SEARCH · Engineering Papers

Results for “entropy functional”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6

All sources NASA NTRS DOE OSTI

DOE OSTI2020

Consequences of sp 2 –sp 3 boron isomerization in supercooled liquid borates

In this study, time-resolved high-energy synchrotron x-ray total scattering measurements on supercooled molten lithium metaborate (LiBO 2 ) reveal an isomerization reaction involving conversion of trigonal sp 2 boron to tetrahedral sp 3 boron during quenching and glass formation. Van't Hoff analysis yields an accurate enthalpy change, ΔH = 21(1) kJ mol –1 boron, from which we develop an analytical model for the sp 3 isomer fraction and its contribution to configurational heat capacity (C p conf ) and entropy as a function of temperature and composition. Isomerization constitutes 40% of the total calorimetric C p conf at the glass transition for LiBO 2 and directly contributes to the observed rise in liquid fragility with the lithium content.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2022

Glass length: Workability and meltability of glass as a function of glass melt fragility

Workability and meltability of molten glass are properties important for balancing glass formulation with the design and operations of glass melting and forming facilities. The working and melting “lengths” are the temperature intervals within which glass viscosity allows the melting and forming glass to be performed. They are related to glass melt structure through the glass melt fragility, which, by the augmented Adam-Gibbs equation, is a function of configuration entropy. Both working length and melting length are high for strong glasses and decrease as the melt fragility increases. In this work, analytical formulas are obtained for three-parameter viscosity models VFT, AM, and MYEGA. These models agree with each other and with the Adam-Gibbs equation on the relationship between workability and fragility of glasses but diverge at high-temperatures. The compositional effects on workability and meltability are mediated via the fragility as a function of glass composition expressed in terms of mass and mole component coefficients.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Anti-$\mathscr{PT}$-symmetric qubit: Decoherence and entanglement entropy

We investigate the dynamics of a general two-level based anti-parity-time (anti-$\mathscr{PT}$)-symmetric qubit and study its decoherence as well as entanglement entropy properties. We compare our findings with that of the corresponding parity-time ($\mathscr{PT}$)-symmetric and Hermitian qubits. To begin, we consider the time-dependent Dyson map to find the exact analytical dynamics for a general non-Hermitian qubit system weakly coupled with a thermal bath for pure dephasing, before specializing it to the case of a general anti-$\mathscr{PT}$-symmetric qubit. Basing the comparison under the same coupling strength or increasing the non-Hermiticity, we observe that the decoherence function and entanglement entropy of the anti-$\mathscr{PT}$-symmetric qubit decays and grows more slowly, respectively, compared to the $\mathscr{PT}$-symmetric and Hermitian qubits. Similarly, the corresponding variance and area of Fisher information are much higher compared to the $\mathscr{PT}$-symmetric and Hermitian qubits. These results demonstrate that anti-$\mathscr{PT}$-symmetric qubits may be better suited for quantum computing and quantum information processing applications than conventional Hermitian or even $\mathscr{PT}$-symmetric qubits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1995

(abstract) Determination of the Specific Heat and Total Hemispherical Total Emissivity of the Highly Undercooled Zr(sub 41.2)Ti(sub 13.8)Cu(sub 12.5)Ni(sub 10.0)Be(sub 22.5) Alloy

High temperature high vacuum electrostatic levitation was combined with DSC experiments to determine the specific heat C(sub p) of the undercooled Zr(sub 41.2)Ti(sub 13.8)Cu(sub 12.5)Ni(sub 10.0)Be(sub 22.5) liquid as a function of temperature. The containerless approach made it possible to undercool the melt to the glass transition temperature without inducing nucleation. Because the cooling process was purely radiative, noncontact temperature measurement techniques could be used to determine the specific heat to total hemispherical emissivity ratio, C(sub p)/epsilon(sub t), for the undercooled liquid region. Using C(sub p) values which were independently obtained by DSC, epsilon(sub t) could be determined. With knowledge of C(sub p) of the undercooled liquid it was possible to determine other thermodynamic properties such as Gibbs free energy and entropy as a function of undercooling.

