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At least 235 records · Page 13

Rotating stall investigation of 0.72 hub-tip ratio single-stage compressor

The rotating stall characteristics of a 0.72 hub-tip ratio, single-stage compressor were investigated. The stage was a 14-inch-diameter replica of the fourth stage of an experimental multistage compressor. No similarity existed between the frequency and propagation rate of the stall patterns observed in the single-stage replica and those observed in the multistage compressor after the fourth stage. A fatigue failure of the rotor blades occurred during the testing which was attributed to a resonance between the stall frequency and the natural bending frequency of the blades.

Graham, Robert W↗

Electron and Light Microscopy Techniques Suitable for Studying Fatigue Damage in a Crystallized Glass Ceramic

The crystals of Pyroceram are randomly oriented and highly reflective so that standard microscopy techniques are not satisfactory for studying this material. Standard replicating procedures proved difficult to use. New microscopy techniques and procedures have therefore been developed. A method for locating, orienting, and identifying specific areas to be viewed with an electron microscope is described. This method not require any special equipment. Plastic replicas were found to be unsatisfactory because of their tendency to adhere to Pryoceram. This caused them to tear when released or resulted in artifacts. Preshadowed silicon monoxide replicas were satisfactory but required a releasing agent. A method of depositing the releasing agent is described. To polish specimens without evidence of fire-polishing, it was found necessary to use a vibratory polishing technique. Chrome oxide was used as the abrasive and either water or kerosene as the lubricant. Vibratory polishing is extremely slow, but surfaces so polished show no evidence of fire polishing, even when examined by electron microscopy. The most satisfactory etching process used for Pyroceram 9608 consisted of a primary etch of 5 milliliters of hydrochloric acid (concentrated), 5 milliliters of hydrogen fluoride (45 percent), and 45 milliliters of water, and a secondary etch with methyl alcohol replacing the water. Best results were obtained with total etching times from 25 to 30 seconds. Staining of the Pyroceram surface with a Sanford's marker was found to be an expedient way to reduce the glare of reflected light.

Harrell, Shelley↗

Physical and Optical/Radiative Characteristics of Aerosol and Cloud Particles in Tropical Cirrus: Importance in Radiation Balance

Whether cirrus clouds heat or cool the Earth-atmosphere system depends on the relative importance of the cloud shortwave albedo effect and the cloud thermal greenhouse effect. Both are determined by the distribution of ice condensate with cloud particle size. The microphysics instrument package flown aboard the NASA DC-8 in TOGA/COARE included an ice crystal replicator, a 2D Greyscale Cloud Particle Probe and a Forward Scattering Spectrometer Aerosol Probe. In combination, the electro-optical instruments permitted particle size measurements between 0.5 micrometer and 2.6 millimeter diameter. Ice crystal replicas were used to validate signals from the electrooptical instruments. Both optical and scanning electron microscopy were utilized to analyze aerosol and ice particle replicas between 0.1 micrometer and several 100 micrometer diameter. In first approximation, the combined aerosol-cloud particle spectrum in several clouds followed a power law N alpha D(sup -2.5). Thus, large cloud particles carried most of the condensate mass, while small cloud and aerosol particles determined the surface area. The mechanism of formation of small particles is growth of (hygroscopic, possibly ocean-derived) aerosol particles along the Kohler curves. The concentration of small particles is higher and less variable in space and time, and their tropospheric residence time is longer, than those of large cloud particles because of lower sedimentation velocities. Small particles shift effective cloud particle radii to sizes much smaller than the mean diameter of the cloud particles. This causes an increase in shortwave reflectivity and IR emissivity, and a decrease in transmissivity. Occasionally, the cloud reflectivity increased with altitude (decreasing temperature) stronger than did cloud emissivity, yielding enhanced radiative cooling at higher altitudes. Thus, cirrus produced by deep convection in the tropics may be critical in controlling processes whereby energy from warm tropical oceans is injected to different levels in the atmosphere to subsequently influence not only tropical but mid-latitude climate.

