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DOE OSTI2026

Quantum critical collapse abhors a naked singularity

Classical critical collapse yields naked singularities from smooth initial data, challenging cosmic censorship, and shaping the spectrum of primordial black holes. We show that one-loop vacuum polarization near the threshold qualitatively changes this outcome by dressing the singularity with a horizon within a controlled semiclassical regime. In analytically tractable Einstein-scalar critical spacetimes, a one-loop $s$-wave treatment linearized around self-similar backgrounds shows that regularity uniquely selects an asymptotically Minkowskian, vacuum-polarization state. Its renormalized stress tensor carries a universal quantum growing mode that competes with the classical unstable mode, shifts the critical point, and generates a trapped surface along with a finite mass gap at the new threshold, thereby enforcing horizon formation even under arbitrary fine-tuning. In primordial collapse, the threshold shift enters exponentially into the formation fraction, while the mass gap truncates the low-mass tail, suggesting potentially important consequences for the predicted mass spectrum. Furthermore, these results provide a self-consistent semiclassical treatment of critical collapse and yield sharp predictions within the one-loop, near-critical, linearized regime.

Anomalies↗

DOE OSTI2025

Weak phonon coupling to nematic quantum critical mode in BaFe 2 ⁢(As 1−𝑥 ⁢P 𝑥 ) 2

Here, in this work, we investigate the softening of the in-plane transverse acoustic phonon driven by electronic nematicity in BaFe 2 ⁢(As 1−𝑥 ⁢P 𝑥 ) 2 using inelastic x-ray scattering, with a focus on the optimally doped sample (𝑥 = 0.31) sample—a system exhibiting signatures of a putative nematic quantum critical point and minimal disorder among iron pnictides. We observe only a modest softening of the phonon frequency and no evidence of critical damping, suggesting that the nematic quantum critical fluctuations couple only weakly to the lattice from our quantum critical model. Given the close proximity of the structural and magnetic transition temperatures in the underdoped sample—which implies that spin-nematic fluctuations couple strongly to the lattice—we conjecture that the quantum critical nematic fluctuations are predominantly orbital in origin.

Wu, S. [University of California, Berkeley, CA (Un↗

DOE OSTI2026

Tensor renormalization group approach to critical phenomena via symmetry-twisted partition functions

The locality of field theories strongly constrains the possible behaviors of symmetry-twisted partition functions, and thus they serve as order parameters to detect low-energy realizations of global symmetries, such as spontaneous symmetry breaking (SSB). We demonstrate that the tensor renormalization group (TRG) offers an efficient framework to compute the symmetry-twisted partition functions, which enables us to detect the symmetry-breaking transition and also to study associated critical phenomena. As concrete examples of SSB, we investigate the two-dimensional (2D) classical Ising model and the three-dimensional (3D) classical 𝑂⁡(2) nonlinear sigma model, and we identify their critical points solely from the twisted partition function. By employing the finite-size scaling argument, we find the critical temperature 𝑇 𝑐 = 2.2017⁢(2) with the critical exponent 𝜈 = 0.663⁢(33) for the 3D 𝑂⁡(2) model. In addition, we also study the Berezinskii–Kosterlitz–Thouless (BKT) criticality of the 2D classical 𝑂⁡(2) model by extracting the helicity modulus from the twisted partition functions, and we obtain the BKT transition temperature, 𝑇 BKT = 0.8928⁢(2).

lattice field theory↗

DOE OSTI2025

Design of Critical Experiments Involving Graphite elements at the IPEN/MB-01 Plate-Type Core

A series of critical experiments were designed involving the use of characterized graphite elements in the new plate-type core of the IPEN/MB-01 reactor. Eleven configurations with different graphite quantities are considered, each producing distinct effects on neutron fluxes and offering opportunities to analyze varying sensitivities to k eff in the system. The analysis shows that the experiments can be performed with acceptably low k eff uncertainties considering an adequate characterization of the graphite elements to be used. The sensitivity results obtained using SCALE TSUNAMI calculations show that the experiments have a notable k eff sensitivity coefficient to graphite. In the configurations tested, the k eff sensitivity to graphite TSL is low. This experiment will be useful for criticality safety validation of applications using uranium fuel enriched to around 19.75 wt % 235 U, light water and graphite. It will also be useful to gain more insight into graphite material properties and their effect on k eff as a result of using the well-characterized graphite elements. The execution of the experiments is planned for the summer of 2025. The 11 designed configurations serve as a basis for the final design, and fewer configurations will be executed. Once executed, these critical experiments will be evaluated and submitted for publication in the International Criticality Safety Benchmark Evaluation Project Handbook, supporting the DOE/NRC Collaboration for Criticality Safety Support for Commercial-Scale HALEU for Fuel Cycles and Transportation project goal.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2025

