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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Measures of complexity and entanglement in many-fermion systems

There is no unique and widely accepted definition of the complexity measure (CM) of a many-fermion wave function in the presence of interactions. The simplest many-fermion wave function is a Slater determinant. In shell-model or configuration interaction (CI) and other related methods, the state is represented as a superposition of a large number of Slater determinants, which in the case of CI calculations reaches about 20 billion terms [Johnson, arXiv:1809.07869]. Although in practice this number has been used as a CM for decades, it is ill defined: it is not unique, and it depends on the particular type and the number of single-particle wave functions used to construct the Slater determinants. Further, the canonical wave functions and/or natural orbitals [Löwdin, Adv. Phys. 5, 1 (1956); Löwdin and Shull, Phys. Rev. 101, 1730 (1956); Bardeen et al., Phys. Rev. 108, 1175 (1957); N. N. Bogoljubov, Il Nuovo Cimento 7, 794 (1958); Valatin, Il Nuovo Cimento 7, 843 (1958); de Gennes, Superconductivity of Metals and Alloys (CRC Press, Boca Raton, FL, 1999); Ring and Schuck, The Nuclear Many-Body Problem, 1st ed. (Springer-Verlag, Berlin, 2004)] and their corresponding occupation probabilities are intrinsic properties of any many-body wave function, irrespective of the representation, and they provide a unique solution to characterize the CM. The non-negative orbital entanglement entropy, which vanishes for a Slater determinant, provides the simplest CM, while a more complete measure of complexity is the entanglement spectrum. We illustrate these aspects in the case of a complex nonequilibrium time-dependent process, induced nuclear fission described within a real-time density functional theory framework extended to superfluid systems, which can describe simultaneously the long-range and the short-range correlations between fermions. The orbital entanglement entropy of the fissioning nucleus illustrates the localization mechanism of the many-body wave function in Fock and/or Hilbert space. The (minimal) number of Slater determinants required to represent such a complex many-body wave function with a well-defined number of particles in the case presented here is about 10 500 . The realistic case of the highly nonequilibrium nuclear fission process illustrated here is equivalent to a system of 23.328×10 9 interacting quantum spin-1/2 particles, a very large system for the study of quantum entanglement.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Correlated Response of Protein Side-Chain Fluctuations and Conformational Entropy to Ligand Binding

The heterogeneous fast side-chain dynamics of proteins plays crucial roles in molecular recognition and binding. Site-specific NMR experiments quantify these motions by measuring the model-free order parameter (O axis 2 ) on a scale of 0 (most flexible) to 1 (least flexible) for each methyl-containing residue of proteins. In this work, we have examined ligand-induced variations in the fast side-chain dynamics and conformational entropy of calmodulin (CaM) using five different CaM–peptide complexes. O axis 2 of CaM in the ligand-free (O axis,U 2 ) and ligand-bound (O axis,B 2 ) states are calculated from molecular dynamics trajectories and conformational energy surfaces obtained using the adaptive biasing force (ABF) method. ΔO axis 2 = O axis,B 2 – O axis,U 2 follows a Gaussian-like unimodal distribution whose second moment is a potential indicator of the binding affinity of these complexes. The probability for the binding-induced O axis,U 2 → O axis,B 2 transition decreases with increasing magnitude of ΔO axis 2 , indicating that large flexibility changes are improbable for side chains of CaM after ligand binding. A linear correlation established between ΔOaxis2 and the conformational entropy change of the protein makes possible the determination of the conformational entropy of binding of protein–ligand complexes. The results not only underscore the functional importance of fast side-chain fluctuations but also highlight key motional and thermodynamic correlates of protein–ligand binding.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Microscopic entropy of AdS3 black holes revisited