Pueschel, R. F.↗

Study of Lightweight Ni-Co Alloy Mirrors Obtained by Electroforming Techniques

One contribution in reducing the costs of optics in space can be provided by production of ultralight mirrors. The decrease in the weight of the primary mirror of a telescope is anticipated to lead to the possibility of increasing the size of the telescopes, therefore increasing the amount and distance from which information is received. An electroplating process of ultralight replica mirrors from nickel sulfamate solution will be described. Based on an experimental setup with cylindrical symmetry, flat mirrors with a diameter of 7 inches and thickness of 1.5 mm are made from a Ni-Co alloy. The composition of the resulting deposit is analyzed using Rutherford Backscattering Spectrometry (RBS) and Proton Induced X-ray Emission (PIXE). In order to resolve Ni and Co, 10 MeV nitrogen ions are used as projectiles in the RBS measurements. Solution parameters monitored during the deposition process using optical absorption and polarography will be correlated with the final concentration of Ni and Co in the deposit. Bath parameters like temperature, current density, agitation level and acidity are chosen at certain values and maintained constant from one sample to another throughout the deposition process. The purpose of the experiment is to obtain mirrors with near zero stress, and predetermined composition and hardness. This study is an intermediate step in obtaining through the same process, but with a larger scale setup, ultralight large aperture replica mirrors.

Jones, Ruth↗

Joint Carrier-Phase Synchronization and LDPC Decoding

A method has been proposed to increase the degree of synchronization of a radio receiver with the phase of a suppressed carrier signal modulated with a binary- phase-shift-keying (BPSK) or quaternary- phase-shift-keying (QPSK) signal representing a low-density parity-check (LDPC) code. This method is an extended version of the method described in Using LDPC Code Constraints to Aid Recovery of Symbol Timing (NPO-43112), NASA Tech Briefs, Vol. 32, No. 10 (October 2008), page 54. Both methods and the receiver architectures in which they would be implemented belong to a class of timing- recovery methods and corresponding receiver architectures characterized as pilotless in that they do not require transmission and reception of pilot signals. The proposed method calls for the use of what is known in the art as soft decision feedback to remove the modulation from a replica of the incoming signal prior to feeding this replica to a phase-locked loop (PLL) or other carrier-tracking stage in the receiver. Soft decision feedback refers to suitably processed versions of intermediate results of iterative computations involved in the LDPC decoding process. Unlike a related prior method in which hard decision feedback (the final sequence of decoded symbols) is used to remove the modulation, the proposed method does not require estimation of the decoder error probability. In a basic digital implementation of the proposed method, the incoming signal (having carrier phase theta theta (sub c) plus noise would first be converted to inphase (I) and quadrature (Q) baseband signals by mixing it with I and Q signals at the carrier frequency [wc/(2 pi)] generated by a local oscillator. The resulting demodulated signals would be processed through one-symbol-period integrate and- dump filters, the outputs of which would be sampled and held, then multiplied by a soft-decision version of the baseband modulated signal. The resulting I and Q products consist of terms proportional to the cosine and sine of the carrier phase cc as well as correlated noise components. These products would be fed as inputs to a digital PLL that would include a number-controlled oscillator (NCO), which provides an estimate of the carrier phase, theta(sub c).

Simon, Marvin↗

Gratings Fabricated on Flat Surfaces and Reproduced on Non-Flat Substrates

A method has been developed for fabricating gratings on flat substrates, and then reproducing the groove pattern on a curved (concave or convex) substrate and a corresponding grating device. First, surface relief diffraction grating grooves are formed on flat substrates. For example, they may be fabricated using photolithography and reactive ion etching, maskless lithography, holography, or mechanical ruling. Then, an imprint of the grating is made on a deformable substrate, such as plastic, polymer, or other materials using thermoforming, hot or cold embossing, or other methods. Interim stamps using electroforming, or other methods, may be produced for the imprinting process or if the same polarity of the grating image is required. The imprinted, deformable substrate is then attached to a curved, rigid substrate using epoxy or other suitable adhesives. The imprinted surface is facing away from the curved rigid substrate. As an alternative fabrication method, after grating is imprinted on the deformable substrate as described above, the grating may be coated with thin conformal conductive layer (for example, using vacuum deposition of gold). Then the membrane may be mounted over an opening in a pressured vessel in a manner of a membrane on a drum, grating side out. The pressure inside of the vessel may be changed with respect to the ambient pressure to produce concave or convex membrane surface. The shape of the opening may control the type of the surface curvature (for example, a circular opening would create spherical surface, oval opening would create toroidal surface, etc.). After that, well-known electroforming methods may be used to create a replica of the grating on the concave or convex membrane. For example, the pressure vessel assembly may be submerged into an electro-forming solution and negative electric potential applied to the metal coated membrane using an insulated wire. Positive electric potential may be then applied to a nickel or other metal plate submerged into the same solution. Metal ions would transfer from the plate through the solution into the membrane, producing high fidelity metal replica of the grating on the membrane. In one variation, an adhesive may be deposited on the deformable substrate, and then cured without touching the rigid, curved substrate. Edges of the deformable substrate may be attached to the rigid substrate to ensure uniform deformation of the deformable substrate. The assembly may be performed in vacuum, and then taken out to atmospheric pressure conditions to ensure that no air is trapped between the deformable and rigid substrates. Alternatively, a rigid surface with complementary curvature to the rigid substrate may be used to ensure uniform adhesion of the deformable substrate to the rigid substrate. Liquid may be applied to the surface of the deformable substrate to uniformly distribute pressure across its surface during the curing or hardening of the adhesive, or the film may be pressed into the surface using a deformable object or surface. After the attachment is complete, the grooves may be coated with reflective or dielectric layers to improve diffraction efficiency.