On a Critical Acceleration Scale of Dark Matter in ΛCDM and Dynamical Dark Energy

Abstract Universal acceleration a 0 emerges in various empirical laws, yet its fundamental nature remains unclear. Using Illustris and Virgo N -body simulations, we focus on the velocity and acceleration fluctuations in collisionless dark matter involving long-range gravity. For comparison, in the kinetic theory of gases, molecules undergo random elastic collisions involving short-range interactions, where only velocity fluctuations are relevant. Hierarchical structure formation proceeds through the merging of smaller halos to form larger halos, which facilitates a continuous energy cascade from small to large halos at a constant rate ε u ≈ −10 −7 m 2 s −3 . Velocity fluctuations involve a critical velocity u c ∝ (1 + z ) −3/4 . Acceleration fluctuations involve a critical acceleration a c ∝ (1 + z ) 3/4 . Two critical quantities are related by the rate of energy cascade ε u ≈ − a c u c /[2(3 π ) 2 ], where factor 3 π is from the angle of incidence during merging. With critical velocity u c on the order of 300 km s −1 at z = 0, the critical acceleration is determined to be a c 0 ≡ a c ( z = 0) ≈ 10 −10 m s −2 , suggesting a c might explain the universal acceleration a 0 ≈ 10 −10 m s −2 in the empirical Tully–Fisher relation or modified Newtonian dynamics. The redshift evolution a c ∝ (1 + z ) 3/4 is in good agreement with Magneticum and EAGLE simulations and in reasonable agreement with limited observations. This suggests a larger a 0 at a higher redshift such that galaxies of fixed mass rotate faster at a higher redshift. Note that for dark energy (DE) density ρ DE 0 ≈ a c 0 2 / G = 1 0 − 10 J m −3 , we postulate an entropic origin of the DE from acceleration fluctuations of dark matter, analogous to the gas pressure from velocity fluctuations. This leads to a dynamical DE coupled to the structure evolution involving a relatively constant DE density followed by a slow weakening phase, suggesting possible deviations from the standard ΛCDM paradigm.

N-body simulations↗

DOE OSTI2024

Opportunities for Process Intensification with Membranes to Promote Circular Economy Development for Critical Minerals

Critical minerals are essential to the future of clean energy, especially energy storage, electric vehicles, and advanced electronics. In this paper, we argue that process systems engineering (PSE) paradigms provide essential frameworks for enhancing the sustainability and efficiency of critical mineral processing pathways. As a concrete example, we review challenges and opportu-nities across material-to-infrastructure scales for process intensification (PI) with membranes. Within critical mineral processing, there is a need to reduce environmental impact, especially con-cerning chemical reagent usage. Feed concentrations and product demand variability require flex-ible, intensified processes. Further, unique feedstocks require unique processes (i.e., no one-size-fits-all recycling or refining system exists). Membrane materials span a vast design space that allows significant optimization. Therefore, there is a need to rapidly identify the best opportunities for membrane implementation, thus informing materials optimization with process and infrastructure scale performance targets. Finally, scale-up must be accelerated and de-risked across the materials-to-process levels to fully realize the opportunity presented by membranes, thereby fostering the development of a circular economy for critical minerals. Tackling these challenges requires integrating efforts across diverse disciplines. We advocate for a holistic molecular-to-systems perspective for fully realizing PI with membranes to address sustainability challenges in critical mineral processing. The opportunities for PI with membranes are excellent applications for emerging research in machine learning, data science, automation, and optimization.

Dougher, Molly↗

NASA NTRS1972

Transport properties of gases and binary liquids near the critical point

A status report is presented on the anomalies observed in the behavior of transport properties near the critical point of gases and binary liquids. The shear viscosity exhibits a weak singularity near the critical point. An analysis is made of the experimental data for those transport properties, thermal conductivity and thermal diffusivity near the gas-liquid critical point and binary diffusion coefficient near the critical mixing point, that determine the critical slowing down of the thermodynamic fluctuations in the order parameter. The asymptotic behavior of the thermal conductivity appears to be closely related to the asymptotic behavior of the correlation length. The experimental data for the thermal conductivity and diffusivity are shown to be in substantial agreement with current theoretical predictions.