A bstract We revisit the microscopic description of AdS 3 black holes in light of recent progress on their higher dimensional analogues. The grand canonical partition function that follows from the AdS 3 /CFT 2 correspondence describes BPS and nearBPS black hole thermodynamics. We formulate an entropy extremization principle that accounts for both the black hole entropy and a constraint on its charges, in close analogy with asymptotically AdS black holes in higher dimensions. We are led to interpret supersymmetric black holes as ensembles of BPS microstates satisfying a charge constraint that is not respected by individual states. This interpretation provides a microscopic understanding of the hitherto mysterious charge constraints satisfied by all BPS black holes in AdS. We also develop thermodynamics and a nAttractor mechanism of AdS 3 black holes in the nearBPS regime.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Measurement of charged particle multiplicity distributions in DIS at HERA and its implication to entanglement entropy of partons

Charged particle multiplicity distributions in positron-proton deep inelastic scattering at a centre-of-mass energy √s = 319 GeV are measured. The data are collected with the H1 detector at HERA corresponding to an integrated luminosity of 136 pb -1 . Charged particle multiplicities are measured as a function of photon virtuality Q 2 , inelasticity y and pseudorapidity η in the laboratory and the hadronic centre-of-mass frames. Predictions from different Monte Carlo models are compared to the data. The first and second moments of the multiplicity distributions are determined and the KNO scaling behaviour is investigated. The multiplicity distributions as a function of Q 2 and the Bjorken variable x bj are converted to the hadron entropy S hadron , and predictions from a quantum entanglement model are tested.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Quantum information approach to high energy interactions

High energy hadron interactions are commonly described by using a probabilistic parton model that ignores quantum entanglement present in the light-cone wave functions. Here, we argue that since a high energy interaction samples an instant snapshot of the hadron wave function, the phases of different Fock state wave functions cannot be measured—therefore the light-cone density matrix has to be traced over these unobservable phases. Performing this trace with the corresponding U(1) Haar integration measure leads to ‘Haar scrambling’ of the density matrix, and to the emergence of entanglement entropy. This entanglement entropy is determined by the Fock state probability distribution, and is thus directly related to the parton structure functions. As proposed earlier, at large rapidity η the hadron state becomes maximally entangled, and the entanglement entropy is S E ~η according to QCD evolution equations. When the phases of Fock state components are controlled, for example in spin asymmetry measurements, the Haar average cannot be performed, and the probabilistic parton description breaks down.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Cholesterol modulates membrane elasticity via unified biophysical laws

Cholesterol and lipid unsaturation underlie a balance of opposing forces that features prominently in adaptive cell responses to diet and environmental cues. These competing factors have resulted in contradictory observations of membrane elasticity across different measurement scales, requiring chemical specificity to explain incompatible structural and elastic effects. Here, we demonstrate that – unlike macroscopic observations – lipid membranes exhibit a unified elastic behavior in the mesoscopic regime between molecular and macroscopic dimensions. Using nuclear spin techniques and computational analysis, we find that mesoscopic bending moduli follow a universal dependence on the lipid packing density regardless of cholesterol content, lipid unsaturation, or temperature. Our observations reveal that compositional complexity can be explained by simple biophysical laws that directly map membrane elasticity to molecular packing associated with biological function, curvature transformations, and protein interactions. The obtained scaling laws closely align with theoretical predictions based on conformational chain entropy and elastic stress fields. These findings provide unique insights into the membrane design rules optimized by nature and unlock predictive capabilities for guiding the functional performance of lipid-based materials in synthetic biology and real-world applications.

Kumarage, Teshani [Virginia Polytechnic Inst. and ↗
NASA NTRS1995

Entropy jump across an inviscid shock wave

The shock jump conditions for the Euler equations in their primitive form are derived by using generalized functions. The shock profiles for specific volume, speed, and pressure are shown to be the same, however density has a different shock profile. Careful study of the equations that govern the entropy shows that the inviscid entropy profile has a local maximum within the shock layer. We demonstrate that because of this phenomenon, the entropy, propagation equation cannot be used as a conservation law.