levitation thermodynamic properties undercooled al↗

NASA NTRS1991

Maximum-entropy probability distributions under Lp-norm constraints

Continuous probability density functions and discrete probability mass functions are tabulated which maximize the differential entropy or absolute entropy, respectively, among all probability distributions with a given L sub p norm (i.e., a given pth absolute moment when p is a finite integer) and unconstrained or constrained value set. Expressions for the maximum entropy are evaluated as functions of the L sub p norm. The most interesting results are obtained and plotted for unconstrained (real valued) continuous random variables and for integer valued discrete random variables. The maximum entropy expressions are obtained in closed form for unconstrained continuous random variables, and in this case there is a simple straight line relationship between the maximum differential entropy and the logarithm of the L sub p norm. Corresponding expressions for arbitrary discrete and constrained continuous random variables are given parametrically; closed form expressions are available only for special cases. However, simpler alternative bounds on the maximum entropy of integer valued discrete random variables are obtained by applying the differential entropy results to continuous random variables which approximate the integer valued random variables in a natural manner. All the results are presented in an integrated framework that includes continuous and discrete random variables, constraints on the permissible value set, and all possible values of p. Understanding such as this is useful in evaluating the performance of data compression schemes.

Dolinar, S.↗

DOE OSTI2024

Entanglement in massive Schwinger model at finite temperature and density

We evaluate the entanglement entropy and entropic function of massive two dimensional quantum electrodynamics (Schwinger model) at finite temperature, density, and θ -angle. In the strong coupling regime, the entropic function is dominated by the boson mass for large spatial intervals, and reduces to the conformal field theory result for small spatial intervals. We also discuss the entanglement spectrum at finite temperature and a finite θ -angle. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1992

Computer program for calculating and fitting thermodynamic functions

A computer program is described which (1) calculates thermodynamic functions (heat capacity, enthalpy, entropy, and free energy) for several optional forms of the partition function, (2) fits these functions to empirical equations by means of a least-squares fit, and (3) calculates, as a function of temperture, heats of formation and equilibrium constants. The program provides several methods for calculating ideal gas properties. For monatomic gases, three methods are given which differ in the technique used for truncating the partition function. For diatomic and polyatomic molecules, five methods are given which differ in the corrections to the rigid-rotator harmonic-oscillator approximation. A method for estimating thermodynamic functions for some species is also given.

Mcbride, Bonnie J.↗

DOE OSTI2025

Holography for BCFTs with multiple boundaries: multi-splitting quenches

We elaborate on the method introduced in arXiv:2403.02165 for holographic duals of Boundary Conformal Field Theories (BCFTs) with multiple boundaries. Naïvely, as the number of boundaries grow large such a calculation becomes unmanageable. We show that is not always the case. Using these advances we calculate the entanglement entropy as a function of time for 1+1-dimensional CFTs that are split into N subsystems. We give explicit results for N = 4 and N = 17. We find that all qualitative differences that arise for larger N are present N = 4.

AdS-CFT correspondence↗

DOE OSTI2022

Microscopic-macroscopic level densities for low excitation energies

Level density ρ(E,Q) is derived within the micro-macroscopic approximation (MMA) for a system of strongly interacting Fermi particles with the energy E and additional integrals of motion Q , in line with several topics of the universal and fruitful activity of A. S. Davydov. Within the extended Thomas Fermi and semiclassical periodic orbit theory beyond the Fermi-gas saddle-point method, we obtain ρ ∝ I ν (S)/S ν , where I ν (S) is the modified Bessel function of the entropy S . For small shell-structure contribution, one finds ν = κ/2 + 1, where κ is the number of additional integrals of motion. This integer number is a dimension of Q, Q = { N, Z , …} for the case of two-component atomic nuclei, where N and Z are the numbers of neutrons and protons, respectively. For much larger shell structure contributions, one obtains ν = κ /2 + 2. The MMA level density ρ reaches the well-known Fermi gas asymptote for large excitation energies and the finite micro-canonical combinatoric limit for low excitation energies. Further, the additional integrals of motion can also be the projection of the angular momentum of a nuclear system for nuclear rotations of deformed nuclei, number of excitons for collective dynamics, and so on. Fitting the MMA total level density ρ( E , Q) for a set of the integrals of motion Q = { N, Z }, to experimental data on a long nuclear isotope chain for low excitation energies, one obtains the results for the inverse level-density parameter K , which differs significantly from those of neutron resonances due to shell, isotopic asymmetry, and pairing effects.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Semiclassical shell-structure micro-macroscopic approach for the level density