Content, David↗

Modified Penning-Malmberg Trap for Storing Antiprotons

A modified Penning-Malmberg trap that could store a small cloud of antiprotons for a relatively long time (weeks) has been developed. This trap is intended for use in research on the feasibility of contemplated future matter/antimatter-annihilation systems as propulsion sources for spacecraft on long missions. This trap is also of interest in its own right as a means of storing and manipulating antiprotons for terrestrial scientific experimentation. The use of Penning-Malmberg traps to store antiprotons is not new. What is new here is the modified trap design, which utilizes state-of-the-art radiofrequency (RF) techniques, including ones that, heretofore, have been used in radio-communication applications but not in iontrap applications. A basic Penning-Malmberg trap includes an evacuated round tube that contains or is surrounded by three or more collinear tube electrodes. A steady axial magnetic field that reaches a maximum at the geometric center of the tube is applied by an external source, and DC bias voltages that give rise to an electrostatic potential that reaches a minimum at the center are applied to the electrodes. The combination of electric and magnetic fields confines the charged particles (ions or electrons) for which it was designed to a prolate spheroidal central region. However, geometric misalignments and the diffusive cooling process prevent the steady fields of a basic Penning- Malmberg trap from confining the particles indefinitely. In the modified Penning-Malmberg trap, the loss of antiprotons is reduced or eliminated by use of a "rotating-wall" RF stabilization scheme that also heats the antiproton cloud to minimize loss by matter/antimatter annihilation. The scheme involves the superposition of a quadrupole electric field that rotates about the cylindrical axis at a suitably chosen radio frequency. The modified Penning-Malmberg trap (see Figure 1) includes several collinear sets of electrodes inside a tubular vacuum chamber. Each set comprises either a single metal tube or else a tube that is segmented into four electrodes that subtend equal angles about the cylindrical axis. The output of an RF signal generator is fed through a 90 hybrid coupler and then through two baluns to generate four replicas of the signal at relative phase shifts of 0 , 90 , 180 , and 270 (see Figure 2). These signal replicas are fed through 6-dB directional couplers, then via coaxial cables to the vacuum chamber. The signal is then routed to a phase cancellation network, which filters out the drive signal with the difference representing the plasma interaction. Inside the vacuum chamber, twisted-pair wires feed the signals from the coaxial cables to the four electrodes of each segmented electrode tube.

Sims, William H.↗

Tunable Optical True-Time Delay Devices Would Exploit EIT

Tunable optical true-time delay devices that would exploit electromagnetically induced transparency (EIT) have been proposed. Relative to prior true-time delay devices (for example, devices based on ferroelectric and ferromagnetic materials) and electronically controlled phase shifters, the proposed devices would offer much greater bandwidths. In a typical envisioned application, an optical pulse would be modulated with an ultra-wideband radio-frequency (RF) signal that would convey the information that one seeks to communicate, and it would be required to couple differently delayed replicas of the RF signal to the radiating elements of a phased-array antenna. One or more of the proposed devices would be used to impose the delays and/or generate the delayed replicas of the RF-modulated optical pulse. The beam radiated or received by the antenna would be steered by use of a microprocessor-based control system that would adjust operational parameters of the devices to tune the delays to the required values. EIT is a nonlinear quantum optical interference effect that enables the propagation of light through an initially opaque medium. A suitable medium must have, among other properties, three quantum states (see Figure 1): an excited state (state 3), an upper ground state (state 2), and a lower ground state (state 1). These three states must form a closed system that exhibits no decays to other states in the presence of either or both of two laser beams: (1) a probe beam having the wavelength corresponding to the photon energy equal to the energy difference between states 3 and 1; and (2) a coupling beam having the wavelength corresponding to the photon energy equal to the energy difference between states 3 and 2. The probe beam is the one that is pulsed and modulated with an RF signal.