Sengers, J. V.↗

NASA NTRS1977

Velocity and temperature profiles in near-critical nitrogen flowing past a horizontal flat plate

Boundary layer velocity and temperature profiles were measured for nitrogen near its thermodynamic critical point flowing past a horizontal flat plate. The heated surface was oriented both facing upward and downward. The results were compared to earlier work in which measurements were made for vertically upward flow. The boundary layer temperatures ranged from below to above the thermodynamic critical temperature. For wall temperatures below the thermodynamic critical temperature there was little variation between the velocity and temperature profiles in the three orientations. In all three orientations the point of crossing into the critical temperature region is marked by a significant flattening of the velocity and temperature profiles and also a decrease in heat transfer coefficient. As the heat flux and, consequently, wall temperature are further increased significant changes occur in the velocity and temperature profiles. Examination of near-critical heat transfer in these three flow orientations offers insights into the relative role of buoyancy forces in this regime.

Simoneau, R. J.↗

NASA NTRS1977

Thermal conductivity of steam in the critical region

The thermal conductivity of fluids exhibits an anomalous enhancement in a large range of densities and temperatures around the critical point. We formulate an equation for the thermal conductivity that connects the anomalous behavior in the vicinity of the critical point with the normal behavior of the thermal conductivity away from the critical point. The critical thermal conductivity enhancement is related to the anomalous behavior of the isothermal compressibility which in turn is represented by a scaled equation of state. The method is used to analyze experimental thermal conductivity data in the critical region of steam.

Basu, R. S.↗

NASA NTRS1979

Comparison of projected critical currents in PbMo6S8 and Nb3Ge

Critical current densities, Jc, of sputtered Chevrel phase PbMo6S8 films have been measured as a function of field to 19 T at several temperatures. The pinning forces were found to obey a scaling law. Assuming an effective upper critical field Bc2 = 45 T, an effective critical temperature Tc = 13 K, together with empirical estimates of numerical factors in the scaling law, the upper limits for critical current density Jc in PbMo6S8 are estimated. Comparisons are made with estimates of Jc for Nb3Ge at 4.2 K. A crossover of Jc vs. B is found for B of the order of 25 to 30 T. Below this point, Nb3Ge is projected to have a higher critical current density. Thus practical use of Chevrel materials in high field magnets only appears to be competitive with Nb3Ge for fields above 25 to 30 T.

Alterovitz, S. A.↗

NASA NTRS1985

Direct Observation of Critical Point Wetting in Microgravity

The objective of this program is to observe the interface shape in single and multicomponent systems at the onset of critical wetting in microgravity using the MSFC drop tower and KC-135 aircraft. Test cells for the drop facility were built and tested up to critical point of CCl. Low temperature drops were conducted for two-component systems near the critical consolute point. Contact angle seems to approach 90 deg near the critical consolute temperature contrary to expectations. It is suspected that since the interfacial energy becomes vanishingly small at the critical consolute temperature, the interface shape has not reached equilibrium in the available low-gravity time.

Kaukler, W. F.↗

NASA NTRS1985

The manifestation of Alfven's hypothesis of critical ionization velocity in the performance of MPD thrusters

The role of Alfven's critical ionization velocity in the performance of the self-field MPD thruster has been investigated. The existence of a well defined characteristic velocity can be attributed to an ionization process involving the production of a population of suprathermal electrons by an electrostatic instability. It is shown that for the MPD thruster plasma, suprathermalization of electrons via this electrostatic instability can only happen if ions are initially accelerated to velocities larger than the Alfven critical ionization velocity. When this occurs the mechanism will be initiated and the ions decelerated to velocities near the critical velocity. This mechanism ceases to be limiting when all neutrals are ionized. A model of MPD thruster terminal behavior, incorporating Alfven's hypothesis, is presented. Experiments with three different propellants reveal that operation at values of the current squared to total mass flow ratio corresponding to the Alfven critical velocity is marked by a transition wherein low frequency voltage oscillations and a notable change in the voltage-current dependence occurs. One major result of this study is the demonstration that the Alfven critical velocity is not a fundamental limitation on MPD exhaust velocity.

Choueiri, E. Y.↗

NASA NTRS1985

On the possibility of critical radius measurements in the homogeneous crystal nucleation of glass

The potential of determining the liquid-crystal surface tension during crystal nucleation in inorganic glasses without measuring the nucleation rate is examined analytically. Attention is focused on the feasibility of measuring the critical radius of the crystal nuclei as a function of temperature in order to obtain the surface tension values. Two approximate expressions are defined for the upper and lower bounds of the bulk free energy of crystallization per unit volume. The expressions, when used for a validated approximation for the critical radius, show that the critical radius is a function of the undercooling and the molar volume. The minimum undercooling necessary for detecting homogeneous crystal nucleation is then calculated, which yields an upper limit to the critical radius in the range 10-15 A. Since the size range is too small for detection, the critical radius is not a useful measure for crystal nucleation studies.