Salas, Manuel D.↗
DOE OSTI2024

Theory-guided design of duplex-phase multi-principal-element alloys

Density-functional theory (DFT) is used to identify phase-equilibria in multi-principal-element and high-entropy alloys (MPEAs/HEAs), including duplex-phase and eutectic microstructures. Here, a combination of composition-dependent formation energy and electronic-structure-based ordering parameters were used to identify a transition from FCC to BCC favoring mixtures, and these predictions experimentally validated in the Al-Co-Cr-Cu-Fe-Ni system. A sharp crossover in lattice structure and dual-phase stability as a function of composition were predicted via DFT and validated experimentally. The impact of solidification kinetics and thermodynamic stability was explored experimentally using a range of techniques, from slow (castings) to rapid (laser remelting), which showed a decoupling of phase fraction from thermal history, i.e., phase fraction was found to be solidification rate-independent, enabling tuning of a multi-modal cell and grain size ranging from nanoscale through macroscale. Strength and ductility tradeoffs for select processing parameters were investigated via uniaxial tension and small-punch testing on specimens manufactured via powder-based additive manufacturing (directed-energy deposition). This work establishes a pathway for design and optimization of next-generation multiphase superalloys via tailoring of structural and chemical ordering in concentrated solid solutions.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Information transfer with a gravitating bath

Late-time dominance of entanglement islands plays a critical role in addressing the information paradox for black holes in AdS coupled to an asymptotic non-gravitational bath. A natural question is how this observation can be extended to gravitational systems. To gain insight into this question, we explore how this story is modified within the context of Karch-Randall braneworlds when we allow the asymptotic bath to couple to dynamical gravity. We find that because of the inability to separate degrees of freedom by spatial location when defining the radiation region, the entanglement entropy of radiation emitted into the bath is a time-independent constant, consistent with recent work on black hole information in asymptotically flat space. If we instead consider an entanglement entropy between two sectors of a specific division of the Hilbert space, we then find non-trivial time-dependence, with the Page time a monotonically decreasing function of the brane angle---provided both branes are below a particular angle. However, the properties of the entropy depend discontinuously on this angle, which is the first example of such discontinuous behavior for an AdS brane in AdS space.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2007

Nonstandard Analysis and Shock Wave Jump Conditions in a One-Dimensional Compressible Gas

Nonstandard analysis is a relatively new area of mathematics in which infinitesimal numbers can be defined and manipulated rigorously like real numbers. This report presents a fairly comprehensive tutorial on nonstandard analysis for physicists and engineers with many examples applicable to generalized functions. To demonstrate the power of the subject, the problem of shock wave jump conditions is studied for a one-dimensional compressible gas. It is assumed that the shock thickness occurs on an infinitesimal interval and the jump functions in the thermodynamic and fluid dynamic parameters occur smoothly across this interval. To use conservations laws, smooth pre-distributions of the Dirac delta measure are applied whose supports are contained within the shock thickness. Furthermore, smooth pre-distributions of the Heaviside function are applied which vary from zero to one across the shock wave. It is shown that if the equations of motion are expressed in nonconservative form then the relationships between the jump functions for the flow parameters may be found unambiguously. The analysis yields the classical Rankine-Hugoniot jump conditions for an inviscid shock wave. Moreover, non-monotonic entropy jump conditions are obtained for both inviscid and viscous flows. The report shows that products of generalized functions may be defined consistently using nonstandard analysis; however, physically meaningful products of generalized functions must be determined from the physics of the problem and not the mathematical form of the governing equations.