Kulikov, Igor↗

Efficient Processing of Data for Locating Lightning Strikes

Two algorithms have been devised to increase the efficiency of processing of data in lightning detection and ranging (LDAR) systems so as to enable the accurate location of lightning strikes in real time. In LDAR, the location of a lightning strike is calculated by solving equations for the differences among the times of arrival (DTOAs) of the lightning signals at multiple antennas as functions of the locations of the antennas and the speed of light. The most difficult part of the problem is computing the DTOAs from digitized versions of the signals received by the various antennas. One way (a time-domain approach) to determine the DTOAs is to compute cross-correlations among variously differentially delayed replicas of the digitized signals and to select, as the DTOAs, those differential delays that yield the maximum correlations. Another way (a frequency-domain approach) to determine the DTOAs involves the computation of cross-correlations among Fourier transforms of variously differentially phased replicas of the digitized signals, along with utilization of the relationship among phase difference, time delay, and frequency.

Medelius, Pedro J.↗

Enabling High-Contrast Imaging of Binary Stars With the Roman Space Telescope Coronagraph Instrument

A large fraction of Sun-like stars is contained in binary systems, in fact within 10 pc there are 67 FGK stars, out of which 42 belong to a multi-star system, and 28 have companion leak that is greater than 1e-9 contrast, assuming typical Hubble-quality space optics. Currently, those binary stars are not included in the Roman Space Telescope Coronagraph Instrument target list, but they could be observed if high-contrast imaging around binary star systems using Roman was possible. The Multi-Star Wavefront Control (MSWC) algorithm can be used to suppress companion star leakage. If the targets have angular separations larger than the Nyquist controllable region of the Deformable Mirror, MSWC must operate in its Super-Nyquist (SN) mode. This mode requires a target star replica within the SN region in order to provide the ability to null speckles at SN angular separations. For the case of Roman, more than half of the targets that can be observed using MSWC, including Alpha Centauri, have angular separations larger than the Nyquist controllable region of the 48x48 actuator Deformable Mirror (DM) to be used. In this paper, we describe how super-Nyquist MSWC can be implemented in Roman CGI adding a mild grating on a replica of the Wide-field Shaped Pupil mask, which would use a spare space in the Shaped Pupil Active Mechanism. We present the feasibility analysis, simulation results, and discuss the latest results on MSWC experiment from three different laboratories at NASA Ames, the Jet Propulsion Laboratory, and the Subaru telescope.

Prada, Camilo Mejia↗

Enabling Interoperability in Earth System Digital Twins (ESDT): Integrating Observations, Models, and AI for Actionable Insights Through NASA'S Intelligent Systems Technology Program