Level density ρ(E,A) is derived for a one-component nucleon system with a given energy E and particle number A within the mean-field semiclassical periodic-orbit theory beyond the saddle-point method of the Fermi gas model. We obtain ρ∝I ν (S)/S ν , with I ν (S) being the modified Bessel function of the entropy S. Within the micro-macro-canonical approximation (MMA), for a small thermal excitation energy U, with respect to rotational excitations E rot , one obtains ν = 3/2 for ρ(E,A). In the case of excitation energy U larger than E rot but smaller than the neutron separation energy, one finds a larger value of ν = 5/2. A role of the fixed spin variables for rotating nuclei is discussed. The MMA level density ρ reaches the well-known grand-canonical ensemble limit (Fermi gas asymptote) for large S related to large excitation energies, and also reaches the finite micro-canonical limit for small combinatorial entropy S at low excitation energies (the constant “temperature” model). Fitting the ρ(E,A) of the MMA to the experimental data for low excitation energies, taking into account shell and, qualitatively, pairing effects, one obtains for the inverse level density parameter K a value which differs essentially from that parameter derived from data on neutron resonances.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Shell-structure and asymmetry effects in level densities

Level density [Formula: see text] is derived for a nuclear system with a given energy [Formula: see text], neutron [Formula: see text], and proton [Formula: see text] particle numbers, within the semiclassical extended Thomas–Fermi and periodic-orbit theory beyond the Fermi-gas saddle-point method. We obtain [Formula: see text], where [Formula: see text] is the modified Bessel function of the entropy [Formula: see text], and [Formula: see text] is related to the number of integrals of motion, except for the energy [Formula: see text]. For small shell structure contribution one obtains within the micro–macroscopic approximation (MMA) the value of [Formula: see text] for [Formula: see text]. In the opposite case of much larger shell structure contributions one finds a larger value of [Formula: see text]. The MMA level density [Formula: see text] reaches the well-known Fermi gas asymptote for large excitation energies, and the finite micro-canonical limit for low excitation energies. Fitting the MMA [Formula: see text] to experimental data on a long isotope chain for low excitation energies, due mainly to the shell effects, one obtains results for the inverse level density parameter [Formula: see text], which differs significantly from that of neutron resonances.

Physics↗

NASA NTRS1972

Computer program for natural gas flow through nozzles

Subroutines, FORTRAN 4 type, were developed for calculating isentropic natural gas mass flow rate through nozzle. Thermodynamic functions covering compressibility, entropy, enthalpy, and specific heat are included.

Johnson, R. C.↗

NASA NTRS1985

Criteria for scaling heat exchangers to miniature size

The purpose of this work is to highlight the particular aspects of miniature heat exchangers performance and to determine an appropriate design approach. A thermodynamic analysis is performed to express the generated entropy as a function of material and geometric characteristics of the heat exchangers. This expression is then used to size miniature heat exchangers.