Baty, Roy S.↗
DOE OSTI2023

Electronic signatures of Lorentzian dynamics and charge fluctuations in lithiated graphite structures

Lithium graphite intercalation compounds (Li-GICs) are essential materials for modern day portable electronics and obtaining insights into their atomic structure and thermodynamics is of fundamental interest. Here we explore the electronic and atomic states of Li-GICs at varying degrees of Lithium loading (i.e., “staging”) by means of ab-initio molecular dynamics simulations and simulated X-ray adsorption spectroscopy (XAS). We analyze the atomic correlation functions and shows that the enhancements of the Li-ion entropy with increased staging result from Lorentzian lithium-ion dynamics and charge fluctuations, which activate low-energy phonon modes. The associated electronic signatures are modulations of the unoccupied π*/σ* orbital energy levels and unambiguous fingerprints in Carbon K-edge XAS spectra. Thus, we extend the canonical view of XAS, establishing that these “static” measurements in fact encode the signature of the thermodynamic response and relaxation dynamics of the system. This causal link between atomic structure, spectroscopy, thermodynamics, and information theory can be generally exploited to better understand stability in solid-state electrochemical systems.

25 ENERGY STORAGE↗
DOE OSTI2021

Modulating effect of evanescent waves on thin film growth

Atomic-scale smooth thin films are keys to successful integration and proper function of many multilayer-structured devices. However, the intrinsic islandlike growth mode prevents human beings from realizing such ultrasmooth films of many important functional materials. To solve this problem, we propose a negative entropy-infusing method that employs evanescent waves to enhance the downward interlayer diffusion of adatoms and thus transform the islandlike growth mode to the layer-by-layer growth mode. In this work, the formulas of the optical force and the lowered diffusion barrier were derived, and the application of this theory on a simplified example demonstrates significantly improved surface morphologies through numerical simulations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1973

A finite-difference solution for unsteady wave interactions with an application to the expansion tube

An analytical study of the unsteady wave interaction of a shock wave overtaking a previously initiated shock tube flow has been conducted for a real gas by solving a finite-difference representation of the one-dimensional Navier-Stokes equations. This analysis has been used to determine the effect on the available test time of opening the secondary diaphragm in the expansion-tube operating cycle prior to the arrival of the incident shock wave. Special emphasis is placed on determining expansion-tube test-time limitations resulting from a nonuniform entropy distribution occurring during the early test-gas flow due to the varying Mach number of the incident shock wave as it traverses the expansion fan caused by the preopening process. Time distributions of velocity, temperature, pressure, and entropy at various distances from the diaphragm are presented as a function of the time required to open the diaphragm.

Weilmuenster, K. J.↗
NASA NTRS1986

A minimum entropy principle in the gas dynamics equations

Let u(x bar,t) be a weak solution of the Euler equations, governing the inviscid polytropic gas dynamics; in addition, u(x bar, t) is assumed to respect the usual entropy conditions connected with the conservative Euler equations. We show that such entropy solutions of the gas dynamics equations satisfy a minimum entropy principle, namely, that the spatial minimum of their specific entropy, (Ess inf s(u(x,t)))/x, is an increasing function of time. This principle equally applies to discrete approximations of the Euler equations such as the Godunov-type and Lax-Friedrichs schemes. Our derivation of this minimum principle makes use of the fact that there is a family of generalized entrophy functions connected with the conservative Euler equations.

Tadmor, E.↗
NASA NTRS1991

Architectures for intelligent machines

The theory of intelligent machines has been recently reformulated to incorporate new architectures that are using neural and Petri nets. The analytic functions of an intelligent machine are implemented by intelligent controls, using entropy as a measure. The resulting hierarchical control structure is based on the principle of increasing precision with decreasing intelligence. Each of the three levels of the intelligent control is using different architectures, in order to satisfy the requirements of the principle: the organization level is moduled after a Boltzmann machine for abstract reasoning, task planning and decision making; the coordination level is composed of a number of Petri net transducers supervised, for command exchange, by a dispatcher, which also serves as an interface to the organization level; the execution level, include the sensory, planning for navigation and control hardware which interacts one-to-one with the appropriate coordinators, while a VME bus provides a channel for database exchange among the several devices. This system is currently implemented on a robotic transporter, designed for space construction at the CIRSSE laboratories at the Rensselaer Polytechnic Institute. The progress of its development is reported.