NASA’s Intelligent Systems Technology Program (IST) is driving a paradigm shift in Earth science through the development of Earth System Digital Twins (ESDT). These integrated information systems create a dynamic "digital replica" of the Earth by harmonizing continuous, multi-source observations with high-fidelity models and state-of-the-art artificial intelligence (AI) that enable “What now?”, “What next?”, and “What if?” scenario building. These scenarios are reflected in NASA IST’s series of ESDTs, from the Coastal Zone Digital Twin that integrates complex data on the current state of the Chesapeake Bay to the Terrestrial Environmental Rapid-Replication and Assimilation Hydrometeorological (TerraHydro) AI-based ESDT that forecasts water movement across Earth’s surface, to the Agriculture Land Information System (AgLIS) which can be used to assess optimal planting dates and crop yield estimates. By bridging the gap between vast data archives and actionable insights, these projects enable a system-of-systems approach to understanding complex, interacting Earth processes. This poster will highlight recent innovations and future directions from NASA’s ESDT initiatives: Continuous Data Assimilation & Multi-Source Fusion. A core requirement of the ESDT work is the transition from static models to dynamic "living" replicas. This involves creating frameworks for the continual assimilation of near-real-time data from uncoordinated, heterogeneous sources, including satellite observations and airborne assets, and ground-based Internet of Things (IoT) sensors. These systems link design, operational status, and environmental data, ensuring the digital twin accurately reflects the current state of the physical Earth system. High-Fidelity Hybrid Modeling & Computational Acceleration to enable interactive "what-if" explorations, programs are moving beyond traditional, slow physical solvers by developing fast surrogate machine learning models and Deep Generative Models (DGMs). These hybrid approaches use neural networks to emulate complex physics, such as cloud feedback or ocean dynamics, at a fraction of the original computing cost, often leveraging advanced hardware like Graphics Processing Units (GPUs) to achieve the necessary scale. Federated Ecosystems & Interoperable Frameworks rather than building isolated tools, NASA IST is moving toward federated ESDTs and reusable analytic collaborative frameworks. This theme focuses on interoperability standards and common ontologies that allow specialized digital twins to interact and share data. This system-of-systems architecture supports multi-discipline investigations, such as analyzing how upstream watershed changes impact downstream urban flooding or how wildfire emissions affect regional air quality. By leveraging these advancements, ESDTs empower researchers and decision-makers to conduct real-time analysis and run complex hypothetical scenarios, ultimately improving our understanding of Earth’s evolving systems and informing critical real-world applications.

Earth System↗

Methods and apparatus for multi-resolution replication of files in a parallel computing system using semantic information

Techniques are provided for storing files in a parallel computing system using different resolutions. A method is provided for storing at least one file generated by a distributed application in a parallel computing system. The file comprises one or more of a complete file and a sub-file. The method comprises the steps of obtaining semantic information related to the file; generating a plurality of replicas of the file with different resolutions based on the semantic information; and storing the file and the plurality of replicas of the file in one or more storage nodes of the parallel computing system. The different resolutions comprise, for example, a variable number of bits and/or a different sub-set of data elements from the file. A plurality of the sub-files can be merged to reproduce the file.

97 MATHEMATICS AND COMPUTING↗

Molecular Insights Into the Ionic Assembly of Poly-Galacturonic Acid Oligomers - Impact of Charge, Ionic Radius, and Polymer Functionalization

Pectin, a major class of matrix polysaccharides present in plant cell walls (PCW), contains widespread anionic saccharides that cross-link in the presence of cations. It modulates important functions such as cell-cell adhesion and determines the PCW's biomechanical properties. It is known that mono-, di-, and tri-valent cations facilitate cross-linking; however, significant knowledge gaps remain in understanding the structure and mechanism of pectin cross-linking. In this study, replica-exchange molecular dynamics (REMD) simulations were employed to elucidate the role of ionic charge, ionic radii, and functional groups on the cross-linking of homogalacturonan (HG), the most abundant pectin molecule. Our enhanced sampling approach in fully solvated environments suggests more effective cross-linking with higher-valent and smaller ions, and that the "zipper" conformation is more favorable than the prevalent "egg-box" conformation. These findings advance our fundamental understanding of pectin matrix structure in PCWs and provide a solid foundation to probe structure-property relationships in pectic polysaccharides.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Structural deformation and transformation of θ'-Al 2 Cu precipitate in Al matrix via interfacial diffusion

Metastable θ'-Al 2 Cu precipitates enhance mechanical properties of Al alloy, but gradually transform to θ phase due to diffusion related coarsening at higher temperatures (>200°C). To improve understanding of the phase instability and transformation of θ'-Al 2 Cu, we investigated the interfacial atomic mobility of θ'-Al2Cu precipitate in Al matrix via molecular dynamics (MD). To characterize the interfacial atomic mobility, diffusion properties (activation energy, diffusivity, and jump attempt frequency) with respect to atomic species, interfacial structure, and temperature are calculated using atomic trajectories from MD. For the enhanced accuracy of this analysis, especially at low temperatures, temporal scale of molecular dynamics is significantly extended by employing the parallel replica dynamics. This study, as the first MD investigation on atomic diffusion of θ'-Al 2 Cu in Al matrix, suggests and discusses (i) structural deformation activated at the semi-coherent θ'-Al 2 Cu/Al interfaces, (ii) transformation initiated at the edge of the coherent θ'-Al 2 Cu/Al interface, and (iii) directional dependence of diffusion properties. Overall, these findings are expected to be employed in a larger scale phase-field modeling of precipitate growth, and to contribute to the understanding of phase transformation process and the development of alloys with θ'-phase retained to higher temperatures.