Weinberg, M. C.↗

NASA NTRS1987

On the turbulent heating and the threshold condition in the critical ionization velocity interaction

On the basis of the nonlinear treatment of the ion beam instability and the modified two-stream instability, threshold conditions for the critical ionization velocity interaction are derived. There are three different regimes of interaction: (1) additional ionization for relative velocities smaller than the critical velocity, (2) the self-sustained discharge for velocities greater than the critical velocity which indeed turns out as a sharp threshold, and (3) an explosive growth regime for velocities exceeding 1.5 times the critical velocity. Additional charge exchange collisions of ions and energy loss of electrons due to excitation do not change the basic threshold behavior but modify the value of the critical velocity.

Moebius, E.↗

NASA NTRS1987

Critical fluid light scattering

Thermal fluctuations give rise to a host of thermodynamic anomalies near critical points. The background for these phenomena is presented, and an experiment design on STS flight experiment called 'Zeno' described. The objective is to measure the decay rates of critical density fluctuations in a simple fluid (xenon) very near its liquid-vapor critical point using laser light-scattering and photon-correlation spectroscopy. Such experiments have been limited on earth by the presence of gravity, which causes large density gradients in the sample. Fluctuation decay rates in xenon will be measured at least 100 times closer to the critical point than is possible on earth. This will require taking data as close as 145 microK to the critical temperature (Tc = 289.72 K), after locating it to + or - 10 microK. The minimum mission time of 100 hours will allow a complete range of temperature points to be covered, limited by the thermal response of the sample. An essential part of the apparatus is the thermostat. Its design principles and key features are given together with some observed performance characteristics of a prototype: + or - 20 microK stability for 18 hours, and one minute programmed step response for steps less than 10 mK.

Gammon, Robert W.↗

NASA NTRS1989

Critical fluid light scattering

Thermal fluctuations give rise to a host of thermodynamic anomalies near critical points. The background for these phenomena is presented, and an experimental design on STS flight experiment called Zeno is described. The objective is to measure the decay rates of critical density fluctuations in a simple fluid (xenon) very near its liquid-vapor critical point using laser light scattering and photon correlation spectroscopy. Such experiments have been limited on Earth by the presence of gravity, which causes large density gradients in the sample. Fluctuation decay rates in xenon will be measured at least 100 times closer to the critical point than is possible on Earth. This will require taking data as close as 145 micro K to the critical temperature, after locating it to + or - 10 micro K. The minimum mission time of 100 hours will allow a complete range of temperature points to be covered, limited by the thermal response of the sample. An essential part of the apparatus is the thermostat. Its design principles and key features are given together with some observed performance characteristics of a prototype: + or - 20 micro K stability for 18 hours, and one minute programmed step response for steps less than 10 mK.

Gammon, Robert W.↗

NASA NTRS1993

Loading and testing a light scattering cell with a binary fluid mixture near its critical composition

Critical phenomena has been the subject of physics research for many years. However, only in recent years has the research effort become intense. The current intensity has caused the study of critical phenomena to be grouped into a previous older era and a present contemporary era. Turbidity cell filling with methanol cyclohexane is one of the first steps toward a further understanding of critical phenomena. Work performed during the research period is outlined. During this period, research was spent developing apparatus and techniques that will make it possible to study critical phenomena through turbidity measurements on methanol cyclohexane. Topics covered range from the orientation of turbidity cell parts for assembly to the filling apparatus and procedure used when th cell is built. The last section will briefly cover some of the observations made when viewing the cell in a controlled water bath. However, before mention is made of the specifics of the summer research, a short introduction to critical phenomena and turbidity and how they relate to this experiment is provided.

Jacobs, Donald T.↗

NASA NTRS1994

Electric field effects on a near-critical fluid in microgravity

The effects of an electric field on a sample of SF6 fluid in the vicinity of the liquid-vapor critical point is studied. The isothermal increase of the density of a near-critical sample as a function of the applied electric field was measured. In agreement with theory, this electrostriction effect diverges near the critical point as the isothermal compressibility diverges. Also as expected, turning on the electric field in the presence of density gradients can induce flow within the fluid, in a way analogous to turning on gravity. These effects were observed in a microgravity environment by using the Critical Point Facility which flew onboard the Space Shuttle Columbia in July 1994 as part of the Second International Microgravity Laboratory Mission. Both visual and interferometric images of two separate sample cells were obtained by means of video downlink. The interferometric images provided quantitative information about the density distribution throughout the sample. The electric field was generated by applying 500 Volts to a fine wire passing through the critical fluid.

Zimmerli, G.↗