Rudolfvonrohr, P. B.↗

NASA NTRS1993

Aspects of a high-resolution scheme for the Navier-Stokes equations

In this paper we emphasize the importance of the form of the numerical dissipation model in computing accurate viscous flow solutions. A high-resolution scheme for viscous flows based on three-point central differencing and a matrix dissipation is considered. The various components of this scheme, including 'entropy fix', limiter function, and boundary-point dissipation are discussed. By analyzing boundary-point dissipation stencils, we confirm that with the matrix dissipation model the normal numerical dissipation terms in the streamwise momentum equation are independent of the Reynolds number. Such independence is not achieved with a scalar dissipation form. The accuracy of the central-difference scheme, with and without matrix dissipation, and the flux-difference split scheme of Roe, which is classified as a high-resolution scheme, is compared. For this comparison, three high Reynolds number laminar flows are considered. Solutions of the Navier-Stokes equations are obtained for low-speed flow over a flat plate, transonic flow over an airfoil with transition near the leading edge, and hypersonic flow over a compression ramp. The emphasis of the comparison is primarily on the details of the viscous flows. The necessity of the high-resolution property is revealed.

Swanson, R. C.↗

NASA NTRS1999

Thin Interface Asymptotics for an Energy/Entropy Approach to Phase-Field Models with Unequal Conductivities

Karma and Rapped recently developed a new sharp interface asymptotic analysis of the phase-field equations that is especially appropriate for modeling dendritic growth at low undercoolings. Their approach relieves a stringent restriction on the interface thickness that applies in the conventional asymptotic analysis, and has the added advantage that interfacial kinetic effects can also be eliminated. However, their analysis focussed on the case of equal thermal conductivities in the solid and liquid phases; when applied to a standard phase-field model with unequal conductivities, anomalous terms arise in the limiting forms of the boundary conditions for the interfacial temperature that are not present in conventional sharp-interface solidification models, as discussed further by Almgren. In this paper we apply their asymptotic methodology to a generalized phase-field model which is derived using a thermodynamically consistent approach that is based on independent entropy and internal energy gradient functionals that include double wells in both the entropy and internal energy densities. The additional degrees of freedom associated with the generalized phased-field equations can be chosen to eliminate the anomalous terms that arise for unequal conductivities.

McFadden, G. B.↗

DOE OSTI2021

Temperature-Dependent Configurational Entropy Calculations for Refractory High-Entropy Alloys

The cluster expansion formalism for alloys is used to construct surrogate models for three refractory high-entropy alloys (NbTiVZr, HfNbTaTiZr, and AlHfNbTaTiZr). These cluster expansion models are then used along with Monte Carlo methods and thermodynamic integration to calculate the configurational entropy of these refractory high-entropy alloys as a function of temperature. Many solid solution alloy design guidelines are based on the ideal entropy of mixing, which increases monotonically with N , the number of elements in the alloy. However, our results show that at low temperatures, the configurational entropy of these materials is largely independent of N , and the assumption described above only holds in the high-temperature limit. This suggests that alloy design guidelines based on the ideal entropy of mixing require further examination.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Generalized approach for rapid entropy calculation of liquids and solids

We build a comprehensive methodology for the fast computation of entropy across both solid and liquid phases. The proposed method utilizes a single trajectory of molecular dynamics (MD) to facilitate the calculation of entropy, which is composed of three components. The electronic entropy is determined through the temporal average acquired from density functional theory MD simulations. The vibrational entropy, typically the predominant contributor to the total entropy, even within the liquid state, is evaluated by computing the phonon density of states via the velocity autocorrelation function. The most arduous component to quantify, the configurational entropy, is assessed by probability analysis of the local structural arrangement and atomic distribution. We illustrate, through a variety of examples, that this method is both a versatile and valid technique for characterizing the thermodynamic states of both solids and liquids. Furthermore, this method is employed to expedite the calculation of melting temperatures, demonstrating its practical utility in computational thermodynamics.

36 MATERIALS SCIENCE↗

NASA NTRS1992

Minimum entropy deconvolution and blind equalisation

Relationships between minimum entropy deconvolution, developed primarily for geophysics applications, and blind equalization are pointed out. It is seen that a large class of existing blind equalization algorithms are directly related to the scale-invariant cost functions used in minimum entropy deconvolution. Thus the extensive analyses of these cost functions can be directly applied to blind equalization, including the important asymptotic results of Donoho.

Satorius, E. H.↗