36 MATERIALS SCIENCE↗

A new smoothing function to introduce long-range electrostatic effects in QM/MM calculations

A new method to account for long range electrostatic contributions is proposed and implemented for quantum mechanics/molecular mechanics long range electrostatic correction (QM/MM-LREC) calculations. This method involves the use of the minimum image convention under periodic boundary conditions and a new smoothing function for energies and forces at the cutoff boundary for the Coulomb interactions. Compared to conventional QM/MM calculations without long-range electrostatic corrections, the new method effectively includes effects on the MM environment in the primary image from its replicas in the neighborhood. QM/MM-LREC offers three useful features including the avoidance of calculations in reciprocal space (k-space), with the concomitant avoidance of having to reproduce (analytically or approximately) the QM charge density in k-space, and the straightforward availability of analytical Hessians. The new method is tested and compared with results from smooth particle mesh Ewald (PME) for three systems including a box of neat water, a double proton transfer reaction, and the geometry optimization of the critical point structures for the rate limiting step of the DNA dealkylase AlkB. As with other smoothing or shifting functions, relatively large cutoffs are necessary to achieve comparable accuracy with PME. For the double-proton transfer reaction, the use of a 22 Å cutoff shows a close reaction energy profile and geometries of stationary structures with QM/MM-LREC compared to conventional QM/MM with no truncation. Geometry optimization of stationary structures for the hydrogen abstraction step by AlkB shows some differences between QM/MM-LREC and the conventional QM/MM. These differences underscore the necessity of the inclusion of the long-range electrostatic contribution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Sub-10 nm low current resistive switching behavior in hafnium oxide stack

In this letter, a tip-induced cell relying on the conductive atomic force microscope is proposed. It is verified as a referable replica of an integrated resistive random access memory (RRAM) device. On the basis of this cell, the functionality of sub-10 nm resistive switching is confirmed in hafnium oxide stack. Moreover, the low current switching behavior in the sub-10 nm dimension is found to be more pronounced than that of a 50 × 50 nm{sup 2} device. It shows better ON/OFF ratio and low leakage current. The enhanced memory performance is ascribed to a change in the shape of the conductive filament as the device dimensions are reduced to sub-10 nm. Therefore, device downscaling provides a promising approach for the resistance optimization that benefits the RRAM array design.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Optical study of the band structure of wurtzite GaP nanowires

We investigated the optical properties of wurtzite (WZ) GaP nanowires by performing photoluminescence (PL) and time-resolved PL measurements in the temperature range from 4 K to 300 K, together with atom probe tomography to identify residual impurities in the nanowires. At low temperature, the WZ GaP luminescence shows donor-acceptor pair emission at 2.115 eV and 2.088 eV, and Burstein-Moss band-filling continuum between 2.180 and 2.253 eV, resulting in a direct band gap above 2.170 eV. Sharp exciton α-β-γ lines are observed at 2.140–2.164–2.252 eV, respectively, showing clear differences in lifetime, presence of phonon replicas, and temperature-dependence. The excitonic nature of those peaks is critically discussed, leading to a direct band gap of ∼2.190 eV and to a resonant state associated with the γ-line ∼80 meV above the Γ{sub 8C} conduction band edge.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Mean-field entanglement transitions in random tree tensor networks

Entanglement phase transitions in quantum chaotic systems subject to projective measurements and in random tensor networks have emerged as a new class of critical points separating phases with different entanglement scaling. We propose a mean-field theory of such transitions by studying the entanglement properties of random tree tensor networks. As a function of bond dimension, we find a phase transition separating area-law from logarithmic scaling of the entanglement entropy. Using a mapping onto a replica statistical mechanics model defined on a Cayley tree and the cavity method, we analyze the scaling properties of such transitions. Our approach provides a tractable, mean-field-like example of an entanglement transition. Furthermore, we verify our predictions numerically by computing directly the entanglement of random tree tensor network states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