also included.

Seiner, J. M.↗

NASA NTRS2016

Precision Landing and Hazard Avoidance Doman

The Precision Landing and Hazard Avoidance (PL&HA) domain addresses the development, integration, testing, and spaceflight infusion of sensing, processing, and GN&C functions critical to the success and safety of future human and robotic exploration missions. PL&HA sensors also have applications to other mission events, such as rendezvous and docking. Autonomous PL&HA builds upon the core GN&C capabilities developed to enable soft, controlled landings on the Moon, Mars, and other solar system bodies. Through the addition of a Terrain Relative Navigation (TRN) function, precision landing within tens of meters of a map-based target is possible. The addition of a 3-D terrain mapping lidar sensor improves the probability of a safe landing via autonomous, real-time Hazard Detection and Avoidance (HDA). PL&HA significantly improves the probability of mission success and enhances access to sites of scientific interest located in challenging terrain. PL&HA can also utilize external navigation aids, such as navigation satellites and surface beacons. Advanced Lidar Sensors High precision ranging, velocimetry, and 3-D terrain mapping Terrain Relative Navigation (TRN) TRN compares onboard reconnaissance data with real-time terrain imaging data to update the S/C position estimate Hazard Detection and Avoidance (HDA) Generates a high-resolution, 3-D terrain map in real-time during the approach trajectory to identify safe landing targets Inertial Navigation During Terminal Descent High precision surface relative sensors enable accurate inertial navigation during terminal descent and a tightly controlled touchdown within meters of the selected safe landing target.

Robertson, Edward A.↗

DOE OSTI2026

High-throughput validation of phase formability and simulation accuracy of Cantor alloys

High-throughput methods enable accelerated discovery of novel materials in complex systems such as high-entropy alloys, which exhibit intricate phase stability across vast compositional spaces. Computational approaches, including Density Functional Theory (DFT) and calculation of phase diagrams (CALPHAD), facilitate screening of phase formability as a function of composition and temperature. However, the integration of computational predictions with experimental validation remains challenging in high-throughput studies. In this work, we introduce a quantitative confidence metric to assess the agreement between predictions and experimental observations, providing a quantitative measure of the confidence of machine learning models trained on either DFT or CALPHAD input in accounting for experimental evidence. The experimental dataset was generated via high-throughput in-situ synchrotron X-ray diffraction on compositionally varied FeNiMnCr alloy libraries, heated from room temperature to ~1000 °C. Agreement between the observed and predicted phases was evaluated using either temperature-independent phase classification or a model that incorporates a temperature-dependent probability of phase formation. This integrated approach demonstrates where strong overall agreement between computation and experiment exists, while also identifying key discrepancies, particularly in FCC/BCC predictions at Mn-rich regions to inform future model refinement.

36 - MATERIALS SCIENCE↗

DOE OSTI2024

Kinetic Study of Polyvinyl Chloride Pyrolysis with Characterization of Dehydrochlorinated PVC

In this paper, we study the kinetics of polyvinyl chloride (PVC) decomposition using a combination of experimental and computational approaches. Here, we develop a simplified kinetic model that contains only two steps: dehydrochlorination of PVC and further decomposition of the PVC residue. The model is consistent with density functional theory (DFT) calculations and experimental data. Dehydrochlorination is an autocatalytic reaction that starts with a tertiary chloride (Cl) and generates hydrogen chloride (HCl) and benzene as the main products. Benzene and HCl formation rates showed similar trends, indicating that HCl likely catalyzes a homolytic carbon-carbon (C-C) bond cleavage, which gives rise to benzene and an aliphatic fragment. We characterized the structure of dehydrochlorinated PVC (PVC residue) by using thermal gravimetric analysis (TGA), Fourier-transform infrared spectroscopy (FTIR), and nuclear magnetic resonance spectroscopy (NMR). FTIR and NMR results indicate that the PVC residue contains 20% quaternary carbon content, indicating a high concentration of cross-linked molecules. We predict that the most probable structure in the cross-linked centers of the PVC residue is cyclohexadiene, which is supported by DFT calculations, FTIR, and NMR.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1985

Interactions between large space power systems and low-Earth-orbit plasmas

There is a growing tendency to plan space missions that will incorporate very large space power systems. These space power systems must function in the space plasma environment, which can impose operational limitations. As the power output increases, the operating voltage also must increase and this voltage, exposed at solar array interconnects, interacts with the local plasma. The implications of such interactions are considered. The available laboratory data for biased array segment tests are reviewed to demonstrate the basic interactions considered. A data set for a floating high voltage array test was used to generate approximate relationships for positive and negative current collection from plasmas. These relationships were applied to a hypothetical 100 kW power system operating in a 400 km, near equatorial orbit. It was found that discharges from the negative regions of the array are the most probable limiting factor in array operation.

Stevens, N. J.↗