Saridis, George N.↗
NASA NTRSDate not supplied

Machine Learning Approaches for Rare-Earth Silicate Environmental Barrier Coating Thermochemical and Thermomechanical Property Predictions

Environmental barrier coatings (EBCs) are a necessary enabling technology for the transition from superalloys to silicon carbide (SiC) ceramic matrix composites (CMCs) in gas turbine engines for increased efficiency and decreased fuel costs. SiC-based CMCs are prone to oxidation-based degradation in the engine hot section, and rare-earth (RE) silicates are promising candidates for EBCs due to their close thermal expansion match to the composite substrate and oxidation resistance. However, the design of EBCs is hindered by the large chemical space of candidate materials and the difficulty in obtaining material properties for engineering optimization. This is especially difficult as research continues into mixed-cation or “high-entropy” RE silicates. First-principles computational methods such as density functional theory (DFT) are highly effective at calculating material properties to guide coating design but are limited by their computational cost. Atomistic simulations have the potential to both accelerate property calculations and expand the properties able to be calculated due to their lower computational compared to DFT. However, they require interatomic potentials (IAPs) specific to the material system of interest, and, to our knowledge, there are no suitable IAPs for RE silicates. Machine learning (ML) is a promising technique to accelerate material property predictions indirectly by generating IAPs for atomistic simulations or via direct prediction. In this work, we present two ML approaches to accelerate the calculation of RE silicate properties relevant to EBC design: 1) a ML-derived interatomic potential (IAP) for atomistic simulations of yttrium disilicate (Y2Si2O7) from DFT training data, and 2) a neural network (NN) model to directly predict thermochemical properties of RE silicates and oxides directly from easily obtainable unit cell parameters. Classical MD simulations using the IAP yield lattice properties and bond lengths in good agreement with both DFT and experimental results from x-ray diffraction. Thermodynamic properties calculated using the finite-displacement phonon method and quasi-harmonic approximation were orders of magnitude faster than DFT with good agreement to the DFT results. The IAP was also used to calculate properties such as coefficient of thermal expansion (CTE) that require large simulation supercells and are therefore difficult with DFT. The IAP correctly predicted the anisotropic nature of the CTE in three different phases of Y2Si2O7. The NN model predicts constant pressure heat capacity, Cp, orders of magnitude faster than DFT calculations, which can enable its use as a surrogate model for multiscale simulations. The two methods presented in this work demonstrate the utility of ML for accelerating the prediction of RE silicate properties, which can in turn accelerate EBC design and optimization.

machine learning↗
DOE OSTI2024

Computational design of high-entropy rare earth aluminum garnets for advanced thermal and environmental barrier coatings

To enhance the protection of Ni-based superalloys in gas turbine engines’ high-temperature environments, it’s crucial to develop advanced thermal/environmental barrier coating (T/EBC) materials with a balanced combination of thermal and mechanical properties. This optimization is essential to safeguard against chemical and thermal challenges. Here, in this study, we harness the power of density functional theory (DFT) in conjunction with combinatorial chemistry methodologies to engineer high-performance high-entropy rare earth disilicates of the RE 3 Al 5 O 12 family (where RE denotes Y, Gd, Er, and Yb). These materials are meticulously designed to exhibit superior phase stability, a targeted coefficient of thermal expansion (CTE), low lattice thermal conductivity, and robust mechanical properties. The determination of CTE values is accomplished through phonon calculations at various volume settings within the quasi-harmonic approximation, while lattice thermal conductivities are rigorously assessed employing the Debye-Callaway model, accounting for three distinct phonon processes. Our findings highlight the remarkable attributes of the solid solution (Y 1/4 Gd 1/4 Er 1/4 Yb 1/4 ) 3 Al 5 O 12 , which displays a reduction in lattice thermal conductivity compared to its individual constituents while maintaining a favorable range of CTE values. The novel T/EBC material, distinguished by their multifaceted functionalities, are poised to use in substantial enhancements in the performance of engines.

36 MATERIALS SCIENCE↗